id
string | setting_key
string | difficulty
string | level
int32 | messages
dict | ground_truth
string | dataset
string | omega_split
string |
|---|---|---|---|---|---|---|---|
math_algebra_func_area_level_2_2_600
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = (3((-2(-1e^(-2x) + 2) + 1)/(3(-1e^(-2x) + 2) + 2)) - 2)/(1((-2(-1e^(-2x) + 2) + 1)/(3(-1e^(-2x) + 2) + 2))) and g(x) = 3|(-2x - 5) + 2| 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}"
]
}
|
54.4
|
math
|
train
|
math_algebra_func_area_level_2_2_601
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (2((1(-4x^2 + 2x + 2) - 3)/(-1(-4x^2 + 2x + 2) - 2)) - 1)/(-1((1(-4x^2 + 2x + 2) - 3)/(-1(-4x^2 + 2x + 2) - 2)) + 3) and g(x) = 1|(-1x^2 - 1x - 5) + 2| - 2 from x = -0.4 to x = 1.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
2.4
|
math
|
train
|
math_algebra_func_area_level_2_2_602
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (2((-1(1|x - 2| - 1) + 1)/(3(1|x - 2| - 1) - 2)) - 2)/(2((-1(1|x - 2| - 1) + 1)/(3(1|x - 2| - 1) - 2))), g(x) = (-2((-1x + 1)/(-3x - 3)) + 3)/(3((-1x + 1)/(-3x - 3)) + 3), x = 0.4, and x = 3.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
6.8
|
math
|
train
|
math_algebra_func_area_level_2_2_603
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 1(1(-2|x + 3| - 1)^2 + 1(-2|x + 3| - 1) - 4)^2 - 1(1(-2|x + 3| - 1)^2 + 1(-2|x + 3| - 1) - 4) + 4 and g(x) = 3|(-3sin(1πx - 1) + 2) - 1| between the vertical lines x = -2.5 and x = -1.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
3.0
|
math
|
train
|
math_algebra_func_area_level_2_2_604
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -2|((3(-2|x - 2| - 3) - 3)/(-2(-2|x - 2| - 3) + 1)) + 3| + 1 and g(x) = -1|(1x^2 - 1x - 3) - 3| from x = -2.4 to x = -1.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.7
|
math
|
train
|
math_algebra_func_area_level_2_2_605
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = (2(-1sin(2π(-2x - 4) - 2) + 2) - 2)/(-3(-1sin(2π(-2x - 4) - 2) + 2)) and g(x) = 1sin(3π((-2x - 3)/(-2x + 1)) + 2) - 1 between the vertical lines x = -4.2 and x = -3.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.1
|
math
|
train
|
math_algebra_func_area_level_2_2_606
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -5((-3(-1x - 4) - 1)/(3(-1x - 4) - 2))^2 + 1((-3(-1x - 4) - 1)/(3(-1x - 4) - 2)) + 1, g(x) = (-1((-3x - 1)/(-3x - 1)) + 2)/(1((-3x - 1)/(-3x - 1)) + 1), x = -4.0, and x = -3.4. 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_2_2_607
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (1(-2|(-4x - 2) + 2| + 2) - 1)/(-1(-2|(-4x - 2) + 2| + 2) + 3) and g(x) = -1(-1x - 2)^2 - 3(-1x - 2) + 3 from x = -3.0 to x = 2.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
19.3
|
math
|
train
|
math_algebra_func_area_level_2_2_608
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (3(-4(3cos(2πx + 1) + 3)^2 - 1(3cos(2πx + 1) + 3) + 2))/(-2(-4(3cos(2πx + 1) + 3)^2 - 1(3cos(2πx + 1) + 3) + 2) - 1), g(x) = -1e^(1((1x)/(1x - 3))) + 3, x = 0.4, and x = 1.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
3.2
|
math
|
train
|
math_algebra_func_area_level_2_2_609
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -1cos(2π(-1(2x^2 + 4x - 3) - 4) - 3) - 2 and g(x) = 3(-2x + 5) - 2 from x = 2.6 to x = 2.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.1
|
math
|
train
|
math_algebra_func_area_level_2_2_610
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 1(5(1e^(1x) - 2)^2 + 4(1e^(1x) - 2) - 5)^2 - 4(5(1e^(1x) - 2)^2 + 4(1e^(1x) - 2) - 5) + 1 and g(x) = 1|(1cos(3πx - 2) + 1) - 3| + 3 between the vertical lines x = 1.0 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_2_2_611
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 3cos(3π((1(3|x + 2| + 2) - 3)/(-3(3|x + 2| + 2))) + 2) - 2, g(x) = -2((-3x - 2)/(-3x))^2 + 2((-3x - 2)/(-3x)) - 3, x = -2.4, and x = -1.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.3
