id
string | setting_key
string | difficulty
string | level
int32 | messages
dict | ground_truth
string | dataset
string | omega_split
string |
|---|---|---|---|---|---|---|---|
math_algebra_func_area_level_4_4_500
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (1(3(-1(1cos(3π(1|x| - 3) - 3) + 2) - 4) + 5) - 3)/(3(3(-1(1cos(3π(1|x| - 3) - 3) + 2) - 4) + 5) + 2), g(x) = -1|(1(-2cos(2π((1x + 1)/(3x - 2)) - 2) - 1)^2 - 5(-2cos(2π((1x + 1)/(3x - 2)) - 2) - 1) + 3) - 3| + 3, x = 0.7, and x = 0.7999999999999999. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.7
|
math
|
train
|
math_algebra_func_area_level_4_4_501
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 1|(-3(-1(-2sin(3π(2|x + 2| + 2) - 3) - 1)^2 + 5(-2sin(3π(2|x + 2| + 2) - 3) - 1) + 4)^2 + 3) + 2| - 3 and g(x) = (3(-4((-2(-3sin(2πx - 3) + 2) - 2)/(1(-3sin(2πx - 3) + 2))) + 2) + 1)/(2(-4((-2(-3sin(2πx - 3) + 2) - 2)/(1(-3sin(2πx - 3) + 2))) + 2) - 3) between the vertical lines x = -2.7 and x = -2.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
23.4
|
math
|
train
|
math_algebra_func_area_level_4_4_502
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = (1(-3|(-3|((-3(1|x - 1| + 1) - 3)/(-1(1|x - 1| + 1) + 2)) + 2| + 1)|) - 3)/(-2(-3|(-3|((-3(1|x - 1| + 1) - 3)/(-1(1|x - 1| + 1) + 2)) + 2| + 1)|) + 1) and g(x) = 1|(-3((-3(2cos(3πx - 2) + 3) + 3)/(1(2cos(3πx - 2) + 3) - 2))^2 + 2((-3(2cos(3πx - 2) + 3) + 3)/(1(2cos(3πx - 2) + 3) - 2)) + 5) + 3| - 1 between the vertical lines x = -0.7 and x = -0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
208.7
|
math
|
train
|
math_algebra_func_area_level_4_4_503
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (3(5(-3|((-2(1|x - 1| + 2) - 2)/(3(1|x - 1| + 2) - 2))| - 2) - 1) + 1)/(-2(5(-3|((-2(1|x - 1| + 2) - 2)/(3(1|x - 1| + 2) - 2))| - 2) - 1) + 3), g(x) = (-2(-1(-2cos(1π(-2x^2 - 5x + 1) + 2) + 1) + 1) - 3)/(-1(-1(-2cos(1π(-2x^2 - 5x + 1) + 2) + 1) + 1) + 2), x = -4.3, and x = -4.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.3
|
math
|
train
|
math_algebra_func_area_level_4_4_504
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (3(2(-1|(-1cos(3π(1x^2 + 4x + 3) - 2)) - 2| - 2)^2 + 1) - 3)/(3(2(-1|(-1cos(3π(1x^2 + 4x + 3) - 2)) - 2| - 2)^2 + 1) + 1) and g(x) = 4((1(2(2x + 2) + 2) - 1)/(1(2(2x + 2) + 2) - 2))^2 - 1((1(2(2x + 2) + 2) - 1)/(1(2(2x + 2) + 2) - 2)) from x = -1.7 to x = -1.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.3
|
math
|
train
|
math_algebra_func_area_level_4_4_505
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 2|((-3(-5(-1((-2x + 1)/(2x + 2)) - 4)^2 + 4(-1((-2x + 1)/(2x + 2)) - 4) + 1) + 3)/(-3(-5(-1((-2x + 1)/(2x + 2)) - 4)^2 + 4(-1((-2x + 1)/(2x + 2)) - 4) + 1) + 2)) - 3| - 3 and g(x) = 1((2(2|(-2x^2 - 4x + 2) + 3| + 3) - 2)/(-1(2|(-2x^2 - 4x + 2) + 3| + 3) - 1))^2 + 4((2(2|(-2x^2 - 4x + 2) + 3| + 3) - 2)/(-1(2|(-2x^2 - 4x + 2) + 3| + 3) - 1)) + 2 between the vertical lines x = -1.5 and x = -1.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.4
|
math
|
train
|
math_algebra_func_area_level_4_4_506
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (-2(-5(-1|(2(3cos(3πx) - 1)^2)| + 3)^2 + 1(-1|(2(3cos(3πx) - 1)^2)| + 3) + 3) - 1)/(3(-5(-1|(2(3cos(3πx) - 1)^2)| + 3)^2 + 1(-1|(2(3cos(3πx) - 1)^2)| + 3) + 3) - 2) and g(x) = 1(-1(3(-2x + 3)^2 - 3(-2x + 3) + 5)^2 + 4(3(-2x + 3)^2 - 3(-2x + 3) + 5) + 4) + 4 from x = 0.9 to x = 1.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
3.5
|
math
|
train
|
math_algebra_func_area_level_4_4_507
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = (3(-3(2|(5(1cos(3πx + 2) + 2) - 2) + 2| + 2) - 1) + 1)/(2(-3(2|(5(1cos(3πx + 2) + 2) - 2) + 2| + 2) - 1) - 1) and g(x) = 4(-3(4((1x - 1)/(3x)) - 4) - 5)^2 - 1(-3(4((1x - 1)/(3x)) - 4) - 5) between the vertical lines x = -1.8 and x = -1.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.7
|
math
|
train
|
math_algebra_func_area_level_4_4_508
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -1(1(-4(2sin(2π(3x^2 + 3x - 3) + 1) - 1)^2 - 2(2sin(2π(3x^2 + 3x - 3) + 1) - 1) + 5)^2 + 1(-4(2sin(2π(3x^2 + 3x - 3) + 1) - 1)^2 - 2(2sin(2π(3x^2 + 3x - 3) + 1) - 1) + 5) + 2) + 3 and g(x) = 2|(-1(-1|(3x^2 + 2x + 3) - 1| - 3)^2 - 4(-1|(3x^2 + 2x + 3) - 1| - 3) + 3) + 2| - 1 between the vertical lines x = -0.7 and x = -0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.9
|
math
|
train
|
math_algebra_func_area_level_4_4_509
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (-2(3|(3|(5((2x + 3)/(-1x + 3)) + 1) + 2| - 3)| + 3) + 1)/(-1(3|(3|(5((2x + 3)/(-1x + 3)) + 1) + 2| - 3)| + 3)), g(x) = 3|(1((3(-3|x| - 2) - 2)/(3(-3|x| - 2) + 1)) - 2) - 1| - 3, x = -0.4, and x = 0.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.3
|
math
|
train
|
math_algebra_func_area_level_4_4_510
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = (-1(2|(3|(2|(-1sin(1πx + 1) - 1) + 1| + 3) + 1| + 1) + 3| + 3) - 2)/(1(2|(3|(2|(-1sin(1πx + 1) - 1) + 1| + 3) + 1| + 1) + 3| + 3)) and g(x) = (3(5(2cos(1π(-3x^2 - 4x + 5) - 3) + 1) - 5) - 3)/(2(5(2cos(1π(-3x^2 - 4x + 5) - 3) + 1) - 5) - 1) between the vertical lines x = 1.3 and x = 1.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.3
|
math
|
train
|
math_algebra_func_area_level_4_4_511
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (-2((-1(5(1(2x^2 + 1x + 3) - 4)^2 - 3(1(2x^2 + 1x + 3) - 4) + 2) + 3)/(-2(5(1(2x^2 + 1x + 3) - 4)^2 - 3(1(2x^2 + 1x + 3) - 4) + 2) - 2)) + 3)/(-1((-1(5(1(2x^2 + 1x + 3) - 4)^2 - 3(1(2x^2 + 1x + 3) - 4) + 2) + 3)/(-2(5(1(2x^2 + 1x + 3) - 4)^2 - 3(1(2x^2 + 1x + 3) - 4) + 2) - 2))) and g(x) = -2|(1((-1((1x - 1)/(-1x + 3)))/(2((1x - 1)/(-1x + 3)) - 3)) + 5) - 1| + 3 from x = 2.2 to x = 3.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
11.2
|
math
|
train
|
math_algebra_func_area_level_4_4_512
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 2|(5(2e^(1(-1|(-2|x + 3| + 1) + 3| + 2)) - 2) - 3)| - 1 and g(x) = (3(5(1(-1sin(3πx - 1) - 1)^2 - 4(-1sin(3πx - 1) - 1) - 3)^2 - 5(1(-1sin(3πx - 1) - 1)^2 - 4(-1sin(3πx - 1) - 1) - 3) - 2) + 3)/(1(5(1(-1sin(3πx - 1) - 1)^2 - 4(-1sin(3πx - 1) - 1) - 3)^2 - 5(1(-1sin(3πx - 1) - 1)^2 - 4(-1sin(3πx - 1) - 1) - 3) - 2)) from x = -0.2 to x = -0.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.5
