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_300
|
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(-3cos(2π(-2x + 2) - 3)) - 3)/(1(-3cos(2π(-2x + 2) - 3)) + 1) and g(x) = 4(-1e^(2x) - 3)^2 + 1(-1e^(2x) - 3) - 4 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}"
]
}
|
22.3
|
math
|
train
|
math_algebra_func_area_level_2_2_301
|
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|(-3e^(1x) + 1)| + 2) - 1)/(1(-1|(-3e^(1x) + 1)| + 2)) and g(x) = 1(-1x^2 + 3x - 2) + 5 between the vertical lines x = 0.1 and x = 4.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
21.5
|
math
|
train
|
math_algebra_func_area_level_2_2_302
|
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 - 5)^2 + 2(2x - 5) - 3) + 3| + 3, g(x) = (2((-3x + 3)/(1x + 2)) + 1)/(3((-3x + 3)/(1x + 2)) - 2), x = 0.5, and x = 1.2. Round your answer 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_303
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 2(-1(2cos(3πx + 3))^2 - 2(2cos(3πx + 3)) - 1)^2 - 1(-1(2cos(3πx + 3))^2 - 2(2cos(3πx + 3)) - 1) and g(x) = (-1(2cos(2πx + 3) + 2))/(-1(2cos(2πx + 3) + 2)) from x = 1.2 to x = 1.3. 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_304
|
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|(-5x^2 + 1x) - 3| - 2)^2 - 1(2|(-5x^2 + 1x) - 3| - 2) - 5, g(x) = (2(-1sin(2πx - 3) - 1) - 1)/(1(-1sin(2πx - 3) - 1) + 1), x = -0.5, and x = -0.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
40.9
|
math
|
train
|
math_algebra_func_area_level_2_2_305
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (-2(-1|(-1sin(3πx - 1)) + 3|) + 2)/(-3(-1|(-1sin(3πx - 1)) + 3|) - 1) and g(x) = -1(-3x + 4)^2 + 4(-3x + 4) - 2 from x = 0.4 to 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_306
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 3|(2|(1cos(3πx + 3) - 1) + 3| - 2) - 3| - 3, g(x) = -3(2x - 2), x = 0.8, and x = 1.0. 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_2_2_307
|
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(3e^(2((1x + 3)/(3x - 1))))^2 + 4(3e^(2((1x + 3)/(3x - 1)))) and g(x) = 3e^(-2(1|x + 3| + 1)) + 1 between the vertical lines x = -4.6 and x = -0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
7.3
|
math
|
train
|
math_algebra_func_area_level_2_2_308
|
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((1x - 1)/(-3x + 1)))/(-3((1x - 1)/(-3x + 1)) - 3)) + 1| and g(x) = 3cos(2π(4x + 5) + 1) between the vertical lines x = 1.8 and 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_309
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -3|(-2|(-2x - 3) + 1| - 2) + 3| + 1 and g(x) = -2(-3sin(2πx + 3) - 1)^2 + 5(-3sin(2πx + 3) - 1) - 2 from x = -1.5 to x = -0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
17.7
|
math
|
train
|
math_algebra_func_area_level_2_2_310
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 1sin(2π(-3|(-3x - 2)| + 2) + 2) - 1 and g(x) = -1|((-2x - 3)/(3x + 1))| - 1 from x = -3.4 to x = -3.3. 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_311
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 3|(3|(-2sin(2πx - 1) - 1) + 3|) - 2| - 1, g(x) = 2e^(-2(2|x - 2| + 3)) - 1, x = 0.3, and x = 0.5. 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_2_2_312
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 3|(2sin(1π(2|x - 3| + 3) - 1) - 3) + 2| - 3, g(x) = (-1(-1|x| + 2) + 3)/(-1(-1|x| + 2) + 2), x = 0.4, and x = 0.8. 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_2_2_313
|
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(-1|x|) - 3) + 2)/(1(-1(-1|x|) - 3)), g(x) = (-2(2cos(3πx - 2) - 2) + 1)/(-2(2cos(3πx - 2) - 2) + 3), x = -4.5, and x = -4.4. 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_314
|
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|(-3e^(-1(3|x + 2| - 2)) + 2) - 3| + 3 and g(x) = 2(-1sin(1πx + 1))^2 - 2 between the vertical lines x = 2.2 and x = 2.3000000000000003. 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_315
|