|
math
|
train
|
math_algebra_func_area_level_2_2_612
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (2(-1(-5x - 4)^2 + 3(-5x - 4) + 4) + 1)/(2(-1(-5x - 4)^2 + 3(-5x - 4) + 4) - 3), g(x) = -4(1cos(1πx - 3) - 2) - 1, x = -1.5, and x = -0.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.8
|
math
|
train
|
math_algebra_func_area_level_2_2_613
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (3(4(-3e^(-1x))^2 - 1(-3e^(-1x)) + 3) + 2)/(-3(4(-3e^(-1x))^2 - 1(-3e^(-1x)) + 3) + 2) and g(x) = 4(2sin(2πx + 2) - 1)^2 + 2(2sin(2πx + 2) - 1) - 4 from x = 1.7 to x = 1.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.2
|
math
|
train
|
math_algebra_func_area_level_2_2_614
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 1(1cos(1π(-2x^2 - 2) - 3) - 3)^2 - 4(1cos(1π(-2x^2 - 2) - 3) - 3) - 3 and g(x) = -2(-3|x| + 3) + 4 from x = 4.5 to x = 4.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.8
|
math
|
train
|
math_algebra_func_area_level_2_2_615
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -5(4(-4x^2 + 1x + 2) - 2) - 4, g(x) = 1|((-3x)/(-3x - 1)) - 2| + 2, x = -0.6, and x = 0.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
39.9
|
math
|
train
|
math_algebra_func_area_level_2_2_616
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 1(-1(-3x^2 - 5x - 2) - 4) - 5 and g(x) = 1(-2|x + 2| + 1)^2 - 5(-2|x + 2| + 1) - 4 from x = -4.3 to x = -1.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
5.8
|
math
|
train
|
math_algebra_func_area_level_2_2_617
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (1(4(3|x| - 2)^2 - 4(3|x| - 2) - 2) + 3)/(-3(4(3|x| - 2)^2 - 4(3|x| - 2) - 2) - 3) and g(x) = 1(4x^2 - 4x + 5) - 4 from x = 0.7 to 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_2_2_618
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -3|(-3sin(1π(-3|x + 1| - 1) + 2) - 2) + 1| - 2 and g(x) = -3|((2x + 2)/(-2x))| + 1 from x = 1.6 to x = 1.7000000000000002. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.2
|
math
|
train
|
math_algebra_func_area_level_2_2_619
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -5(2(-2|x - 3| + 2)^2 - 1(-2|x - 3| + 2) - 4) - 3 and g(x) = (1(-2|x - 2|) + 1)/(1(-2|x - 2|) + 2) from x = 3.3 to x = 4.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
13.4
|
math
|
train
|
math_algebra_func_area_level_2_2_620
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -5(1|(4x^2 - 1x + 3) - 1| - 2) - 5 and g(x) = -1|((1x + 2)/(2x + 2))| between the vertical lines x = -1.0 and x = -0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
11.2
|
math
|
train
|
math_algebra_func_area_level_2_2_621
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 2((-1(-1|x - 3| + 1) - 2)/(3(-1|x - 3| + 1) - 2)) + 5, g(x) = 3cos(3π(1x^2 + 1x - 3) - 1), x = 2.9, and x = 3.0. 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_2_2_622
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -1(5(2x - 5)^2 - 5(2x - 5) - 4)^2 + 5(5(2x - 5)^2 - 5(2x - 5) - 4) - 1 and g(x) = -1sin(2π((3x)/(1x + 2)) - 3) + 3 between the vertical lines x = 3.3 and x = 3.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.2
|
math
|
train
|
math_algebra_func_area_level_2_2_623
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -2cos(1π((3(2x^2 - 3x - 3) + 2)/(1(2x^2 - 3x - 3) + 1)) + 3) and g(x) = 2((2x + 2)/(2x - 1)) + 3 between the vertical lines x = -0.5 and x = -0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.2
|
math
|
train
|
math_algebra_func_area_level_2_2_624
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (-1(3(-1x + 4)^2 - 5(-1x + 4) - 3) - 2)/(2(3(-1x + 4)^2 - 5(-1x + 4) - 3) - 3) and g(x) = 1|(2x^2 + 1x + 4) + 2| + 2 from x = 1.7 to x = 4.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