|
math
|
train
|
math_algebra_func_area_level_4_4_513
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 2(1|(4(2(3|x - 1| - 3)^2 - 1(3|x - 1| - 3) - 2)^2 - 5(2(3|x - 1| - 3)^2 - 1(3|x - 1| - 3) - 2) + 5) - 1| - 1)^2 + 2(1|(4(2(3|x - 1| - 3)^2 - 1(3|x - 1| - 3) - 2)^2 - 5(2(3|x - 1| - 3)^2 - 1(3|x - 1| - 3) - 2) + 5) - 1| - 1) - 2 and g(x) = 3(4(-1|(3sin(2πx - 3) + 2) - 2| - 3)^2 + 2(-1|(3sin(2πx - 3) + 2) - 2| - 3) - 4) + 5 between the vertical lines x = 1.6 and x = 1.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
61.9
|
math
|
train
|
math_algebra_func_area_level_4_4_514
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 3sin(3π(1(5(-3(3|x|) + 4)^2 + 5(-3(3|x|) + 4) - 4) + 4) - 1) - 2 and g(x) = (1(2(-1|((2x - 1)/(-2x - 3)) + 1| - 2)) - 2)/(2(2(-1|((2x - 1)/(-2x - 3)) + 1| - 2)) + 2) between the vertical lines x = -4.4 and x = -4.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.3
|
math
|
train
|
math_algebra_func_area_level_4_4_515
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -2|(2(-2cos(2π((-1(-1x^2 + 1x - 1))/(-3(-1x^2 + 1x - 1) - 3)) - 3)) + 5)| and g(x) = (-2(-3sin(3π(-2|(-5x^2 - 5x + 2) - 3| + 1) + 2) - 1) + 2)/(-3(-3sin(3π(-2|(-5x^2 - 5x + 2) - 3| + 1) + 2) - 1) + 2) from x = -3.5 to x = -3.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.5
|
math
|
train
|
math_algebra_func_area_level_4_4_516
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -4(-3sin(1π(2((-1((2x - 2)/(-3x)) + 2)/(3((2x - 2)/(-3x)) + 3))^2 + 2((-1((2x - 2)/(-3x)) + 2)/(3((2x - 2)/(-3x)) + 3)) - 3) - 2))^2 + 1(-3sin(1π(2((-1((2x - 2)/(-3x)) + 2)/(3((2x - 2)/(-3x)) + 3))^2 + 2((-1((2x - 2)/(-3x)) + 2)/(3((2x - 2)/(-3x)) + 3)) - 3) - 2)) + 3 and g(x) = 2sin(2π(2|((-2(2|x + 2| - 1) - 3)/(-1(2|x + 2| - 1) - 2)) + 2| + 3) - 3) - 3 from x = -4.8 to x = -4.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.7
|
math
|
train
|
math_algebra_func_area_level_4_4_517
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (2(2sin(1π(1(-1|(2x^2 + 2x - 3) - 2| + 1) - 4) - 1) + 2) + 1)/(2(2sin(1π(1(-1|(2x^2 + 2x - 3) - 2| + 1) - 4) - 1) + 2) - 1) and g(x) = (1(3sin(1π(4(-2|x - 3| + 2) + 5)) - 2) + 2)/(3(3sin(1π(4(-2|x - 3| + 2) + 5)) - 2) + 1) from x = -3.3 to x = -3.1999999999999997. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.8
|
math
|
train
|
math_algebra_func_area_level_4_4_518
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 4((-1((-3(3(-5x + 4)^2 - 5(-5x + 4)) + 2)/(1(3(-5x + 4)^2 - 5(-5x + 4)) - 2)) - 2)/(-1((-3(3(-5x + 4)^2 - 5(-5x + 4)) + 2)/(1(3(-5x + 4)^2 - 5(-5x + 4)) - 2)) + 3)) - 2 and g(x) = -1(2|(2(3x^2 - 5x + 3)^2 + 2(3x^2 - 5x + 3) + 4) - 3| - 2) + 2 from x = 0.4 to x = 0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
3.8
|
math
|
train
|
math_algebra_func_area_level_4_4_519
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -3|(-1(-4(1(1sin(2πx + 3) - 3)^2 + 4(1sin(2πx + 3) - 3) - 3) + 2) + 2) + 2| - 1 and g(x) = -5(-1(2|(2e^(1x) - 3) - 2| + 3) + 5)^2 + 2 between the vertical lines x = 0.3 and x = 1.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
53.2
|
math
|
train
|
math_algebra_func_area_level_4_4_520
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -3e^(2((-3(-3|((1((-2x - 2)/(3x + 2)))/(2((-2x - 2)/(3x + 2)) - 1)) + 1| - 1) - 1)/(3(-3|((1((-2x - 2)/(3x + 2)))/(2((-2x - 2)/(3x + 2)) - 1)) + 1| - 1) + 2))) + 1, g(x) = 3cos(1π(2|((2(2x^2 - 3x + 4) - 2)/(3(2x^2 - 3x + 4) + 3)) - 1| - 1) + 2) + 1, x = -1.2, and x = 2.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
6.5
|
math
|
train
|
math_algebra_func_area_level_4_4_521
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -1|((2(3|(4(1x^2 - 2x + 3) + 5) - 1|) + 2)/(-1(3|(4(1x^2 - 2x + 3) + 5) - 1|) + 2)) + 1| + 1 and g(x) = (-1((-1(3sin(3π(-2|x + 1| - 1) + 1) - 1) + 1)/(2(3sin(3π(-2|x + 1| - 1) + 1) - 1) - 1)))/(2((-1(3sin(3π(-2|x + 1| - 1) + 1) - 1) + 1)/(2(3sin(3π(-2|x + 1| - 1) + 1) - 1) - 1)) - 1) between the vertical lines x = 1.8 and x = 2.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.1
|
math
|
train
|
math_algebra_func_area_level_4_4_522
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 1cos(3π(-2|(-3(-5((1x)/(-1x - 2)) + 5) + 4) + 1| + 2) + 2) + 3 and g(x) = 2|(1e^(2((2((1x + 2)/(2x - 1)) - 3)/(-2((1x + 2)/(2x - 1))))) + 1) - 2| + 2 from x = -1.8 to x = -1.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.1
|
math
|
train
|
math_algebra_func_area_level_4_4_523
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -5(4(3(3((-1x + 1)/(-1x - 1)) - 1)^2 + 2(3((-1x + 1)/(-1x - 1)) - 1) - 1)^2 - 1(3(3((-1x + 1)/(-1x - 1)) - 1)^2 + 2(3((-1x + 1)/(-1x - 1)) - 1) - 1) - 5) + 4 and g(x) = -5(-2|(-3|(-1cos(3πx + 1) + 3)| + 2) + 3| + 3)^2 + 3(-2|(-3|(-1cos(3πx + 1) + 3)| + 2) + 3| + 3) + 5 from x = 0.7 to x = 1.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
151.0
|
math
|
train
|
math_algebra_func_area_level_4_4_524
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -3|(-1|((2(-4(-5x^2 - 3x)^2 + 4(-5x^2 - 3x) - 5) - 2)/(-1(-4(-5x^2 - 3x)^2 + 4(-5x^2 - 3x) - 5) + 2)) - 3|) - 1| - 1 and g(x) = 5(-2(-1(3x^2 + 2x + 2)^2 + 2(3x^2 + 2x + 2) + 1) - 5) + 3 from x = -0.9 to x = 0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
15.1
|
math
|
train
|
math_algebra_func_area_level_4_4_525
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 1cos(3π(1((2(-5(-4x + 3)^2 - 4(-4x + 3) + 1) - 1)/(3(-5(-4x + 3)^2 - 4(-4x + 3) + 1) - 2))^2 - 5((2(-5(-4x + 3)^2 - 4(-4x + 3) + 1) - 1)/(3(-5(-4x + 3)^2 - 4(-4x + 3) + 1) - 2)) - 1) - 3) + 3 and g(x) = -1(-2((1(-1|x + 2| + 2))/(-1(-1|x + 2| + 2) + 2)) + 5) + 2 between the vertical lines x = -2.5 and x = -1.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
179.6
|
math
|
train
|
math_algebra_func_area_level_4_4_526