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(2x^2 + 4x - 1))/(-3(2x^2 + 4x - 1) + 2)) + 5 and g(x) = (3(-2|x + 1| - 1) + 3)/(2(-2|x + 1| - 1) + 2) between the vertical lines x = -2.3 and x = 0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
9.6
|
math
|
train
|
math_algebra_func_area_level_2_2_316
|
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|(1x^2 + 3x - 4) - 1| - 2) - 2)/(3(3|(1x^2 + 3x - 4) - 1| - 2) + 2) and g(x) = 1sin(3π(2|x - 2| - 1) + 3) - 2 between the vertical lines x = 1.1 and x = 1.3. 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_317
|
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(2|x + 1| + 3) + 2) - 3) - 1)/(1(-1sin(1π(2|x + 1| + 3) + 2) - 3) - 3), g(x) = (3(2|x| - 1) - 3)/(1(2|x| - 1) + 2), x = -1.5, and x = 1.5. 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_2_2_318
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -1|(-2|(2cos(1πx - 2) + 1) + 3| + 2) + 3| - 1 and g(x) = (3(2x^2 - 1x) + 2)/(-1(2x^2 - 1x) - 1) from x = -2.0 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_2_2_319
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -3(1cos(3π(2|x + 3| + 2)) + 2)^2 + 1(1cos(3π(2|x + 3| + 2)) + 2) - 2, g(x) = -3(1x^2 + 2x)^2 - 3(1x^2 + 2x), x = -2.7, and x = -2.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.9
|
math
|
train
|
math_algebra_func_area_level_2_2_320
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 2|(-3(3e^(2x) + 1)^2 + 1(3e^(2x) + 1) + 4) + 3| - 2 and g(x) = 1(3sin(2πx - 2) + 2) + 1 from x = -0.8 to x = -0.5. 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_321
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (1(3e^(-2(-1x + 2)) - 2) - 2)/(2(3e^(-2(-1x + 2)) - 2) - 1), g(x) = -2cos(2π(-2x - 2) + 2) + 3, x = 1.6, and x = 1.7. 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_322
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 1cos(3π((-1(4x^2 + 2x + 2))/(-2(4x^2 + 2x + 2) + 3))) + 2 and g(x) = (3((2x + 3)/(-1x + 3)) - 1)/(1((2x + 3)/(-1x + 3))) from x = -0.4 to x = -0.30000000000000004. 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_323
|
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|(4(-1x + 3) - 3) - 3| + 1 and g(x) = (1(-3|x - 3| + 3) - 2)/(2(-3|x - 3| + 3) - 1) between the vertical lines x = 2.2 and x = 3.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
26.4
|
math
|
train
|
math_algebra_func_area_level_2_2_324
|
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(2x^2 + 4x + 2) - 2) - 3))/(1(2cos(1π(2x^2 + 4x + 2) - 2) - 3) + 2) and g(x) = 5(3cos(3πx - 2) - 3)^2 - 4 between the vertical lines x = 1.0 and x = 1.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
43.0
|
math
|
train
|
math_algebra_func_area_level_2_2_325
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -3|((3((-1x + 1)/(-2x + 3)))/(-3((-1x + 1)/(-2x + 3)) + 1)) - 1| + 3 and g(x) = 4(-3cos(2πx + 2) - 2)^2 + 3(-3cos(2πx + 2) - 2) - 3 from x = 1.0 to x = 1.1. 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_326
|
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(-3|x| - 3)^2 + 4(-3|x| - 3) + 1))/(3(1(-3|x| - 3)^2 + 4(-3|x| - 3) + 1) + 3) and g(x) = -4((1x + 3)/(-3x - 2)) - 1 between the vertical lines x = -0.1 and x = 0.2. 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_327
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (-3((-1(-1x - 2) + 1)/(2(-1x - 2) + 1)) - 3)/(-1((-1(-1x - 2) + 1)/(2(-1x - 2) + 1)) + 2) and g(x) = -1cos(1π((-2x + 2)/(3x + 3))) + 3 from x = -1.6 to x = -1.4. 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_328
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (2((1(-3x^2 + 4x - 2) + 2)/(-1(-3x^2 + 4x - 2))) + 1)/(2((1(-3x^2 + 4x - 2) + 2)/(-1(-3x^2 + 4x - 2))) + 3) and g(x) = -5((2x + 2)/(-1x))^2 + 1((2x + 2)/(-1x)) + 1 from x = -1.3 to x = -0.8. 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_329
|
