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_700
|
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|(-5x^2 + 3x - 2) + 1| + 2) - 5 and g(x) = -3cos(1π((-2x + 1)/(3x)) - 3) 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}"
]
}
|
0.2
|
math
|
train
|
math_algebra_func_area_level_2_2_701
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -1e^(2(-5((-2x)/(1x + 1))^2 + 2((-2x)/(1x + 1)) + 3)) - 1 and g(x) = (2(1x^2 - 3x - 4) + 3)/(-1(1x^2 - 3x - 4) + 2) between the vertical lines x = 0.6 and x = 2.6. 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_702
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -1|(-2|(5x^2 - 2x) - 3|) + 1| + 2 and g(x) = (-1(-3|x| - 3) - 2)/(1(-3|x| - 3) + 1) from x = -0.8 to x = -0.3. 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_703
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -3sin(1π(-2(3|x + 3| + 3) + 4) - 1) - 2 and g(x) = 5(3e^(-1x)) - 1 from x = 3.1 to x = 3.3. 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_704
|
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((2((-1x)/(2x + 3)) + 1)/(2((-1x)/(2x + 3)) + 3))^2 - 1((2((-1x)/(2x + 3)) + 1)/(2((-1x)/(2x + 3)) + 3)) + 3 and g(x) = 2sin(3π(2|x + 3|) - 2) + 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}"
]
}
|
0.1
|
math
|
train
|
math_algebra_func_area_level_2_2_705
|
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((-2x + 1)/(-2x + 3))^2 + 5((-2x + 1)/(-2x + 3)) + 1) + 2)/(1(-1((-2x + 1)/(-2x + 3))^2 + 5((-2x + 1)/(-2x + 3)) + 1) + 2), g(x) = 5(-2sin(1πx + 3) - 2)^2 - 3(-2sin(1πx + 3) - 2) - 2, x = -1.6, and x = -1.3. 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_706
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 2(-4(-1x + 1)^2 - 4(-1x + 1) + 4)^2 + 5(-4(-1x + 1)^2 - 4(-1x + 1) + 4) + 3 and g(x) = 5(1cos(2πx - 1) + 2) - 1 from x = 0.5 to x = 2.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
84.3
|
math
|
train
|
math_algebra_func_area_level_2_2_707
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -3|(-1cos(2π(-2x - 2) - 3) - 3) + 2| and g(x) = -2e^(-2(1x - 5)) + 1 from x = 4.6 to x = 4.9. 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_708
|
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(-5x^2 + 4x - 5) + 5))/(-2(1(-5x^2 + 4x - 5) + 5) + 1) and g(x) = (-3(-2cos(3πx + 1) - 1))/(2(-2cos(3πx + 1) - 1) + 2) between the vertical lines x = 0.1 and x = 0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
3.9
|
math
|
train
|
math_algebra_func_area_level_2_2_709
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 3(-1|(2x^2 - 3x - 5) - 1| + 1) + 1, g(x) = 4(-3e^(2x)) - 2, x = -1.4, and x = -0.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
2.5
|
math
|
train
|
math_algebra_func_area_level_2_2_710
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 1|(2|(3cos(2πx - 1) + 1) + 1| - 3) - 1| - 3 and g(x) = (-2((-1x + 2)/(2x + 3)) + 1)/(2((-1x + 2)/(2x + 3)) - 3) from x = -0.0 to x = 0.3. 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_711
|
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(-1x^2 + 3x - 2)^2 + 5(-1x^2 + 3x - 2) + 3) - 1)/(-2(5(-1x^2 + 3x - 2)^2 + 5(-1x^2 + 3x - 2) + 3) - 2) and g(x) = (3(1|x + 1| - 3) + 1)/(2(1|x + 1| - 3)) between the vertical lines x = -3.8 and x = 1.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
8.1
|
math
|
train
|
math_algebra_func_area_level_2_2_712
|
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(3sin(2π(1x^2 - 5x) - 2))^2 + 2(3sin(2π(1x^2 - 5x) - 2)) + 4 and g(x) = -4((3x)/(-2x - 3)) - 5 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}"
]
}
|
1.5
|
math
|
train
|
math_algebra_func_area_level_2_2_713