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (-1(3cos(3π(-5(2((-3x - 1)/(-1x + 2)) - 1)^2 - 3(2((-3x - 1)/(-1x + 2)) - 1) + 5) + 3) - 1) + 1)/(-1(3cos(3π(-5(2((-3x - 1)/(-1x + 2)) - 1)^2 - 3(2((-3x - 1)/(-1x + 2)) - 1) + 5) + 3) - 1) + 2) and g(x) = -5(-4(1(-1x^2 + 5x - 3) + 3) - 2)^2 + 2(-4(1(-1x^2 + 5x - 3) + 3) - 2) + 3 from x = -0.2 to x = -0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
4.5
|
math
|
train
|
math_algebra_func_area_level_4_4_527
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -3(-3(-1|(3|(-3sin(1πx + 2) - 2) - 2| - 1) - 1| + 2) - 2) and g(x) = -2|((2((-3(-1e^(1x) - 3) + 3)/(-1(-1e^(1x) - 3) + 3)))/(-1((-3(-1e^(1x) - 3) + 3)/(-1(-1e^(1x) - 3) + 3)) + 3)) + 1| - 3 between the vertical lines x = -0.9 and x = 0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
113.6
|
math
|
train
|
math_algebra_func_area_level_4_4_528
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -3(1|(-3(3cos(1π(3|x - 2| + 3) + 3) - 1)^2 - 5(3cos(1π(3|x - 2| + 3) + 3) - 1) - 3)| - 3) - 3 and g(x) = 4((-1(-2sin(3π((-1x - 3)/(2x + 3)) - 1) - 1) - 2)/(-2(-2sin(3π((-1x - 3)/(2x + 3)) - 1) - 1) - 1)) - 3 from x = -3.2 to x = -2.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
16.0
|
math
|
train
|
math_algebra_func_area_level_4_4_529
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = (2(-2|(2(-3sin(1π(-5x - 5) - 2) - 2)^2 + 3(-3sin(1π(-5x - 5) - 2) - 2) + 4) - 1| + 2) - 2)/(-1(-2|(2(-3sin(1π(-5x - 5) - 2) - 2)^2 + 3(-3sin(1π(-5x - 5) - 2) - 2) + 4) - 1| + 2) + 2) and g(x) = -3cos(3π(4((-1((1x - 3)/(2x - 1)) - 2)/(3((1x - 3)/(2x - 1)) - 2))^2 + 1)) between the vertical lines x = -3.8 and x = -3.6999999999999997. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.2
|
math
|
train
|
math_algebra_func_area_level_4_4_530
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 1sin(1π(2|(3(4(-4x^2 + 3x + 1) - 1)^2 - 1(4(-4x^2 + 3x + 1) - 1) + 1)| - 1) + 2) + 1 and g(x) = (3((2(-5(2cos(2πx + 3) - 1) + 3) + 3)/(-1(-5(2cos(2πx + 3) - 1) + 3) + 2)) - 2)/(-2((2(-5(2cos(2πx + 3) - 1) + 3) + 3)/(-1(-5(2cos(2πx + 3) - 1) + 3) + 2)) + 3) from x = -1.4 to x = -0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.9
|
math
|
train
|
math_algebra_func_area_level_4_4_531
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = (-3(-3(-1(-3|((3x - 2)/(2x - 1))| - 1) - 2)^2 + 1(-1(-3|((3x - 2)/(2x - 1))| - 1) - 2) + 5) - 1)/(-2(-3(-1(-3|((3x - 2)/(2x - 1))| - 1) - 2)^2 + 1(-1(-3|((3x - 2)/(2x - 1))| - 1) - 2) + 5) - 1) and g(x) = -4(-4(-1e^(-1((-1x - 2)/(3x + 2))) + 3)^2 - 5(-1e^(-1((-1x - 2)/(3x + 2))) + 3) + 4) between the vertical lines x = -0.3 and x = 0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
6.4
|
math
|
train
|
math_algebra_func_area_level_4_4_532
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -3(-1((-3(-2((-1x - 3)/(-1x + 2))) - 1)/(-2(-2((-1x - 3)/(-1x + 2))) + 1)) - 1) + 2 and g(x) = -4(-3|(-2|(-3|x + 1| + 3) - 1|) + 3| - 1) - 4 between the vertical lines x = -1.7 and x = -1.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.7
|
math
|
train
|
math_algebra_func_area_level_4_4_533
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (-3(1((-3(1|(-2|x - 3| - 1) + 2| - 1) - 3)/(-2(1|(-2|x - 3| - 1) + 2| - 1) + 3))) + 2)/(-1(1((-3(1|(-2|x - 3| - 1) + 2| - 1) - 3)/(-2(1|(-2|x - 3| - 1) + 2| - 1) + 3))) + 2), g(x) = (-3(-2(2|(-2|x + 3| + 3) + 3|) + 2) - 2)/(-2(-2(2|(-2|x + 3| + 3) + 3|) + 2) - 3), x = 2.9, and x = 3.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.0
|
math
|
train
|
math_algebra_func_area_level_4_4_534
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -4(2sin(1π((2(4(-1|x + 3| + 1) - 2) - 1)/(-3(4(-1|x + 3| + 1) - 2) + 2)) - 2) + 2)^2 + 2 and g(x) = 2(-2|(-3sin(3π(1x + 1)) + 2) + 3| - 3) - 3 from x = -2.6 to x = -2.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
2.4
|
math
|
train
|
math_algebra_func_area_level_4_4_535
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 5(1|(-1|(-3|(5x^2 + 2x + 1) - 3| + 2) + 1| - 3) - 2| - 3)^2 - 5(1|(-1|(-3|(5x^2 + 2x + 1) - 3| + 2) + 1| - 3) - 2| - 3) and g(x) = 1e^(2(-3|(1|(-3|x| + 2) + 2| - 1) - 2| + 2)) + 3 from x = 0.3 to x = 0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
2.0
|
math
|
train
|
math_algebra_func_area_level_4_4_536
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = (-3(-3sin(3π((2((2(-1|x - 1| + 3) - 3)/(-3(-1|x - 1| + 3) + 4)))/(-1((2(-1|x - 1| + 3) - 3)/(-3(-1|x - 1| + 3) + 4)) - 1)) + 2) + 3) - 1)/(-2(-3sin(3π((2((2(-1|x - 1| + 3) - 3)/(-3(-1|x - 1| + 3) + 4)))/(-1((2(-1|x - 1| + 3) - 3)/(-3(-1|x - 1| + 3) + 4)) - 1)) + 2) + 3) + 3) and g(x) = -3((2(2(-4x)) + 2)/(3(2(-4x)) - 2))^2 + 4((2(2(-4x)) + 2)/(3(2(-4x)) - 2)) between the vertical lines x = -0.3 and x = -0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.1
|
math
|
train
|
math_algebra_func_area_level_4_4_537
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 1(2((-1(1(4x^2 - 1x + 5) - 4) - 2)/(2(1(4x^2 - 1x + 5) - 4) - 1))^2 + 2((-1(1(4x^2 - 1x + 5) - 4) - 2)/(2(1(4x^2 - 1x + 5) - 4) - 1)) - 3)^2 - 4(2((-1(1(4x^2 - 1x + 5) - 4) - 2)/(2(1(4x^2 - 1x + 5) - 4) - 1))^2 + 2((-1(1(4x^2 - 1x + 5) - 4) - 2)/(2(1(4x^2 - 1x + 5) - 4) - 1)) - 3) - 5, g(x) = (1(-1|(-3((-2x + 2)/(-2x + 3))^2 + 3((-2x + 2)/(-2x + 3)) + 5) - 3| + 3) + 2)/(-1(-1|(-3((-2x + 2)/(-2x + 3))^2 + 3((-2x + 2)/(-2x + 3)) + 5) - 3| + 3) + 2), x = -0.1, and x = 0.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
22.6
|
math
|
train
|
math_algebra_func_area_level_4_4_538
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -1cos(1π(-5(3(-1(1|x + 3| + 3)^2 + 3(1|x + 3| + 3) + 2) + 1) - 4) + 1) + 2 and g(x) = (3(-1|(-2sin(3π(-3x^2 + 4x + 3) + 2) + 2) + 1| - 1) - 3)/(1(-1|(-2sin(3π(-3x^2 + 4x + 3) + 2) + 2) + 1| - 1) - 2) from x = -1.8 to x = -1.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.1
|
math
|
train
|
math_algebra_func_area_level_4_4_539