93.5
|
math
|
train
|
math_algebra_func_area_level_2_2_625
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -3(-3(4x^2 + 1x - 5) - 1)^2 + 2 and g(x) = 1sin(2π(-2|x - 2| - 2) + 2) + 1 from x = -1.2 to x = -1.0999999999999999. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.8
|
math
|
train
|
math_algebra_func_area_level_2_2_626
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -3sin(2π(1|(5x^2 + 3x - 3)| - 2) - 3) + 3 and g(x) = (-3(-1e^(2x) + 1))/(-2(-1e^(2x) + 1) - 3) from x = 2.4 to x = 2.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.2
|
math
|
train
|
math_algebra_func_area_level_2_2_627
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (1(-1sin(3π(5x^2 - 2x - 2) - 2)))/(-3(-1sin(3π(5x^2 - 2x - 2) - 2)) + 1), g(x) = 2sin(3π(2|x + 3| - 2) + 2) - 1, x = 0.7, and x = 0.8. 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_2_2_628
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = (2(-4(-2e^(2x) + 2)^2 - 4(-2e^(2x) + 2) + 5))/(2(-4(-2e^(2x) + 2)^2 - 4(-2e^(2x) + 2) + 5) - 1) and g(x) = -2cos(1π((2x)/(2x + 3)) - 3) + 3 between the vertical lines x = -0.2 and x = 0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.8
|
math
|
train
|
math_algebra_func_area_level_2_2_629
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 2|(-2|(-2x^2 - 2) + 2| - 2)| - 3 and g(x) = (3(-4x^2 - 3x + 1) + 2)/(1(-4x^2 - 3x + 1) + 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}"
]
}
|
0.2
|
math
|
train
|
math_algebra_func_area_level_2_2_630
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = (1(-1sin(3π((-2x - 2)/(-1x)) + 2) + 2) + 3)/(2(-1sin(3π((-2x - 2)/(-1x)) + 2) + 2) + 1) and g(x) = (-3(3sin(3πx + 2) - 1))/(2(3sin(3πx + 2) - 1) + 1) between the vertical lines x = -2.8 and x = -2.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.5
|
math
|
train
|
math_algebra_func_area_level_2_2_631
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = (-2(-1cos(2π(-1x - 3) - 1) - 1) + 3)/(-2(-1cos(2π(-1x - 3) - 1) - 1)) and g(x) = 2|(1x + 4) + 1| + 1 between the vertical lines x = 2.4 and x = 3.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
11.7
|
math
|
train
|
math_algebra_func_area_level_2_2_632
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -1|((3(3|x + 3| - 2) + 2)/(-3(3|x + 3| - 2) + 4)) - 3| and g(x) = -1((-2x + 1)/(-2x + 3))^2 + 4((-2x + 1)/(-2x + 3)) + 2 from x = 1.0 to x = 1.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
-12.6
|
math
|
train
|
math_algebra_func_area_level_2_2_633
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -2|(1|((-2x + 1)/(-3x - 1)) + 3| - 2) - 3| - 2 and g(x) = -5(2x^2 + 3x + 5)^2 - 1(2x^2 + 3x + 5) between the vertical lines x = -0.4 and x = -0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
47.9
|
math
|
train
|
math_algebra_func_area_level_2_2_634
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -2|(5((-3x + 3)/(1x)) - 5) + 2| - 2 and g(x) = 5(-1sin(1πx - 2)) - 3 between the vertical lines x = 0.8 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_2_2_635
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -2|(2|(1x + 2) + 3|)| + 2, g(x) = -3e^(-2(3x^2 + 1x - 2)) - 3, x = -3.8, and x = -0.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
15.7
|
math
|
train
|
math_algebra_func_area_level_2_2_636
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = (-3(-1(3cos(1πx + 1) - 2)^2 + 5(3cos(1πx + 1) - 2) - 5) - 3)/(-1(-1(3cos(1πx + 1) - 2)^2 + 5(3cos(1πx + 1) - 2) - 5) - 1) and g(x) = 2|((1x + 3)/(1x + 2)) - 2| + 2 between the vertical lines x = -1.3 and x = -0.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.6
|
math
|
train
|
math_algebra_func_area_level_2_2_637