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (1((-1(2x) + 2)/(2(2x) - 1)))/(-2((-1(2x) + 2)/(2(2x) - 1)) + 1) and g(x) = 1|(-2|x| + 2) + 2| - 1 from x = 0.7 to x = 1.6. 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_714
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (-1(2sin(2π(4x^2 + 3x - 1) + 1) + 3) + 2)/(-2(2sin(2π(4x^2 + 3x - 1) + 1) + 3) + 3) and g(x) = -2|((2x + 1)/(2x + 1)) - 3| + 2 from x = 4.0 to x = 4.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.3
|
math
|
train
|
math_algebra_func_area_level_2_2_715
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 2|(-3sin(3π(1x^2 + 3x + 2) + 3) + 3)| and g(x) = (1((-3x + 3)/(2x - 1)) + 1)/(3((-3x + 3)/(2x - 1))) from x = -3.7 to x = -3.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.0
|
math
|
train
|
math_algebra_func_area_level_2_2_716
|
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(1π(2x^2 - 4x + 5) - 3)), g(x) = -5(-2sin(1πx + 2) + 3)^2 + 1(-2sin(1πx + 2) + 3) + 3, x = 4.0, and x = 4.1. 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_2_2_717
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 2|(4(2|x + 3|)) + 2| - 2, g(x) = -1(3x + 1) + 4, x = -3.8, and x = -2.5. 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_2_2_718
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -1cos(1π(3(-1|x + 1| - 2) - 5)), g(x) = (1(1x^2 - 5x + 2) + 3)/(2(1x^2 - 5x + 2) + 1), x = -0.9, and x = -0.4. 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_2_2_719
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 1sin(3π((-2(-3x - 4) - 3)/(-2(-3x - 4) - 3)) - 1) + 1 and g(x) = 2|((-2x + 1)/(3x + 1)) + 2| + 1 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}"
]
}
|
0.1
|
math
|
train
|
math_algebra_func_area_level_2_2_720
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -3((2(-2|x - 3| + 3) - 3)/(-1(-2|x - 3| + 3) + 3)) - 1 and g(x) = 2|((-2x + 1)/(3x - 2)) + 1| - 1 from x = 0.6 to x = 0.7. Round 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_721
|
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(2(-1x) + 4) - 2) and g(x) = (1(-1|x - 2| + 2) - 1)/(1(-1|x - 2| + 2) + 2) between the vertical lines x = -0.1 and x = 0.4. 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_722
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 2(4(-1x - 4) + 1) + 4, g(x) = -3|((-3x + 1)/(-2x - 1)) - 1| - 2, x = -2.6, and x = -0.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
8.9
|
math
|
train
|
math_algebra_func_area_level_2_2_723
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 1(4(3x^2 + 2x - 2)^2 + 1(3x^2 + 2x - 2) - 3) - 3 and g(x) = -2(3x + 3) - 4 from x = -1.4 to x = -1.0. 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_724
|
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|(2x + 4)| - 3) - 5, g(x) = (1(-3e^(2x) - 3))/(-2(-3e^(2x) - 3)), x = -2.6, and x = -1.4. Round your answer 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_725
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -3|(4((-1x - 2)/(-1x - 1)) - 3) + 2| and g(x) = -3sin(1π(-1x + 5) + 2) - 1 from x = -3.1 to x = -2.3. 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_726
|
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 - 3x - 3) - 1)) + 1| and g(x) = 3sin(1π((1x - 1)/(-2x + 1)) - 2) - 1 between the vertical lines x = 0.6 and 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_727
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 5(1|(-3x^2 - 3x + 4) - 2| - 2)^2 + 4, g(x) = -1(2x^2 + 2x - 4) + 4, x = -1.8, and x = -1.7. 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_2_2_728
|
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(1|(2x - 2) + 3| - 3) - 2) + 1 and g(x) = 1e^(1(5x - 5)) between the vertical lines x = -4.6 and x = -4.0. 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_729
|