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (-2(-1(2(2(2|x - 3| + 1) + 2)^2 + 1(2(2|x - 3| + 1) + 2))^2 - 5(2(2(2|x - 3| + 1) + 2)^2 + 1(2(2|x - 3| + 1) + 2)) - 3) - 1)/(-2(-1(2(2(2|x - 3| + 1) + 2)^2 + 1(2(2|x - 3| + 1) + 2))^2 - 5(2(2(2|x - 3| + 1) + 2)^2 + 1(2(2|x - 3| + 1) + 2)) - 3) - 1), g(x) = 1(-3(-3(-1x^2 + 5x - 5)^2 + 3(-1x^2 + 5x - 5) + 5) + 1)^2 - 3, x = 3.9, and x = 4.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.3
|
math
|
train
|
math_algebra_func_area_level_4_4_540
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (2(-5(2|(-2(1|x - 2| + 2) + 4) - 3| + 2)^2 - 4(2|(-2(1|x - 2| + 2) + 4) - 3| + 2) + 3) + 2)/(2(-5(2|(-2(1|x - 2| + 2) + 4) - 3| + 2)^2 - 4(2|(-2(1|x - 2| + 2) + 4) - 3| + 2) + 3) + 3), g(x) = 3cos(2π(3(2|(3x^2 + 3x) + 2| + 3)^2 + 2(2|(3x^2 + 3x) + 2| + 3) - 4) + 3) + 2, x = 1.4, and x = 1.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.2
|
math
|
train
|
math_algebra_func_area_level_4_4_541
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (-1(1((-1(2|(-2cos(3πx) - 3) + 3| + 2) + 1)/(2(2|(-2cos(3πx) - 3) + 3| + 2) + 1))^2 + 4((-1(2|(-2cos(3πx) - 3) + 3| + 2) + 1)/(2(2|(-2cos(3πx) - 3) + 3| + 2) + 1)) - 3))/(1(1((-1(2|(-2cos(3πx) - 3) + 3| + 2) + 1)/(2(2|(-2cos(3πx) - 3) + 3| + 2) + 1))^2 + 4((-1(2|(-2cos(3πx) - 3) + 3| + 2) + 1)/(2(2|(-2cos(3πx) - 3) + 3| + 2) + 1)) - 3)), g(x) = 1(-2sin(2π((-2(-3|x - 3| + 1) - 1)/(3(-3|x - 3| + 1) - 2)) - 2) - 1)^2 - 3(-2sin(2π((-2(-3|x - 3| + 1) - 1)/(3(-3|x - 3| + 1) - 2)) - 2) - 1) - 1, x = 3.1, and x = 3.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.8
|
math
|
train
|
math_algebra_func_area_level_4_4_542
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (-1((3(1(-2cos(2π(-4x^2 - 5x - 4) - 1) + 2)^2 + 2(-2cos(2π(-4x^2 - 5x - 4) - 1) + 2)) + 3)/(1(1(-2cos(2π(-4x^2 - 5x - 4) - 1) + 2)^2 + 2(-2cos(2π(-4x^2 - 5x - 4) - 1) + 2)) - 3)) + 1)/(1((3(1(-2cos(2π(-4x^2 - 5x - 4) - 1) + 2)^2 + 2(-2cos(2π(-4x^2 - 5x - 4) - 1) + 2)) + 3)/(1(1(-2cos(2π(-4x^2 - 5x - 4) - 1) + 2)^2 + 2(-2cos(2π(-4x^2 - 5x - 4) - 1) + 2)) - 3)) + 2), g(x) = (-1((1(-3|(-2x^2 - 4x + 2) + 1|) + 2)/(2(-3|(-2x^2 - 4x + 2) + 1|) - 1)) + 1)/(-2((1(-3|(-2x^2 - 4x + 2) + 1|) + 2)/(2(-3|(-2x^2 - 4x + 2) + 1|) - 1)) - 2), x = -2.7, and x = -2.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.2
|
math
|
train
|
math_algebra_func_area_level_4_4_543
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 1(5(1|(1(1x - 2) + 2) - 1| + 1) - 2)^2 + 3(5(1|(1(1x - 2) + 2) - 1| + 1) - 2) + 1 and g(x) = 3|(1(-4(2cos(2πx + 1) + 1)^2 - 5(2cos(2πx + 1) + 1) + 5) - 2) + 2| + 3 from x = 1.1 to x = 1.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
11.7
|
math
|
train
|
math_algebra_func_area_level_4_4_544
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 3sin(2π((2((1(-1(-5x^2 + 5) + 1) - 3)/(-3(-1(-5x^2 + 5) + 1) + 4)) + 3)/(-2((1(-1(-5x^2 + 5) + 1) - 3)/(-3(-1(-5x^2 + 5) + 1) + 4)) - 3)) - 2) - 2 and g(x) = -1|(-4(-3(-1x - 2) - 4)^2 - 4(-3(-1x - 2) - 4)) - 1| - 1 between the vertical lines x = -1.2 and x = -0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.6
|
math
|
train
|
math_algebra_func_area_level_4_4_545
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 1|((-1(2|((-2((3x + 3)/(-1x + 2)) - 1)/(1((3x + 3)/(-1x + 2)) + 1)) + 1| - 1) - 3)/(2(2|((-2((3x + 3)/(-1x + 2)) - 1)/(1((3x + 3)/(-1x + 2)) + 1)) + 1| - 1))) - 2| - 2 and g(x) = (2(-1e^(-2((3(3|x - 2|) + 3)/(2(3|x - 2|) + 3))) - 3) + 1)/(-2(-1e^(-2((3(3|x - 2|) + 3)/(2(3|x - 2|) + 3))) - 3) - 1) between the vertical lines x = -1.2 and x = -1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.1
|
math
|
train
|
math_algebra_func_area_level_4_4_546
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (-1(1(5((-2(2|x| - 2) - 2)/(1(2|x| - 2) + 2)) - 2) + 3) - 3)/(-1(1(5((-2(2|x| - 2) - 2)/(1(2|x| - 2) + 2)) - 2) + 3) - 2) and g(x) = (2(-1|(-3|(-3x + 3) - 2|) - 2| + 1) - 3)/(-1(-1|(-3|(-3x + 3) - 2|) - 2| + 1) - 2) from x = -0.7 to x = 0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
33.0
|
math
|
train
|
math_algebra_func_area_level_4_4_547
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -5((-1(-4((-1(1x^2 + 3x - 2) - 1)/(2(1x^2 + 3x - 2) - 1))^2 - 5((-1(1x^2 + 3x - 2) - 1)/(2(1x^2 + 3x - 2) - 1)) + 3))/(-1(-4((-1(1x^2 + 3x - 2) - 1)/(2(1x^2 + 3x - 2) - 1))^2 - 5((-1(1x^2 + 3x - 2) - 1)/(2(1x^2 + 3x - 2) - 1)) + 3) - 3))^2 + 4, g(x) = (-1(-1(1cos(2π(1x^2 - 4) + 1) - 1)^2 + 4(1cos(2π(1x^2 - 4) + 1) - 1) + 1) - 2)/(2(-1(1cos(2π(1x^2 - 4) + 1) - 1)^2 + 4(1cos(2π(1x^2 - 4) + 1) - 1) + 1) - 1), x = -4.1, and x = -4.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.3
|
math
|
train
|
math_algebra_func_area_level_4_4_548
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 5(-2|((-3(-1|(-2cos(2πx + 3) + 1) - 1| + 1) + 2)/(-2(-1|(-2cos(2πx + 3) + 1) - 1| + 1) - 3)) - 1| - 3) + 2 and g(x) = (1(2cos(2π(-5(2|x + 1| - 2) - 1) + 3)) + 3)/(-3(2cos(2π(-5(2|x + 1| - 2) - 1) + 3)) - 2) from x = -2.7 to x = -2.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
3.0
|
math
|
train
|
math_algebra_func_area_level_4_4_549
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = (2(2(-1|((2(2x^2 - 1x + 4) + 1)/(2(2x^2 - 1x + 4) - 1)) - 2| - 2)^2 - 2(-1|((2(2x^2 - 1x + 4) + 1)/(2(2x^2 - 1x + 4) - 1)) - 2| - 2) - 2) + 2)/(2(2(-1|((2(2x^2 - 1x + 4) + 1)/(2(2x^2 - 1x + 4) - 1)) - 2| - 2)^2 - 2(-1|((2(2x^2 - 1x + 4) + 1)/(2(2x^2 - 1x + 4) - 1)) - 2| - 2) - 2) - 3) and g(x) = (-1(5((-2(3cos(2πx - 3) + 3) + 3)/(-1(3cos(2πx - 3) + 3) - 1))^2 + 5((-2(3cos(2πx - 3) + 3) + 3)/(-1(3cos(2πx - 3) + 3) - 1))) + 2)/(2(5((-2(3cos(2πx - 3) + 3) + 3)/(-1(3cos(2πx - 3) + 3) - 1))^2 + 5((-2(3cos(2πx - 3) + 3) + 3)/(-1(3cos(2πx - 3) + 3) - 1))) + 2) between the vertical lines x = -4.9 and x = -4.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.5
|
math
|
train
|
math_algebra_func_area_level_4_4_550
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (1(2(2|((-3(-1|x + 2| + 2) + 3)/(2(-1|x + 2| + 2) - 3)) + 1| + 1)^2 + 1(2|((-3(-1|x + 2| + 2) + 3)/(2(-1|x + 2| + 2) - 3)) + 1| + 1) - 5))/(-1(2(2|((-3(-1|x + 2| + 2) + 3)/(2(-1|x + 2| + 2) - 3)) + 1| + 1)^2 + 1(2|((-3(-1|x + 2| + 2) + 3)/(2(-1|x + 2| + 2) - 3)) + 1| + 1) - 5)), g(x) = -2cos(1π(1(2|(-3x - 4) - 1| - 1) + 4) - 3) - 1, x = 2.7, and x = 2.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.2