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -4(-3(-3cos(1πx + 1) - 3)^2 + 2(-3cos(1πx + 1) - 3) + 5)^2 + 1(-3(-3cos(1πx + 1) - 3)^2 + 2(-3cos(1πx + 1) - 3) + 5) + 4 and g(x) = 2cos(3π((-2x - 3)/(-1x + 2))) - 3 between the vertical lines x = -3.1 and x = -3.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.9
|
math
|
train
|
math_algebra_func_area_level_2_2_638
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -3(-1|(1|x + 1|)| + 2)^2 + 3(-1|(1|x + 1|)| + 2) and g(x) = 1cos(3π(-2x^2 + 4x + 5) - 2) - 1 from x = -3.2 to x = -3.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.1
|
math
|
train
|
math_algebra_func_area_level_2_2_639
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (-1(-1(-4x^2 + 2x + 2)^2 - 4(-4x^2 + 2x + 2) + 5) + 1)/(3(-1(-4x^2 + 2x + 2)^2 - 4(-4x^2 + 2x + 2) + 5) - 1), g(x) = 4(3x + 2) - 2, x = -1.1, and x = -0.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
2.0
|
math
|
train
|
math_algebra_func_area_level_2_2_640
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 3(-2|(-1|x| - 3) + 3| + 3) + 2 and g(x) = 5(-2sin(3πx + 3) - 3)^2 + 2(-2sin(3πx + 3) - 3) - 2 between the vertical lines x = 1.5 and x = 1.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.2
|
math
|
train
|
math_algebra_func_area_level_2_2_641
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (-1(-1(-2cos(1πx + 3) + 1) - 3) - 2)/(2(-1(-2cos(1πx + 3) + 1) - 3) + 2), g(x) = 1|(-2|x + 3| + 3) + 3| - 3, x = -1.4, and x = 1.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
3.8
|
math
|
train
|
math_algebra_func_area_level_2_2_642
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 4(-1(-2x - 1)^2 - 5(-2x - 1) - 5) and g(x) = -1(-2sin(3πx) + 2)^2 + 2(-2sin(3πx) + 2) + 4 between the vertical lines x = 0.7 and x = 0.7999999999999999. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.0
|
math
|
train
|
math_algebra_func_area_level_2_2_643
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -2sin(2π(1|(3|x + 1| - 2) - 2| - 3) + 2) - 1, g(x) = -1|(-2|x - 3| - 3)| + 3, x = 2.0, and x = 2.2. 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_2_2_644
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -2cos(2π(-5(2|x + 2| + 2)^2 + 5(2|x + 2| + 2) - 2)) + 3 and g(x) = -3cos(3π(-5x^2 - 4x - 5) - 3) + 1 between the vertical lines x = -4.4 and x = -4.300000000000001. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.2
|
math
|
train
|
math_algebra_func_area_level_2_2_645
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = (2(2e^(-1(-5x - 1)) + 2))/(-3(2e^(-1(-5x - 1)) + 2) - 2) and g(x) = 3((-2x + 1)/(2x - 3))^2 - 4((-2x + 1)/(2x - 3)) - 3 between the vertical lines x = -0.3 and x = 1.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
2.7
|
math
|
train
|
math_algebra_func_area_level_2_2_646
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (-3(3(-1sin(3πx) + 1)^2 - 1(-1sin(3πx) + 1) - 3) + 1)/(1(3(-1sin(3πx) + 1)^2 - 1(-1sin(3πx) + 1) - 3) - 3) and g(x) = 2((2x)/(1x - 2)) + 1 from x = 3.3 to x = 3.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
4.7
|
math
|
train
|
math_algebra_func_area_level_2_2_647
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 2|((2(-3|x + 3| + 2))/(3(-3|x + 3| + 2) + 3)) + 2| and g(x) = 2|(1|x + 2| - 2)| between the vertical lines x = -3.9 and x = -3.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.2
|
math
|
train
|
math_algebra_func_area_level_2_2_648
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (1(-3(-3cos(2πx + 3) - 1) - 3) + 2)/(1(-3(-3cos(2πx + 3) - 1) - 3) + 2) and g(x) = (-1(1cos(3πx - 2) + 3) + 1)/(1(1cos(3πx - 2) + 3) - 3) from x = -3.4 to x = -2.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
13.4
|
math
|
train
|
math_algebra_func_area_level_2_2_649
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (3(2|(-1|x + 3| - 3) + 1| - 3))/(-3(2|(-1|x + 3| - 3) + 1| - 3) + 4) and g(x) = -3((-1x + 1)/(-3x + 4))^2 + 4((-1x + 1)/(-3x + 4)) from x = 1.1 to x = 1.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