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|((2x - 2)/(3x + 2)) + 1| - 1) + 2)/(-3(2|((2x - 2)/(3x + 2)) + 1| - 1) + 2) and g(x) = -4(5x - 2) + 1 between the vertical lines x = 0.4 and x = 0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
16.7
|
math
|
train
|
math_algebra_func_area_level_2_2_730
|
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(2e^(-1(1|x| + 1)) - 1) - 2)/(3(2e^(-1(1|x| + 1)) - 1) + 3) and g(x) = -2sin(2π(-5x + 2) - 1) - 2 between the vertical lines x = 1.9 and x = 2.0. 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_731
|
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(-2|(1|x + 3| + 3) + 2| - 1) - 1) - 3, g(x) = -5(2x - 3)^2 - 2(2x - 3) - 2, x = 1.2, and x = 1.4. 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_2_2_732
|
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|((3(-3|x + 2| - 2) - 2)/(-1(-3|x + 2| - 2) - 3)) + 3| and g(x) = (-3(-1cos(3πx + 3)) + 3)/(1(-1cos(3πx + 3))) between the vertical lines x = 1.9 and x = 2.1. 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_733
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 1cos(1π(2|(2|x - 3| + 2) + 1| - 1) - 3) + 1 and g(x) = -2(3cos(1πx - 2) - 1) + 3 from x = -3.6 to x = -3.0. 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_734
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -5((-2(-2x) - 3)/(3(-2x) + 3))^2 + 2((-2(-2x) - 3)/(3(-2x) + 3)) + 1 and g(x) = -3cos(2π(-1x - 3) + 1) + 1 from x = 2.1 to x = 2.2. 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_735
|
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(1π((1x - 2)/(-2x + 1)) - 3) - 1) + 5, g(x) = 2cos(3π(3x^2 + 3x - 4) + 1) + 2, x = 1.3, and x = 1.4000000000000001. 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_2_2_736
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -1e^(-1((1(3|x| + 1) - 3)/(2(3|x| + 1) - 1))) and g(x) = -1|(-1x^2 + 1x + 2) - 1| - 3 from x = -0.1 to x = 0.0. 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_737
|
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 + 3)^2 - 4(-4x + 3) - 4) + 1|, g(x) = -2(3cos(2πx - 2) - 1) - 4, x = 0.7, and x = 1.0. 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_2_2_738
|
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|(-5x^2 - 5x - 3) - 1| + 3), g(x) = -2(2sin(2πx) + 3)^2 - 5(2sin(2πx) + 3) + 5, x = -2.4, and x = -2.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
3.1
|
math
|
train
|
math_algebra_func_area_level_2_2_739
|
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((-3x + 1)/(3x - 2)) - 4) + 3, g(x) = -3(-5x - 4)^2 - 1(-5x - 4) + 5, x = -1.1, and x = -0.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
2.8
|
math
|
train
|
math_algebra_func_area_level_2_2_740
|
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|((-1x - 2)/(1x + 2)) + 3| - 2) - 2)/(-3(-2|((-1x - 2)/(1x + 2)) + 3| - 2) - 2) and g(x) = 3cos(1π(1x^2 + 2x + 2) - 2) - 1 between the vertical lines x = -4.4 and x = -4.2. 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_741
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 3(5(-1x^2 - 4x + 3) - 3) - 5, g(x) = -5(1x^2 + 1x + 1)^2 + 3(1x^2 + 1x + 1) - 4, x = 0.8, and x = 1.3. Round your answer 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_742
|
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(4(3cos(2πx) + 2) - 5) + 3 and g(x) = 1((-2x - 1)/(-2x)) + 4 between the vertical lines x = 0.0 and x = 0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
17.6
|
math
|
train
|
math_algebra_func_area_level_2_2_743
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (-1(-1|((-3x - 3)/(-2x - 3)) - 3| + 3) + 3)/(1(-1|((-3x - 3)/(-2x - 3)) - 3| + 3)) and g(x) = 1(3|x + 2|)^2 + 4(3|x + 2|) - 1 from x = -2.1 to x = -1.9. 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_744