|
math
|
train
|
math_algebra_func_area_level_4_4_551
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -2sin(1π(-2(-3(-3(5x)^2 + 5(5x) + 4)^2 - 2(-3(5x)^2 + 5(5x) + 4) + 3)) - 2) and g(x) = (-1((-2(-5(-1|x - 3| + 1)^2 + 1(-1|x - 3| + 1) + 5) + 2)/(-2(-5(-1|x - 3| + 1)^2 + 1(-1|x - 3| + 1) + 5) - 1)) + 1)/(2((-2(-5(-1|x - 3| + 1)^2 + 1(-1|x - 3| + 1) + 5) + 2)/(-2(-5(-1|x - 3| + 1)^2 + 1(-1|x - 3| + 1) + 5) - 1)) + 1) between the vertical lines x = 0.0 and x = 0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.1
|
math
|
train
|
math_algebra_func_area_level_4_4_552
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (-1(-1(2(4((2x + 3)/(-3x - 2))^2 + 5((2x + 3)/(-3x - 2)) + 1) - 5) - 2))/(3(-1(2(4((2x + 3)/(-3x - 2))^2 + 5((2x + 3)/(-3x - 2)) + 1) - 5) - 2) + 3), g(x) = 1|(3sin(2π(-1|(1x + 5) - 3| - 1) - 3) - 1) - 3| - 1, x = -1.3, and x = 0.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
5.5
|
math
|
train
|
math_algebra_func_area_level_4_4_553
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -4(2((-3(2cos(2π(-2|x - 3| - 2)) + 1) + 3)/(-3(2cos(2π(-2|x - 3| - 2)) + 1) - 3))^2 + 3((-3(2cos(2π(-2|x - 3| - 2)) + 1) + 3)/(-3(2cos(2π(-2|x - 3| - 2)) + 1) - 3)))^2 - 3(2((-3(2cos(2π(-2|x - 3| - 2)) + 1) + 3)/(-3(2cos(2π(-2|x - 3| - 2)) + 1) - 3))^2 + 3((-3(2cos(2π(-2|x - 3| - 2)) + 1) + 3)/(-3(2cos(2π(-2|x - 3| - 2)) + 1) - 3))) and g(x) = -1(-2e^(2(-3(1x^2 + 4x - 1) - 3)) - 2)^2 + 3(-2e^(2(-3(1x^2 + 4x - 1) - 3)) - 2) - 1 between the vertical lines x = -4.4 and x = -4.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
9.5
|
math
|
train
|
math_algebra_func_area_level_4_4_554
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -2((3(5(2(2|x + 1| + 2)^2 - 3(2|x + 1| + 2) - 3)^2 - 1(2(2|x + 1| + 2)^2 - 3(2|x + 1| + 2) - 3)) + 1)/(3(5(2(2|x + 1| + 2)^2 - 3(2|x + 1| + 2) - 3)^2 - 1(2(2|x + 1| + 2)^2 - 3(2|x + 1| + 2) - 3)) + 1)) + 1 and g(x) = 3(-2((-3(-2x^2 + 5x - 1) + 1)/(-2(-2x^2 + 5x - 1) + 3)) + 2) - 2 between the vertical lines x = -0.0 and x = 2.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
178.7
|
math
|
train
|
math_algebra_func_area_level_4_4_555
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (-2(1(-5(3(1cos(2πx) + 2)^2 - 5(1cos(2πx) + 2) + 3)^2 + 2(3(1cos(2πx) + 2)^2 - 5(1cos(2πx) + 2) + 3) + 4)) - 3)/(-3(1(-5(3(1cos(2πx) + 2)^2 - 5(1cos(2πx) + 2) + 3)^2 + 2(3(1cos(2πx) + 2)^2 - 5(1cos(2πx) + 2) + 3) + 4)) - 3), g(x) = (1(-5(-2sin(2π(1|x + 2| + 2)) + 3)^2 + 4(-2sin(2π(1|x + 2| + 2)) + 3) - 3) - 3)/(-2(-5(-2sin(2π(1|x + 2| + 2)) + 3)^2 + 4(-2sin(2π(1|x + 2| + 2)) + 3) - 3) - 2), x = 2.4, and x = 2.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.5
|
math
|
train
|
math_algebra_func_area_level_4_4_556
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -1|((2(1(-2(-4x - 2)^2 + 4(-4x - 2) + 1) - 5) - 1)/(3(1(-2(-4x - 2)^2 + 4(-4x - 2) + 1) - 5))) - 3| - 2 and g(x) = -1|(-2|(1|(-2|x - 2| - 3) + 3| - 2) - 2| - 3) + 2| + 2 between the vertical lines x = -1.3 and x = 1.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
7.0
|
math
|
train
|
math_algebra_func_area_level_4_4_557
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 3(-3(-1(-2|(-2x^2 - 1x + 2) + 3|)^2 - 5(-2|(-2x^2 - 1x + 2) + 3|) + 5)^2 + 4(-1(-2|(-2x^2 - 1x + 2) + 3|)^2 - 5(-2|(-2x^2 - 1x + 2) + 3|) + 5)) - 2 and g(x) = -4((-1(-2|(-2x - 3) + 3| - 1) - 2)/(2(-2|(-2x - 3) + 3| - 1) - 1))^2 - 2((-1(-2|(-2x - 3) + 3| - 1) - 2)/(2(-2|(-2x - 3) + 3| - 1) - 1)) between the vertical lines x = 0.8 and x = 0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
5.7
|
math
|
train
|
math_algebra_func_area_level_4_4_558
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 5(1(-1e^(-1(5(-3|x - 1| + 2) - 4)) + 3) + 2) - 4, g(x) = (1(-4(-2|(2|x - 2| + 1) + 1| - 1)^2 + 2(-2|(2|x - 2| + 1) + 1| - 1) + 1) + 1)/(-2(-4(-2|(2|x - 2| + 1) + 1| - 1)^2 + 2(-2|(2|x - 2| + 1) + 1| - 1) + 1) + 3), x = 0.5, and x = 1.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
18.5
|
math
|
train
|
math_algebra_func_area_level_4_4_559
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 4((-2((1(2|((-2x - 2)/(1x)) + 1| - 2) + 3)/(1(2|((-2x - 2)/(1x)) + 1| - 2) - 2)) - 3)/(-2((1(2|((-2x - 2)/(1x)) + 1| - 2) + 3)/(1(2|((-2x - 2)/(1x)) + 1| - 2) - 2)) - 2))^2 + 4((-2((1(2|((-2x - 2)/(1x)) + 1| - 2) + 3)/(1(2|((-2x - 2)/(1x)) + 1| - 2) - 2)) - 3)/(-2((1(2|((-2x - 2)/(1x)) + 1| - 2) + 3)/(1(2|((-2x - 2)/(1x)) + 1| - 2) - 2)) - 2)) + 1 and g(x) = 2(1|(1|(1x + 4) + 3| + 3)| + 3) + 1 between the vertical lines x = -2.6 and x = -1.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
2.5
|
math
|
train
|
math_algebra_func_area_level_4_4_560
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -4(2cos(1π((-1((-2(-5x + 2) + 3)/(3(-5x + 2) - 2)) + 3)/(-2((-2(-5x + 2) + 3)/(3(-5x + 2) - 2)) - 1)) - 1) - 3)^2 + 2(2cos(1π((-1((-2(-5x + 2) + 3)/(3(-5x + 2) - 2)) + 3)/(-2((-2(-5x + 2) + 3)/(3(-5x + 2) - 2)) - 1)) - 1) - 3) - 5, g(x) = -5(-2e^(2(-3|(4x^2 - 3x) - 3| + 2)) - 3)^2 - 3(-2e^(2(-3|(4x^2 - 3x) - 3| + 2)) - 3) + 4, x = -0.3, and x = -0.19999999999999998. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
3.5
|
math
|
train
|
math_algebra_func_area_level_4_4_561
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -1(2(-1|((3(-2x^2 - 4) - 1)/(1(-2x^2 - 4))) - 1| + 3)^2 + 5(-1|((3(-2x^2 - 4) - 1)/(1(-2x^2 - 4))) - 1| + 3) - 4)^2 - 3(2(-1|((3(-2x^2 - 4) - 1)/(1(-2x^2 - 4))) - 1| + 3)^2 + 5(-1|((3(-2x^2 - 4) - 1)/(1(-2x^2 - 4))) - 1| + 3) - 4) + 5 and g(x) = -1((-1(5(3x^2 - 2) - 2) + 1)/(3(5(3x^2 - 2) - 2) + 2)) + 4 from x = -0.9 to x = 0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
7.3
|
math
|
train
|
math_algebra_func_area_level_4_4_562
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 3|((3(-2(-1(-2|x - 3| + 1) + 3) + 1) + 1)/(-1(-2(-1(-2|x - 3| + 1) + 3) + 1) + 3)) + 1| + 1 and g(x) = 1(3|(4((2x - 3)/(2x)) + 4) + 2| - 2) + 4 from x = 0.5 to x = 0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.3