-1.1
|
math
|
train
|
math_algebra_func_area_level_2_2_650
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = (-3(-1(-3e^(-2x) + 3)^2 + 3(-3e^(-2x) + 3) + 1) - 3)/(3(-1(-3e^(-2x) + 3)^2 + 3(-3e^(-2x) + 3) + 1) + 2) and g(x) = -3(-5x + 4)^2 - 1(-5x + 4) - 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}"
]
}
|
0.0
|
math
|
train
|
math_algebra_func_area_level_2_2_651
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (1((-3((1x - 2)/(1x + 3)))/(2((1x - 2)/(1x + 3)) + 2)) - 1)/(-2((-3((1x - 2)/(1x + 3)))/(2((1x - 2)/(1x + 3)) + 2)) - 2) and g(x) = 3sin(1π(1x^2 + 4x - 2) + 2) + 1 from x = -0.9 to x = -0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.4
|
math
|
train
|
math_algebra_func_area_level_2_2_652
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 3sin(2π(-5(5x - 2) - 3) + 3) - 2, g(x) = 4(-2|x + 1| + 2) + 2, x = 0.4, and x = 0.5. 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_2_2_653
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (2(2(2|x| + 1)^2 - 2(2|x| + 1)) - 1)/(-1(2(2|x| + 1)^2 - 2(2|x| + 1)) - 1) and g(x) = (2(2cos(1πx - 1)))/(1(2cos(1πx - 1)) + 1) from x = 1.7 to x = 2.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
3.2
|
math
|
train
|
math_algebra_func_area_level_2_2_654
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -3(-5(-2x + 3)^2 - 4(-2x + 3) + 1)^2 + 3 and g(x) = 5((-1x - 3)/(2x - 1)) - 5 from x = 1.2 to x = 2.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
12.4
|
math
|
train
|
math_algebra_func_area_level_2_2_655
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = (3(1e^(-1(-1|x - 3| - 2))) - 1)/(-2(1e^(-1(-1|x - 3| - 2))) + 1) and g(x) = -1|(-3x + 5) + 3| + 2 between the vertical lines x = 1.5 and x = 3.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
4.1
|
math
|
train
|
math_algebra_func_area_level_2_2_656
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -1cos(3π(-1|(2x^2 + 5x - 1) - 3| - 1) - 2) + 2 and g(x) = -1|(3|x| - 2) - 1| + 3 from x = -0.3 to x = -0.19999999999999998. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.2
|
math
|
train
|
math_algebra_func_area_level_2_2_657
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -1|(-3(1|x| - 3)^2 - 4(1|x| - 3) + 5) - 3| and g(x) = (-3(-3x^2 + 1x - 1) - 2)/(3(-3x^2 + 1x - 1)) between the vertical lines x = -3.5 and x = -3.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.2
|
math
|
train
|
math_algebra_func_area_level_2_2_658
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -5(-1(2|x| - 3))^2 + 4 and g(x) = (-2(-1sin(3πx + 3) - 3) + 3)/(-2(-1sin(3πx + 3) - 3) - 1) between the vertical lines x = -1.8 and x = -1.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.9
|
math
|
train
|
math_algebra_func_area_level_2_2_659
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -1((2(3cos(1πx + 2) - 1) - 2)/(-3(3cos(1πx + 2) - 1) - 2)) + 1, g(x) = 1|(-5x^2 + 5x - 3) + 2| + 3, x = -1.1, and x = -0.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
9.4
|
math
|
train
|
math_algebra_func_area_level_2_2_660
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 1cos(1π(1(1|x + 3| + 3)^2 - 3(1|x + 3| + 3) + 5) + 2) - 3 and g(x) = -3(4x - 3) - 4 from x = 0.6 to x = 0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.1
|
math
|
train
|
math_algebra_func_area_level_2_2_661
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (1(3cos(1π((2x)/(2x - 3)) - 1) - 2) + 1)/(2(3cos(1π((2x)/(2x - 3)) - 1) - 2)), g(x) = 4((1x - 1)/(3x + 1))^2 - 4((1x - 1)/(3x + 1)), x = 2.4, and x = 3.0. 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_2_2_662
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 1(-5(-3cos(1πx + 3) - 2)^2 - 3(-3cos(1πx + 3) - 2) + 5)^2 + 3(-5(-3cos(1πx + 3) - 2)^2 - 3(-3cos(1πx + 3) - 2) + 5) - 2 and g(x) = (2(-2|x - 2| - 1) - 1)/(-3(-2|x - 2| - 1) - 2) from x = 1.6 to x = 1.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