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 1e^(-2(-2|(4x^2 - 1x - 4) - 3| + 2)) - 3 and g(x) = 2(-2x^2 - 3x + 1)^2 - 2 between the vertical lines x = -1.3 and x = -1.0. 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_745
|
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((-3x)/(-1x - 3)) - 1) - 1| and g(x) = (2(1|x| + 3) + 2)/(1(1|x| + 3) + 3) between the vertical lines x = -0.6 and x = -0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.3
|
math
|
train
|
math_algebra_func_area_level_2_2_746
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -3|(1|(-2x^2 - 5x + 2) + 3| - 3)| - 3 and g(x) = -5(-3|x + 1| + 1)^2 - 3(-3|x + 1| + 1) - 4 from x = -2.0 to x = -0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
17.8
|
math
|
train
|
math_algebra_func_area_level_2_2_747
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 4(3sin(1π(-1|x + 2| - 3) - 1) + 1)^2 + 4(3sin(1π(-1|x + 2| - 3) - 1) + 1) - 3, g(x) = 4(-1x^2 + 1x - 4)^2 + 2(-1x^2 + 1x - 4) + 5, x = 0.0, and x = 0.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
5.4
|
math
|
train
|
math_algebra_func_area_level_2_2_748
|
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(3π(3(1x^2 - 3x - 1) + 2) - 2) - 2 and g(x) = 4((3x - 1)/(2x - 1)) - 3 between the vertical lines x = 0.3 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_749
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 4(3|(2x - 2) + 1|) - 3 and g(x) = -3e^(1(1x^2 - 3x)) + 2 from x = 0.3 to x = 0.7. 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_750
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 4((2(2x - 4) + 1)/(2(2x - 4) + 2))^2 - 3((2(2x - 4) + 1)/(2(2x - 4) + 2)), g(x) = 5(1|x - 3| + 3) - 5, x = 1.3, and x = 1.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
-7.7
|
math
|
train
|
math_algebra_func_area_level_2_2_751
|
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((-2x - 3)/(3x + 1)) - 2)/(-2((-2x - 3)/(3x + 1)) - 3)) - 3| - 3, g(x) = -3|(-4x^2 + 2x + 1) - 2| + 2, x = -0.5, and x = 1.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
74.0
|
math
|
train
|
math_algebra_func_area_level_2_2_752
|
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|(3(3e^(2x))^2 - 4(3e^(2x)) - 4) + 1| + 3 and g(x) = 1sin(3π(1x^2 - 1x - 5) + 1) - 3 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}"
]
}
|
0.3
|
math
|
train
|
math_algebra_func_area_level_2_2_753
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -3e^(1(-2(-1x + 1)^2 + 2(-1x + 1) - 3)) - 2, g(x) = -2|(2|x + 3| - 2) + 2| - 1, x = -3.2, and x = -2.8. 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_754
|
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(-1sin(3πx + 1) + 1) + 2)^2 - 2(4(-1sin(3πx + 1) + 1) + 2) + 2 and g(x) = 5(1e^(-1x) + 1) - 3 between the vertical lines x = -1.8 and x = -1.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
37.2
|
math
|
train
|
math_algebra_func_area_level_2_2_755
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 2(2|(-3|x + 3|) + 2|) - 5 and g(x) = 2|(-2e^(1x) + 2) + 3| - 3 from x = -4.7 to x = -1.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
21.7
|
math
|
train
|
math_algebra_func_area_level_2_2_756
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -1sin(1π((-3(-3x - 5) + 1)/(-2(-3x - 5) + 1)) + 1) and g(x) = 2|(1x^2 + 5x - 3) - 3| - 2 from x = 0.8 to x = 1.2. 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_757
|
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(1x + 1))/(3(1x + 1) + 1))^2 + 5((1(1x + 1))/(3(1x + 1) + 1)) - 1, g(x) = -1sin(2π(-5x^2 - 1x) - 3) - 3, x = -1.2, and x = -1.0999999999999999. 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_2_2_758
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 3(-5(4x + 2)^2 - 5(4x + 2) + 5) - 1 and g(x) = -1|(1|x + 3| - 3) - 2| + 2 from x = -0.9 to x = -0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