|
math
|
train
|
math_algebra_func_area_level_4_4_563
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (-1(-2|((2(5(-2|x - 3| + 1) - 3) - 3)/(-3(5(-2|x - 3| + 1) - 3) - 3)) - 2| - 2) + 3)/(-3(-2|((2(5(-2|x - 3| + 1) - 3) - 3)/(-3(5(-2|x - 3| + 1) - 3) - 3)) - 2| - 2) + 2), g(x) = (-2(-1(2(1sin(1πx - 1) + 3) - 2)^2 + 4(2(1sin(1πx - 1) + 3) - 2) - 1) + 1)/(-1(-1(2(1sin(1πx - 1) + 3) - 2)^2 + 4(2(1sin(1πx - 1) + 3) - 2) - 1) + 2), x = 1.4, and x = 2.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
13.8
|
math
|
train
|
math_algebra_func_area_level_4_4_564
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -2|(-2|((-2(-3|(-1e^(1x) - 2) + 3|) + 2)/(-3(-3|(-1e^(1x) - 2) + 3|))) + 3| + 1) + 3| + 3 and g(x) = -2cos(3π(5((2(1x - 1) + 2)/(2(1x - 1) - 1))^2 - 2((2(1x - 1) + 2)/(2(1x - 1) - 1)) + 1) - 2) - 3 between the vertical lines x = 2.9 and x = 3.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.1
|
math
|
train
|
math_algebra_func_area_level_4_4_565
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 3|((-1(-1(1(2x)^2 - 2(2x) + 4)^2 + 4(1(2x)^2 - 2(2x) + 4) - 5) + 3)/(1(-1(1(2x)^2 - 2(2x) + 4)^2 + 4(1(2x)^2 - 2(2x) + 4) - 5) - 3)) + 1| - 1 and g(x) = -3(-3(-1(1|x - 1| - 3))) + 3 from x = -2.4 to x = 4.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
106.8
|
math
|
train
|
math_algebra_func_area_level_4_4_566
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (-2(-3sin(1π((2(-2(3|x - 3| - 3) + 3) - 2)/(-1(-2(3|x - 3| - 3) + 3) + 3)) - 1)) - 2)/(-2(-3sin(1π((2(-2(3|x - 3| - 3) + 3) - 2)/(-1(-2(3|x - 3| - 3) + 3) + 3)) - 1)) + 3), g(x) = -3|((-2(4(-1x - 4)^2 + 2(-1x - 4)) + 3)/(-2(4(-1x - 4)^2 + 2(-1x - 4)) + 3)) - 3|, x = 2.2, and x = 2.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.6
|
math
|
train
|
math_algebra_func_area_level_4_4_567
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -1e^(-1((3(-2(2(-2|x - 1| - 3) + 3)^2 - 1(2(-2|x - 1| - 3) + 3) - 3) + 2)/(-3(-2(2(-2|x - 1| - 3) + 3)^2 - 1(2(-2|x - 1| - 3) + 3) - 3)))) - 2 and g(x) = (3(5(-1(-2x - 2) + 4)^2 + 2(-1(-2x - 2) + 4) - 4) + 1)/(-1(5(-1(-2x - 2) + 4)^2 + 2(-1(-2x - 2) + 4) - 4) + 2) from x = -3.8 to x = -2.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
12.3
|
math
|
train
|
math_algebra_func_area_level_4_4_568
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 4(3(-1|(-2cos(1π((3x + 1)/(2x - 3)) - 3) - 2)| + 1)^2 + 4(-1|(-2cos(1π((3x + 1)/(2x - 3)) - 3) - 2)| + 1) + 1)^2 - 4(3(-1|(-2cos(1π((3x + 1)/(2x - 3)) - 3) - 2)| + 1)^2 + 4(-1|(-2cos(1π((3x + 1)/(2x - 3)) - 3) - 2)| + 1) + 1) - 5, g(x) = -2cos(2π(-3(4((-1x - 1)/(-1x + 2)))^2 - 5(4((-1x - 1)/(-1x + 2))) + 2) - 2) + 3, x = 1.5, and x = 1.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
22.3
|
math
|
train
|
math_algebra_func_area_level_4_4_569
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -3((-1(-5(-5(-3sin(2πx) - 1)^2 - 4(-3sin(2πx) - 1) + 3) - 5) - 1)/(-1(-5(-5(-3sin(2πx) - 1)^2 - 4(-3sin(2πx) - 1) + 3) - 5) - 3))^2 + 2((-1(-5(-5(-3sin(2πx) - 1)^2 - 4(-3sin(2πx) - 1) + 3) - 5) - 1)/(-1(-5(-5(-3sin(2πx) - 1)^2 - 4(-3sin(2πx) - 1) + 3) - 5) - 3)) + 2 and g(x) = (-3(-1|((-2(-2|x + 3|) - 1)/(3(-2|x + 3|))) + 3| - 3) - 3)/(-2(-1|((-2(-2|x + 3|) - 1)/(3(-2|x + 3|))) + 3| - 3)) between the vertical lines x = 1.6 and x = 1.7000000000000002. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.0
|
math
|
train
|
math_algebra_func_area_level_4_4_570
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -2(-1(-1|(-5(-1|x - 1| + 3)^2 - 2(-1|x - 1| + 3) + 1) + 2| - 1) - 3) + 2 and g(x) = -4(2(-3(3cos(2πx + 2) + 3)^2 - 3(3cos(2πx + 2) + 3) + 1) + 1) + 2 between the vertical lines x = -0.9 and x = -0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.3
|
math
|
train
|
math_algebra_func_area_level_4_4_571
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -1((-1((3(-2|((3x - 1)/(-2x + 3)) + 1| + 2) - 2)/(2(-2|((3x - 1)/(-2x + 3)) + 1| + 2) - 3)) + 1)/(3((3(-2|((3x - 1)/(-2x + 3)) + 1| + 2) - 2)/(2(-2|((3x - 1)/(-2x + 3)) + 1| + 2) - 3))))^2 - 3((-1((3(-2|((3x - 1)/(-2x + 3)) + 1| + 2) - 2)/(2(-2|((3x - 1)/(-2x + 3)) + 1| + 2) - 3)) + 1)/(3((3(-2|((3x - 1)/(-2x + 3)) + 1| + 2) - 2)/(2(-2|((3x - 1)/(-2x + 3)) + 1| + 2) - 3)))) and g(x) = (3(5(5((1x - 2)/(-2x + 1))^2 + 1((1x - 2)/(-2x + 1)) - 5)^2 - 2(5((1x - 2)/(-2x + 1))^2 + 1((1x - 2)/(-2x + 1)) - 5) - 1) + 3)/(3(5(5((1x - 2)/(-2x + 1))^2 + 1((1x - 2)/(-2x + 1)) - 5)^2 - 2(5((1x - 2)/(-2x + 1))^2 + 1((1x - 2)/(-2x + 1)) - 5) - 1) + 1) from x = 1.0 to x = 1.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.3
|
math
|
train
|
math_algebra_func_area_level_4_4_572
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 2sin(3π(-4(1|(-1|(-1|x| + 3) + 2| + 1) + 1| - 2)^2 - 4(1|(-1|(-1|x| + 3) + 2| + 1) + 1| - 2) + 5) - 1) - 1 and g(x) = 1cos(1π(5((2(-5x + 5) - 1)/(-2(-5x + 5) + 3)) + 2) + 2) + 1 between the vertical lines x = -1.8 and x = -1.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.1
|
math
|
train
|
math_algebra_func_area_level_4_4_573
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (-2((2(-2|((-3(1|x - 2|) - 3)/(1(1|x - 2|) - 2)) + 1| + 2) + 2)/(3(-2|((-3(1|x - 2|) - 3)/(1(1|x - 2|) - 2)) + 1| + 2))) + 1)/(-3((2(-2|((-3(1|x - 2|) - 3)/(1(1|x - 2|) - 2)) + 1| + 2) + 2)/(3(-2|((-3(1|x - 2|) - 3)/(1(1|x - 2|) - 2)) + 1| + 2)))), g(x) = -4(-2sin(1π(-3|((-3x - 3)/(-2x + 3)) + 3| - 3) - 2) + 2)^2 - 3(-2sin(1π(-3|((-3x - 3)/(-2x + 3)) + 3| - 3) - 2) + 2) + 1, x = 1.8, and x = 1.9000000000000001. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
2.9
|
math
|
train
|
math_algebra_func_area_level_4_4_574
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 4(1(2((-2(-3|x|) - 3)/(-3(-3|x|) + 4))^2 - 5((-2(-3|x|) - 3)/(-3(-3|x|) + 4)) - 3) - 1) + 1 and g(x) = (3(3(2|((2x - 1)/(2x - 1)) + 3| + 3) + 5) - 2)/(-1(3(2|((2x - 1)/(2x - 1)) + 3| + 3) + 5) + 3) between the vertical lines x = -0.1 and x = 0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.7
|
math
|
train
|
math_algebra_func_area_level_4_4_575