7.4
|
math
|
train
|
math_algebra_func_area_level_2_2_663
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 1|((3(-5x^2 - 2x + 5) - 3)/(-1(-5x^2 - 2x + 5) - 3)) - 3| + 2 and g(x) = (-1(2cos(3πx) + 2) - 1)/(2(2cos(3πx) + 2) - 3) between the vertical lines x = 0.9 and x = 1.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
43.9
|
math
|
train
|
math_algebra_func_area_level_2_2_664
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 3(-2|(-2sin(1πx - 3) - 3) - 1| + 2) - 3 and g(x) = (2(-3x^2 - 5x + 3) - 2)/(2(-3x^2 - 5x + 3) + 2) between the vertical lines x = -2.2 and x = 0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
61.7
|
math
|
train
|
math_algebra_func_area_level_2_2_665
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -1(-5(2|x + 2| - 3) - 5)^2 - 4(-5(2|x + 2| - 3) - 5) - 1 and g(x) = -2(-3sin(2πx - 3)) - 1 from x = -1.0 to x = -0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
2.9
|
math
|
train
|
math_algebra_func_area_level_2_2_666
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = (-2(3sin(1π(-4x^2 + 2x + 1) + 2) - 1) + 2)/(2(3sin(1π(-4x^2 + 2x + 1) + 2) - 1) - 3) and g(x) = 4((-1x + 1)/(-2x - 3)) + 1 between the vertical lines x = 3.9 and x = 4.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.5
|
math
|
train
|
math_algebra_func_area_level_2_2_667
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (-1(-1((-1x)/(-3x + 4)) + 1))/(1(-1((-1x)/(-3x + 4)) + 1) + 1) and g(x) = (-1(-5x - 2) - 3)/(-3(-5x - 2) - 1) from x = -0.1 to x = 1.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
8.8
|
math
|
train
|
math_algebra_func_area_level_2_2_668
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (2(3cos(2π(2|x - 3| - 3) + 1) - 2) - 2)/(3(3cos(2π(2|x - 3| - 3) + 1) - 2) + 2), g(x) = 1e^(2(2x - 5)) - 2, x = -0.8, and x = -0.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.9
|
math
|
train
|
math_algebra_func_area_level_2_2_669
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = (1(-4(-4x^2 + 1x - 2) - 3))/(-1(-4(-4x^2 + 1x - 2) - 3) + 3) and g(x) = 3|((3x - 2)/(2x + 3))| - 3 between the vertical lines x = 0.3 and x = 2.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.5
|
math
|
train
|
math_algebra_func_area_level_2_2_670
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (3(-4((-2x)/(1x + 1))^2 - 4((-2x)/(1x + 1)) + 4) - 2)/(1(-4((-2x)/(1x + 1))^2 - 4((-2x)/(1x + 1)) + 4) + 3), g(x) = -2cos(3π((2x - 3)/(-3x + 4)) + 3) - 3, x = -0.3, and x = 4.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
13.4
|
math
|
train
|
math_algebra_func_area_level_2_2_671
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -1(2cos(1π(-2x + 2) + 1) - 1)^2 + 3, g(x) = (1((-1x + 2)/(-1x + 2)) + 1)/(1((-1x + 2)/(-1x + 2)) + 3), x = -3.1, and x = -2.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.1
|
math
|
train
|
math_algebra_func_area_level_2_2_672
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 1(-3(4x + 5) - 3)^2 - 4(-3(4x + 5) - 3) + 2 and g(x) = 1|(4x^2 - 3x) + 3| + 2 from x = -2.1 to x = -1.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
12.9
|
math
|
train
|
math_algebra_func_area_level_2_2_673
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = (2(1|(-3|x + 2| - 2)| - 2) - 3)/(-1(1|(-3|x + 2| - 2)| - 2) - 3) and g(x) = (-2((2x - 1)/(-3x + 2)) - 1)/(-2((2x - 1)/(-3x + 2)) + 3) 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}"
]
}
|
0.4
|
math
|
train
|
math_algebra_func_area_level_2_2_674
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (3(3e^(-1(4x + 3)) + 3) - 3)/(-1(3e^(-1(4x + 3)) + 3) - 2) and g(x) = -4(-1cos(1πx - 3) + 1) + 5 from x = 3.6 to x = 4.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.8