6.6
|
math
|
train
|
math_algebra_func_area_level_2_2_759
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 4(-3(4x + 1)^2 + 3(4x + 1) - 5)^2 - 3(-3(4x + 1)^2 + 3(4x + 1) - 5) - 1, g(x) = 5(-3sin(2πx + 3) - 3)^2 + 4(-3sin(2πx + 3) - 3) + 1, x = -0.3, and x = -0.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
8.6
|
math
|
train
|
math_algebra_func_area_level_2_2_760
|
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(-3x) - 2) - 1)/(-3(5(-3x) - 2) + 4), g(x) = 3sin(2π(-1|x - 3| - 2) - 1) + 1, x = 1.1, and x = 1.7. 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_2_2_761
|
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(3|(-3|x - 3| + 3) + 1| + 3) - 2)/(1(3|(-3|x - 3| + 3) + 1| + 3) - 2) and g(x) = 1|(-1x^2 + 5x) + 2| - 3 between the vertical lines x = -0.5 and 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_762
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -4((2(2x) + 1)/(1(2x) + 3))^2 - 4((2(2x) + 1)/(1(2x) + 3)) + 5 and g(x) = 3cos(2π(-5x - 1)) from x = 0.2 to x = 0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.4
|
math
|
train
|
math_algebra_func_area_level_2_2_763
|
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 + 1x - 5) + 1)/(3(-4x^2 + 1x - 5) - 1)) + 1)/(-2((1(-4x^2 + 1x - 5) + 1)/(3(-4x^2 + 1x - 5) - 1)) + 3), g(x) = -2cos(2π((-2x - 3)/(3x - 2)) + 2) + 1, x = 0.8, and x = 0.9. 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_2_2_764
|
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 + 2)/(-1x + 2))^2 - 5((-2x + 2)/(-1x + 2)) - 2)^2 + 3(1((-2x + 2)/(-1x + 2))^2 - 5((-2x + 2)/(-1x + 2)) - 2) + 5 and g(x) = (2((3x - 2)/(1x)) + 2)/(1((3x - 2)/(1x)) + 3) between the vertical lines x = 2.5 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_765
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (3(-1((1x + 3)/(3x - 1)) - 4) - 3)/(2(-1((1x + 3)/(3x - 1)) - 4) + 1) and g(x) = 1(-2e^(1x) + 2)^2 + 5(-2e^(1x) + 2) - 2 from x = 0.1 to x = 1.4. Round 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_766
|
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^2 + 2x + 2) - 4) + 2)/(3(1(5x^2 + 2x + 2) - 4) - 2), g(x) = 2(5x^2 + 5x - 5) + 3, x = 0.4, and x = 0.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
7.1
|
math
|
train
|
math_algebra_func_area_level_2_2_767
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -1(3(-3x^2 - 2x - 2))^2 - 5(3(-3x^2 - 2x - 2)) - 2, g(x) = -5(-2cos(3πx - 1) + 2)^2 - 3(-2cos(3πx - 1) + 2) - 2, x = -1.0, and x = -0.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
14.1
|
math
|
train
|
math_algebra_func_area_level_2_2_768
|
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|((-2x)/(-2x - 1)) - 2| + 2)^2 - 1(2|((-2x)/(-2x - 1)) - 2| + 2) + 4, g(x) = -5(-1|x - 1| + 2)^2 - 2(-1|x - 1| + 2) - 3, x = -1.0, and x = -0.9. 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_2_2_769
|
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(-4x^2 - 1x + 1)) + 1)/(-2(4(-4x^2 - 1x + 1)) + 3), g(x) = -2|(1x^2 + 2x - 5) + 3| - 3, x = -0.6, and x = 0.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
9.5
|
math
|
train
|
math_algebra_func_area_level_2_2_770
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 1(-5(-2x + 5) - 1)^2 and g(x) = 2|(-3x^2 + 1x - 2) + 1| from x = 2.1 to x = 3.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
34.3
|
math
|
train
|
math_algebra_func_area_level_2_2_771
|
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(3|x + 2| - 2)^2 - 3(3|x + 2| - 2) + 2)^2 - 2(5(3|x + 2| - 2)^2 - 3(3|x + 2| - 2) + 2) + 4 and g(x) = -2(-3cos(1πx + 1) - 2) + 1 between the vertical lines x = -2.9 and x = -2.6. 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_772
|