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 3(-1|(1(3cos(1π((1x + 3)/(-1x - 2)) + 3))^2 + 1(3cos(1π((1x + 3)/(-1x - 2)) + 3))) - 3| + 2)^2 + 5(-1|(1(3cos(1π((1x + 3)/(-1x - 2)) + 3))^2 + 1(3cos(1π((1x + 3)/(-1x - 2)) + 3))) - 3| + 2) - 1 and g(x) = (2(-2|(5(1cos(2πx + 2) - 1) - 5) - 2| - 3) - 3)/(-2(-2|(5(1cos(2πx + 2) - 1) - 5) - 2| - 3) + 3) from x = -2.4 to x = -2.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.5
|
math
|
train
|
math_algebra_func_area_level_4_4_576
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 4((2(4((-3(-2x^2 + 4x + 5) + 2)/(-1(-2x^2 + 4x + 5))) + 3) - 2)/(2(4((-3(-2x^2 + 4x + 5) + 2)/(-1(-2x^2 + 4x + 5))) + 3))) - 3 and g(x) = -1(2sin(2π((2(-5x + 5) - 2)/(2(-5x + 5) - 1)) - 2) + 1)^2 + 5(2sin(2π((2(-5x + 5) - 2)/(2(-5x + 5) - 1)) - 2) + 1) between the vertical lines x = 0.9 and x = 1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.4
|
math
|
train
|
math_algebra_func_area_level_4_4_577
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -1cos(3π(-4(2(2(-1x^2 - 2x + 3) + 3)^2 - 4(2(-1x^2 - 2x + 3) + 3) + 2) - 2) + 1) - 2, g(x) = (-2(1((1(3|x - 3| - 1) + 3)/(3(3|x - 3| - 1) - 2))^2 - 3((1(3|x - 3| - 1) + 3)/(3(3|x - 3| - 1) - 2)) + 2) + 1)/(1(1((1(3|x - 3| - 1) + 3)/(3(3|x - 3| - 1) - 2))^2 - 3((1(3|x - 3| - 1) + 3)/(3(3|x - 3| - 1) - 2)) + 2) - 2), x = 2.6, and x = 2.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.1
|
math
|
train
|
math_algebra_func_area_level_4_4_578
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = (-3(3sin(2π(-2|((1(-2|x - 1|) - 1)/(1(-2|x - 1|) + 3)) + 1| + 1) - 3) - 3) - 3)/(1(3sin(2π(-2|((1(-2|x - 1|) - 1)/(1(-2|x - 1|) + 3)) + 1| + 1) - 3) - 3) + 2) and g(x) = (2(2sin(3π((1(2|x + 2| + 1) - 3)/(1(2|x + 2| + 1) - 2)) + 1) + 2) - 2)/(-2(2sin(3π((1(2|x + 2| + 1) - 3)/(1(2|x + 2| + 1) - 2)) + 1) + 2) + 1) between the vertical lines x = -1.4 and x = -1.2999999999999998. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.0
|
math
|
train
|
math_algebra_func_area_level_4_4_579
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 2e^(-2(1(-4(-1(-4x + 1)^2 - 4(-4x + 1) + 3) + 2) + 1)) - 3, g(x) = (-1(4(1(2e^(-1x) - 2)^2 - 3(2e^(-1x) - 2) - 1) - 4) - 2)/(2(4(1(2e^(-1x) - 2)^2 - 3(2e^(-1x) - 2) - 1) - 4) + 1), x = -1.0, and x = 0.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
2.8
|
math
|
train
|
math_algebra_func_area_level_4_4_580
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -2|(-2(2(-3cos(3π((2x - 2)/(-3x - 2)) + 3) + 3)^2 - 1(-3cos(3π((2x - 2)/(-3x - 2)) + 3) + 3) + 4) - 4) + 1| - 2 and g(x) = -2|(-3|(5(-1x^2 + 2x + 1)^2 - 4) - 3| + 1) + 1| between the vertical lines x = -0.4 and x = -0.30000000000000004. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
9.9
|
math
|
train
|
math_algebra_func_area_level_4_4_581
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 1(-3|(3((3((1x - 2)/(-3x + 1)) + 3)/(-1((1x - 2)/(-3x + 1)) + 2))^2 + 5((3((1x - 2)/(-3x + 1)) + 3)/(-1((1x - 2)/(-3x + 1)) + 2)) - 3) - 3| - 2)^2 + 3(-3|(3((3((1x - 2)/(-3x + 1)) + 3)/(-1((1x - 2)/(-3x + 1)) + 2))^2 + 5((3((1x - 2)/(-3x + 1)) + 3)/(-1((1x - 2)/(-3x + 1)) + 2)) - 3) - 3| - 2) + 3, g(x) = 3|(-3|(-4(-1x - 2)) + 2| - 1) - 2|, x = 0.3, and x = 0.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
196.9
|
math
|
train
|
math_algebra_func_area_level_4_4_582
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (2((-2(3|((3(-3x^2 - 5x + 1))/(2(-3x^2 - 5x + 1) - 3)) + 2| + 1) - 2)/(2(3|((3(-3x^2 - 5x + 1))/(2(-3x^2 - 5x + 1) - 3)) + 2| + 1) + 3)))/(1((-2(3|((3(-3x^2 - 5x + 1))/(2(-3x^2 - 5x + 1) - 3)) + 2| + 1) - 2)/(2(3|((3(-3x^2 - 5x + 1))/(2(-3x^2 - 5x + 1) - 3)) + 2| + 1) + 3))) and g(x) = -3|(-3sin(1π(-2|(-4x^2 - 4x + 3) - 2| - 3) + 2) - 1) - 1| + 2 from x = -2.8 to x = -2.6999999999999997. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.7
|
math
|
train
|
math_algebra_func_area_level_4_4_583
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (1(-4((3(4(-4x + 3) + 2) + 3)/(-1(4(-4x + 3) + 2) + 3))^2 + 2((3(4(-4x + 3) + 2) + 3)/(-1(4(-4x + 3) + 2) + 3)) + 2) + 3)/(2(-4((3(4(-4x + 3) + 2) + 3)/(-1(4(-4x + 3) + 2) + 3))^2 + 2((3(4(-4x + 3) + 2) + 3)/(-1(4(-4x + 3) + 2) + 3)) + 2) + 3) and g(x) = -3(-1(2((-3x - 3)/(3x - 2))^2 - 3((-3x - 3)/(3x - 2)) + 2) + 3)^2 - 4(-1(2((-3x - 3)/(3x - 2))^2 - 3((-3x - 3)/(3x - 2)) + 2) + 3) from x = -3.0 to x = -1.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.7
|
math
|
train
|
math_algebra_func_area_level_4_4_584
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (2(5(1|(-2|(-2cos(3πx) - 3) + 3| + 1) - 1| - 2)^2 + 4(1|(-2|(-2cos(3πx) - 3) + 3| + 1) - 1| - 2) - 4) + 2)/(2(5(1|(-2|(-2cos(3πx) - 3) + 3| + 1) - 1| - 2)^2 + 4(1|(-2|(-2cos(3πx) - 3) + 3| + 1) - 1| - 2) - 4)) and g(x) = (2(1(2e^(1(-5x^2 - 3x - 3)) + 1) - 3) - 1)/(-1(1(2e^(1(-5x^2 - 3x - 3)) + 1) - 3) - 1) from x = -1.9 to x = -1.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.6
|
math
|
train
|
math_algebra_func_area_level_4_4_585
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -1|(-2(2|(3sin(2π(-1x^2 + 4x - 1) - 1) + 2) - 2|) - 4) - 3| + 1 and g(x) = -3(-2|(-1e^(1(-2|x - 3| + 2))) + 2| + 1)^2 + 5(-2|(-1e^(1(-2|x - 3| + 2))) + 2| + 1) + 3 from x = 1.7 to x = 2.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
11.7
|
math
|
train
|
math_algebra_func_area_level_4_4_586
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 3((1(2((-2((1x + 1)/(3x + 1)) - 1)/(1((1x + 1)/(3x + 1)) - 3)) - 2) + 3)/(2(2((-2((1x + 1)/(3x + 1)) - 1)/(1((1x + 1)/(3x + 1)) - 3)) - 2)))^2 - 4((1(2((-2((1x + 1)/(3x + 1)) - 1)/(1((1x + 1)/(3x + 1)) - 3)) - 2) + 3)/(2(2((-2((1x + 1)/(3x + 1)) - 1)/(1((1x + 1)/(3x + 1)) - 3)) - 2))) + 1, g(x) = 4(3|(5((-2x - 1)/(-3x)) + 4) - 2| + 2)^2 - 2(3|(5((-2x - 1)/(-3x)) + 4) - 2| + 2) + 2, x = 0.3, and x = 0.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
-468.2
|
math
|
train
|
math_algebra_func_area_level_4_4_587