|
math
|
train
|
math_algebra_func_area_level_2_2_675
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -3(3|(-1x + 3) - 3| - 1) + 5 and g(x) = 4(-2sin(2πx - 3) + 2) - 1 from x = -0.0 to x = 0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
3.2
|
math
|
train
|
math_algebra_func_area_level_2_2_676
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (-3(-1|((-1x + 3)/(2x - 1)) - 3| - 1) + 2)/(2(-1|((-1x + 3)/(2x - 1)) - 3| - 1) + 1) and g(x) = 3e^(-2(-2|x - 2| + 3)) - 3 from x = 1.0 to x = 3.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.7
|
math
|
train
|
math_algebra_func_area_level_2_2_677
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -4(-4(-2sin(1πx + 1))^2 + 4(-2sin(1πx + 1)) - 1) - 4 and g(x) = -2e^(-1(3|x - 1| + 3)) - 1 from x = -2.5 to x = -2.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.4
|
math
|
train
|
math_algebra_func_area_level_2_2_678
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -1(-1cos(2π(1|x - 2| - 2) - 2) - 2)^2 + 5(-1cos(2π(1|x - 2| - 2) - 2) - 2) + 3 and g(x) = 3(-2sin(2πx - 1) - 3) + 1 between the vertical lines x = 1.5 and x = 2.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
8.8
|
math
|
train
|
math_algebra_func_area_level_2_2_679
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = (3((-2(1x - 4) + 3)/(3(1x - 4) + 3)))/(1((-2(1x - 4) + 3)/(3(1x - 4) + 3)) - 3) and g(x) = -2|(-3cos(1πx - 3) + 3) - 3| + 1 between the vertical lines x = -2.6 and x = -2.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.0
|
math
|
train
|
math_algebra_func_area_level_2_2_680
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (-1(1sin(3π((-1x + 1)/(2x)) - 1) - 3) - 1)/(3(1sin(3π((-1x + 1)/(2x)) - 1) - 3) - 2), g(x) = -1(-1|x| - 1)^2 - 5(-1|x| - 1) - 3, x = -3.4, and x = 3.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
16.5
|
math
|
train
|
math_algebra_func_area_level_2_2_681
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (-3((-1(3x^2 + 4x - 3) + 3)/(-2(3x^2 + 4x - 3) - 1)) + 3)/(-2((-1(3x^2 + 4x - 3) + 3)/(-2(3x^2 + 4x - 3) - 1)) - 1) and g(x) = 3e^(1(3x)) from x = -1.2 to x = 0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
26.3
|
math
|
train
|
math_algebra_func_area_level_2_2_682
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 3|(1|((-2x + 3)/(2x)) - 1|)| - 3 and g(x) = 1(-1cos(1πx - 2) + 2) - 2 from x = 0.6 to x = 1.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.3
|
math
|
train
|
math_algebra_func_area_level_2_2_683
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -2cos(3π((3(2x^2 - 1x - 1) - 1)/(2(2x^2 - 1x - 1)))) - 2 and g(x) = (-3((2x + 1)/(-1x + 2)) + 1)/(1((2x + 1)/(-1x + 2)) + 1) from x = 1.1 to x = 1.2000000000000002. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.1
|
math
|
train
|
math_algebra_func_area_level_2_2_684
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -2|(-3|(2sin(3πx) - 1) + 1| + 3) + 3| + 3 and g(x) = (1((1x - 3)/(-1x + 2)) - 2)/(-1((1x - 3)/(-1x + 2)) - 3) from x = -4.2 to x = -4.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.1
|
math
|
train
|
math_algebra_func_area_level_2_2_685
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 1|(5(-1x^2 + 3x) + 5) + 2| - 1, g(x) = -3sin(3π(1x + 1) + 2) + 2, x = 3.2, and x = 3.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.9
|
math
|
train
|
math_algebra_func_area_level_2_2_686
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 3|(-3cos(1π(4x - 4) + 2) - 2) + 1| + 1 and g(x) = 2|(-3|x + 3| + 1) - 3| + 1 between the vertical lines x = -2.8 and x = -2.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.8
|
math
|
train
|
math_algebra_func_area_level_2_2_687
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -1(-1e^(2(-1x^2 + 1)) + 1)^2 + 3(-1e^(2(-1x^2 + 1)) + 1) + 5, g(x) = -3cos(3π(-2x - 2) - 2) + 1, x = -0.7, and x = 0.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