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(-2cos(1π(-3x + 5) - 3) + 1) - 1)/(2(-2cos(1π(-3x + 5) - 3) + 1) - 3) and g(x) = -3|((-2x)/(2x)) - 2| - 3 between the vertical lines x = 0.2 and x = 0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
4.2
|
math
|
train
|
math_algebra_func_area_level_2_2_773
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 2sin(3π((-1(-2x^2 + 4x - 2) - 1)/(1(-2x^2 + 4x - 2) - 3))) - 2 and g(x) = 2cos(1π(2|x + 3| + 1) + 2) - 2 between the vertical lines x = -1.0 and 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_774
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 2|(-3(-5x^2 + 1x - 2) - 3) - 2| + 1 and g(x) = 2sin(2π((-2x - 1)/(-1x)) - 1) + 1 from x = 0.1 to x = 0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.2
|
math
|
train
|
math_algebra_func_area_level_2_2_775
|
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(-2sin(3π(-4x^2 - 3x - 1) + 2) - 1)^2 + 5 and g(x) = -4((3x)/(3x - 2))^2 + 4((3x)/(3x - 2)) + 4 between the vertical lines x = -4.0 and x = -3.9. 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_776
|
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(3π(-1|x + 2| - 2)) + 1) + 2)/(-2(1cos(3π(-1|x + 2| - 2)) + 1) + 3) and g(x) = -1(-3|x - 2| - 3) - 4 between the vertical lines x = -4.5 and x = -4.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
19.7
|
math
|
train
|
math_algebra_func_area_level_2_2_777
|
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(-3sin(1πx) + 1)^2 - 3(-3sin(1πx) + 1) - 5) - 3, g(x) = 5((1x)/(-2x + 3)) - 2, x = 0.6, and x = 0.9. 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_2_2_778
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 5(1sin(3π(1|x| - 1)) - 1)^2 + 2(1sin(3π(1|x| - 1)) - 1) + 5 and g(x) = 1(4x + 1)^2 - 1(4x + 1) - 1 from x = -1.0 to x = 0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
15.4
|
math
|
train
|
math_algebra_func_area_level_2_2_779
|
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|(3|((3x)/(3x)) - 3|) - 1| + 3 and g(x) = 5(1|x + 3| + 2) + 1 between the vertical lines x = -3.4 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_780
|
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(3|x + 3| + 3)^2 - 1(3|x + 3| + 3) + 4) - 3)/(3(2(3|x + 3| + 3)^2 - 1(3|x + 3| + 3) + 4) - 1), g(x) = -1|(3x^2 + 3x - 4) + 1| + 1, x = 0.6, and x = 0.7. 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_2_2_781
|
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(4x^2 - 4x - 4) - 4) + 3| + 2 and g(x) = 2|(3x^2 - 1x + 1)| + 1 between the vertical lines x = 1.4 and x = 1.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
2.5
|
math
|
train
|
math_algebra_func_area_level_2_2_782
|
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((3x - 2)/(-3x - 2)) - 4) + 2)/(-2(1((3x - 2)/(-3x - 2)) - 4) - 3), g(x) = 3(2|x + 1| + 2)^2 - 5(2|x + 1| + 2) - 5, x = -1.2, and x = -0.8. Round your answer 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_783
|
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|(1x + 5) + 3| - 1) + 3, g(x) = -4(3e^(2x) + 3) + 4, x = -3.0, and x = -0.4. Round your answer 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_784
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (-2(-1|(1|x - 2| + 1)| - 1) - 1)/(-2(-1|(1|x - 2| + 1)| - 1) + 1) and g(x) = -1cos(2π((1x + 2)/(-1x - 3)) - 3) from x = -3.1 to 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_2_2_785
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -2cos(1π((-2(-2|x + 2| + 2))/(2(-2|x + 2| + 2) - 1)) - 3) - 2 and g(x) = 3(5x^2 + 2x - 4) + 1 from x = -1.0 to x = 0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
9.0
|
math
|
train
|
math_algebra_func_area_level_2_2_786
|