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (3((-1(-2(-5(1|x - 1|) + 5) - 2) - 2)/(1(-2(-5(1|x - 1|) + 5) - 2) + 3)) + 1)/(2((-1(-2(-5(1|x - 1|) + 5) - 2) - 2)/(1(-2(-5(1|x - 1|) + 5) - 2) + 3)) - 1) and g(x) = 2(3(2e^(1(-3x^2 + 1x + 5)) - 2)^2 - 4(2e^(1(-3x^2 + 1x + 5)) - 2) - 5) + 1 from x = 1.5 to x = 2.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
11.6
|
math
|
train
|
math_algebra_func_area_level_4_4_588
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (3(3((3(-3sin(3π(1x) + 1) - 1) + 1)/(-3(-3sin(3π(1x) + 1) - 1) + 1)) + 1))/(-3(3((3(-3sin(3π(1x) + 1) - 1) + 1)/(-3(-3sin(3π(1x) + 1) - 1) + 1)) + 1) - 2) and g(x) = 1(-1e^(2(-2|(-2x^2 + 2) + 1|)) + 1) - 3 from x = 3.5 to x = 4.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.3
|
math
|
train
|
math_algebra_func_area_level_4_4_589
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 2(1(-1(-1(-2x - 1) + 1)^2 + 4(-1(-2x - 1) + 1) + 4)^2 - 4(-1(-1(-2x - 1) + 1)^2 + 4(-1(-2x - 1) + 1) + 4) - 5) + 2, g(x) = (-2(-4(-1((-2x - 2)/(2x))^2 + 1((-2x - 2)/(2x)) + 5)^2 - 2) - 3)/(-3(-4(-1((-2x - 2)/(2x))^2 + 1((-2x - 2)/(2x)) + 5)^2 - 2) - 2), x = -0.9, and x = 0.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
60.6
|
math
|
train
|
math_algebra_func_area_level_4_4_590
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (-1(-3((3(4(3x) - 2) + 1)/(2(4(3x) - 2) - 1))^2 - 1((3(4(3x) - 2) + 1)/(2(4(3x) - 2) - 1)) - 1) - 1)/(1(-3((3(4(3x) - 2) + 1)/(2(4(3x) - 2) - 1))^2 - 1((3(4(3x) - 2) + 1)/(2(4(3x) - 2) - 1)) - 1) - 2), g(x) = 1|(-2sin(3π(-1((2x + 1)/(1x)) - 4) + 3) + 3) - 1| - 1, x = 0.2, and x = 0.30000000000000004. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.2
|
math
|
train
|
math_algebra_func_area_level_4_4_591
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 1(2(4(1(-2|x - 1| - 3)^2 + 4(-2|x - 1| - 3)) - 5) - 5)^2 + 4(2(4(1(-2|x - 1| - 3)^2 + 4(-2|x - 1| - 3)) - 5) - 5), g(x) = (2(3sin(2π(-3(-4x^2 + 5x - 4) + 3) - 1) - 3) + 3)/(1(3sin(2π(-3(-4x^2 + 5x - 4) + 3) - 1) - 3) + 2), x = 0.3, and x = 0.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.0
|
math
|
train
|
math_algebra_func_area_level_4_4_592
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = (-1(-1(1((1(3x^2 - 2x - 4) - 3)/(-2(3x^2 - 2x - 4) + 3)) - 5) + 3) + 2)/(1(-1(1((1(3x^2 - 2x - 4) - 3)/(-2(3x^2 - 2x - 4) + 3)) - 5) + 3) + 1) and g(x) = -1(3((-3(1|x + 1| - 1) + 1)/(3(1|x + 1| - 1) - 2))^2 + 1((-3(1|x + 1| - 1) + 1)/(3(1|x + 1| - 1) - 2))) + 2 between the vertical lines x = -2.5 and x = -1.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
2.9
|
math
|
train
|
math_algebra_func_area_level_4_4_593
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 3cos(3π(-2|(1(2(-1x + 3)^2 - 5(-1x + 3))^2 + 1(2(-1x + 3)^2 - 5(-1x + 3)) - 3) + 3| + 3) - 3) + 3 and g(x) = (3(-1(1(-1x + 5) - 4)^2 - 4(1(-1x + 5) - 4) - 3) + 3)/(2(-1(1(-1x + 5) - 4)^2 - 4(1(-1x + 5) - 4) - 3) + 3) from x = -2.3 to x = -2.1999999999999997. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.2
|
math
|
train
|
math_algebra_func_area_level_4_4_594
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = (2((3((-1(-1e^(1(3x - 4)) + 3) + 3)/(-3(-1e^(1(3x - 4)) + 3) - 3)) - 1)/(-1((-1(-1e^(1(3x - 4)) + 3) + 3)/(-3(-1e^(1(3x - 4)) + 3) - 3)) - 2)) + 1)/(2((3((-1(-1e^(1(3x - 4)) + 3) + 3)/(-3(-1e^(1(3x - 4)) + 3) - 3)) - 1)/(-1((-1(-1e^(1(3x - 4)) + 3) + 3)/(-3(-1e^(1(3x - 4)) + 3) - 3)) - 2)) + 2) and g(x) = (1(3|((1((1x + 2)/(-3x)) + 1)/(2((1x + 2)/(-3x)) - 3)) + 1| + 1) + 3)/(3(3|((1((1x + 2)/(-3x)) + 1)/(2((1x + 2)/(-3x)) - 3)) + 1| + 1) - 2) between the vertical lines x = 0.5 and x = 1.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.0
|
math
|
train
|
math_algebra_func_area_level_4_4_595
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -3(1((-2(3|(-1x - 1) - 3| - 2) + 3)/(1(3|(-1x - 1) - 3| - 2) - 3)) - 3)^2 + 1(1((-2(3|(-1x - 1) - 3| - 2) + 3)/(1(3|(-1x - 1) - 3| - 2) - 3)) - 3) + 1 and g(x) = -2|(-3(-4(1|x - 2|)^2 - 1(1|x - 2|) + 1)^2 + 3(-4(1|x - 2|)^2 - 1(1|x - 2|) + 1) + 3)| - 2 from x = 1.1 to x = 2.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
125.3
|
math
|
train
|
math_algebra_func_area_level_4_4_596
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 1(-2((-1((-1(3x + 3) + 2)/(1(3x + 3) + 3)) + 2)/(-2((-1(3x + 3) + 2)/(1(3x + 3) + 3)) - 3)) + 5)^2 - 1(-2((-1((-1(3x + 3) + 2)/(1(3x + 3) + 3)) + 2)/(-2((-1(3x + 3) + 2)/(1(3x + 3) + 3)) - 3)) + 5) - 5 and g(x) = 2(2|((1(-5x^2 + 2x - 2))/(-2(-5x^2 + 2x - 2) + 1))| - 3) from x = -3.3 to x = -2.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.4
|
math
|
train
|
math_algebra_func_area_level_4_4_597
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 4(3(-1(-1((1x - 2)/(2x - 1)) - 3) - 4) - 5), g(x) = -1(1|((-1(4x^2 + 5x - 3) - 3)/(-1(4x^2 + 5x - 3) - 2))| - 2)^2 + 3(1|((-1(4x^2 + 5x - 3) - 3)/(-1(4x^2 + 5x - 3) - 2))| - 2) - 1, x = -1.4, and x = -1.2999999999999998. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.7
|
math
|
train
|
math_algebra_func_area_level_4_4_598
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (3(-1(-2|(-1|(-1x^2 + 4x - 4) + 1| - 1) + 2|)^2 - 5(-2|(-1|(-1x^2 + 4x - 4) + 1| - 1) + 2|) - 4) - 1)/(-2(-1(-2|(-1|(-1x^2 + 4x - 4) + 1| - 1) + 2|)^2 - 5(-2|(-1|(-1x^2 + 4x - 4) + 1| - 1) + 2|) - 4) - 1), g(x) = (-1(4((2((-3x - 1)/(-1x - 2)) + 1)/(-1((-3x - 1)/(-1x - 2)) - 3))^2 - 4((2((-3x - 1)/(-1x - 2)) + 1)/(-1((-3x - 1)/(-1x - 2)) - 3)) - 2) - 3)/(2(4((2((-3x - 1)/(-1x - 2)) + 1)/(-1((-3x - 1)/(-1x - 2)) - 3))^2 - 4((2((-3x - 1)/(-1x - 2)) + 1)/(-1((-3x - 1)/(-1x - 2)) - 3)) - 2)), x = 2.9, and x = 3.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.0
|
math
|
train
|
math_algebra_func_area_level_4_4_599
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -1|((1((1(3|((1x - 1)/(-2x - 1))| + 1) - 2)/(1(3|((1x - 1)/(-2x - 1))| + 1) + 2)) - 1)/(1((1(3|((1x - 1)/(-2x - 1))| + 1) - 2)/(1(3|((1x - 1)/(-2x - 1))| + 1) + 2)))) - 1| + 1, g(x) = -1|(-1sin(3π(-1(-1|x - 3|) + 4)))| - 1, x = -1.6, and x = -1.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.1
|
math
|
train
|
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