46.0
|
math
|
train
|
math_algebra_func_area_level_2_2_688
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (-2(-1(-5x)^2 + 2(-5x) + 5) + 1)/(1(-1(-5x)^2 + 2(-5x) + 5)) and g(x) = -3sin(1π(-1x^2 - 5x) - 3) + 1 from x = 0.1 to x = 0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.1
|
math
|
train
|
math_algebra_func_area_level_2_2_689
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 1cos(2π(-3|(2|x + 2| + 2)| + 1) - 1) + 1 and g(x) = 3(2e^(-2x) - 2) + 1 from x = 0.0 to x = 0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.0
|
math
|
train
|
math_algebra_func_area_level_2_2_690
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (2(-2|(-4x - 2) + 3| - 1) - 1)/(-1(-2|(-4x - 2) + 3| - 1) - 2) and g(x) = -1(-2sin(1πx - 2) - 3)^2 - 1(-2sin(1πx - 2) - 3) - 5 from x = -0.0 to x = 0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
39.1
|
math
|
train
|
math_algebra_func_area_level_2_2_691
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -1|(1e^(2(-3|x - 1| + 2)) + 1) - 2| + 3 and g(x) = 1(2x + 1) - 2 from x = 1.6 to x = 1.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.1
|
math
|
train
|
math_algebra_func_area_level_2_2_692
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = (3(1sin(1π((2x + 2)/(2x + 2)) - 3) - 3) + 3)/(3(1sin(1π((2x + 2)/(2x + 2)) - 3) - 3) + 2) and g(x) = 3(-2sin(3πx - 3)) - 3 between the vertical lines x = -0.4 and x = 0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
2.8
|
math
|
train
|
math_algebra_func_area_level_2_2_693
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -3(2sin(3π(-3x^2 + 5x + 5) - 1))^2 - 3(2sin(3π(-3x^2 + 5x + 5) - 1)) + 3 and g(x) = -5(-2x^2 - 3x - 3)^2 - 5(-2x^2 - 3x - 3) + 5 from x = -0.7 to x = -0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.5
|
math
|
train
|
math_algebra_func_area_level_2_2_694
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = (-1(-2|(2|x + 2| + 1) - 2| + 1) - 1)/(-3(-2|(2|x + 2| + 1) - 2| + 1) + 1) and g(x) = (-1(3cos(3πx + 2) - 3) - 2)/(-1(3cos(3πx + 2) - 3)) between the vertical lines x = -3.4 and x = -3.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.2
|
math
|
train
|
math_algebra_func_area_level_2_2_695
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 4(5((3x + 3)/(-1x)) - 3)^2 - 3(5((3x + 3)/(-1x)) - 3), g(x) = 3sin(1π((2x + 1)/(-3x + 4)) + 1) - 2, x = -0.8, and x = -0.7000000000000001. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.3
|
math
|
train
|
math_algebra_func_area_level_2_2_696
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -1|((2(3|x - 1| - 1) - 3)/(-2(3|x - 1| - 1) - 3)) + 1| + 2 and g(x) = 1e^(-1((3x - 3)/(2x))) - 3 from x = 0.6 to x = 0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.2
|
math
|
train
|
math_algebra_func_area_level_2_2_697
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 1(1cos(2π((1x - 1)/(2x + 2)) - 1) + 2)^2 - 5(1cos(2π((1x - 1)/(2x + 2)) - 1) + 2) + 2 and g(x) = 4(-3cos(3πx + 3) + 1) - 4 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}"
]
}
|
1.2
|
math
|
train
|
math_algebra_func_area_level_2_2_698
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -3|(5(-1cos(1πx - 2) + 1)^2 - 1(-1cos(1πx - 2) + 1) - 1) - 3| - 1 and g(x) = -1cos(3π(2|x + 3|) + 1) - 2 between the vertical lines x = 1.1 and x = 2.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
23.7
|
math
|
train
|
math_algebra_func_area_level_2_2_699
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = (1(-1(2e^(2x))^2 + 2(2e^(2x)) + 2))/(3(-1(2e^(2x))^2 + 2(2e^(2x)) + 2) - 1) and g(x) = 2cos(3π(-1|x + 1| - 1) - 1) + 2 between the vertical lines x = 3.5 and x = 3.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.0
|
math
|
train
|
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