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(-2x^2 + 5x - 3)) + 2) + 3)/(-3(3cos(2π(-2x^2 + 5x - 3)) + 2) - 3), g(x) = 1(-2x^2 + 3) - 2, x = -4.5, and x = -4.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
3.6
|
math
|
train
|
math_algebra_func_area_level_2_2_787
|
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|(2|x - 1| - 1) - 1| + 3) + 2)/(3(-1|(2|x - 1| - 1) - 1| + 3) - 1), g(x) = 2|(-3cos(2πx) - 3) - 1| + 1, x = -1.3, and x = 3.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
37.9
|
math
|
train
|
math_algebra_func_area_level_2_2_788
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -3sin(1π((1(-2x - 2) + 1)/(-3(-2x - 2) + 2)) + 2) + 1 and g(x) = -2((3x + 3)/(-1x + 2))^2 - 2((3x + 3)/(-1x + 2)) between the vertical lines x = -1.3 and x = -1.2. 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_789
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -1(-3(-3sin(1πx + 1) + 2) - 4)^2 + 2, g(x) = 3|(-1x - 5) + 2| - 3, x = -1.9, and x = -1.8. 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_2_2_790
|
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(3|x - 1| - 1)^2 - 2(3|x - 1| - 1) - 5) + 2)/(3(2(3|x - 1| - 1)^2 - 2(3|x - 1| - 1) - 5) + 1) and g(x) = -1cos(3π(-2|x - 3| + 2) + 3) - 2 between the vertical lines x = -0.0 and x = 2.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
4.3
|
math
|
train
|
math_algebra_func_area_level_2_2_791
|
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(2π(3|x + 3| - 2) + 2) + 2)^2 - 1(3sin(2π(3|x + 3| - 2) + 2) + 2) + 3 and g(x) = 4(-4x^2 - 2x - 2) + 5 between the vertical lines x = 0.4 and x = 0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
2.2
|
math
|
train
|
math_algebra_func_area_level_2_2_792
|
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) - 2) + 3)/(-2(-3cos(1πx) - 2) - 3)) + 3| - 2 and g(x) = -3sin(1π(-2x + 3) - 3) - 3 between the vertical lines x = -0.6 and x = -0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
34.8
|
math
|
train
|
math_algebra_func_area_level_2_2_793
|
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((-1(-1x^2 - 1x + 4))/(-3(-1x^2 - 1x + 4))) + 1), g(x) = -1(-5x^2 + 2x + 2)^2 + 5, x = -0.8, and x = 1.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
5.6
|
math
|
train
|
math_algebra_func_area_level_2_2_794
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 5(3sin(1π(-4x^2 + 1x - 5) + 2))^2 + 3(3sin(1π(-4x^2 + 1x - 5) + 2)) - 4, g(x) = -2e^(2(1x - 5)) + 1, x = 1.4, and x = 1.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
2.3
|
math
|
train
|
math_algebra_func_area_level_2_2_795
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 1(4(-3cos(1πx - 1) + 1) - 1) + 4 and g(x) = -3(2|x - 1| - 2)^2 - 2(2|x - 1| - 2) - 2 from x = 2.1 to x = 2.4. 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_796
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 3(2cos(3π(3|x - 3| - 2) + 1) - 2) + 2, g(x) = 1cos(1π(-3x - 2) - 3) - 1, x = 4.9, and x = 5.0. 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_797
|
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(3πx))^2 - 5(-2cos(3πx)) - 4) + 1| + 1, g(x) = (-3(3x - 4) + 2)/(3(3x - 4) - 1), x = -2.2, and x = -2.1. 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_2_2_798
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (-3(-2((1x - 3)/(2x - 1)) + 1) - 3)/(2(-2((1x - 3)/(2x - 1)) + 1) - 3) and g(x) = -4(-3cos(1πx) - 3) + 3 from x = 2.4 to x = 2.6. 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_799
|
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(-1x + 3) - 1)/(1(-1x + 3))) - 3| + 2 and g(x) = -3(-5x^2 - 5x + 1)^2 + 2(-5x^2 - 5x + 1) + 4 between the vertical lines x = -0.9 and x = -0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
2.8
|
math
|
train
|
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