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|(3cos(2π((2x + 2)/(-2x + 3)) - 2) + 2) + 2| - 3 and g(x) = 1sin(2π(2x^2 - 4x - 3) - 2) + 2 between the vertical lines x = 1.3 and x = 1.4000000000000001. 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_330
|
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|(-1x^2 + 4x - 1) - 3| - 3)^2 - 2(-3|(-1x^2 + 4x - 1) - 3| - 3) - 4, g(x) = -5(-3x + 3) + 2, x = 1.7, and x = 2.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
5.9
|
math
|
train
|
math_algebra_func_area_level_2_2_331
|
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(2π(-4((-2x - 3)/(3x + 2))^2 - 2((-2x - 3)/(3x + 2)) + 1)) + 2 and g(x) = 3cos(1π(5x^2 + 3x - 2) + 2) - 1 between the vertical lines x = -4.9 and x = -4.8. 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_332
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -3|(3(1e^(-1x) - 2)) + 3| + 2, g(x) = 2cos(2π(4x - 3) - 1) - 3, x = 0.6, and x = 0.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.2
|
math
|
train
|
math_algebra_func_area_level_2_2_333
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 5((1(-3x^2 + 2x) + 3)/(1(-3x^2 + 2x) + 1))^2 - 5((1(-3x^2 + 2x) + 3)/(1(-3x^2 + 2x) + 1)) + 5 and g(x) = 3sin(1π(-3|x + 3| + 3) - 1) + 3 from x = -4.3 to x = -3.8. 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_334
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 1(-4(-2|x + 1| + 3)^2 + 4) + 2, g(x) = 3((-1x - 1)/(-3x + 4)) - 3, x = -3.2, and x = -1.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
8.4
|
math
|
train
|
math_algebra_func_area_level_2_2_335
|
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 + 3| + 1) + 3)/(-1(3|x + 3| + 1))) - 1| - 2 and g(x) = (-1(1|x + 1| - 3) - 3)/(-2(1|x + 1| - 3) - 2) between the vertical lines x = -3.7 and x = 2.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
29.2
|
math
|
train
|
math_algebra_func_area_level_2_2_336
|
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 - 2| - 2) + 1| - 1) + 3)/(3(2|(3|x - 2| - 2) + 1| - 1) - 2), g(x) = 1(-3|x - 1| + 1)^2 - 3(-3|x - 1| + 1), x = 2.0, and x = 2.1. Round your answer 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_337
|
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 + 1| + 3) + 1) + 2| - 1 and g(x) = 5((1x - 1)/(-3x))^2 - 4((1x - 1)/(-3x)) + 5 between the vertical lines x = -0.8 and x = 0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
-2.1
|
math
|
train
|
math_algebra_func_area_level_2_2_338
|
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| - 3) + 3| - 3) + 2| - 2 and g(x) = 3sin(3π(-4x^2 - 5x + 1) - 2) - 2 between the vertical lines x = 1.3 and x = 1.4000000000000001. 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_339
|
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(3π(2x^2 - 2x + 2) - 2)) - 2| + 2 and g(x) = -3cos(1π(3x - 5) - 2) - 1 between the vertical lines x = -3.3 and x = -3.2. 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_340
|
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(3|(-2x^2 - 3x) + 2| - 2)) and g(x) = (2(1x^2 - 1x) - 2)/(1(1x^2 - 1x) - 3) 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}"
]
}
|
0.1
|
math
|
train
|
math_algebra_func_area_level_2_2_341
|
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(2cos(3πx + 1) + 2) + 1)/(-1(2cos(3πx + 1) + 2) + 2))^2 + 2, g(x) = -1(-1|x - 3|)^2 - 2(-1|x - 3|) + 4, x = 0.8, and x = 1.0. 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_2_2_342
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 2(1(2x)^2 + 2(2x) + 2) - 3 and g(x) = 1(-2e^(-1x) + 3) + 5 from x = -1.1 to x = 0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
6.4
|
math
|
train
|
math_algebra_func_area_level_2_2_343
|
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(5x^2 - 3x - 3) - 2)/(-2(5x^2 - 3x - 3) - 3)))/(-1((1(5x^2 - 3x - 3) - 2)/(-2(5x^2 - 3x - 3) - 3)) - 1), g(x) = 3|((-3x)/(-1x - 1)) - 3| + 1, x = 0.1, and x = 0.7. 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_2_2_344
|
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|(2cos(3πx) + 1) - 1| - 2) + 1| - 1, g(x) = 2((-1x + 1)/(-2x - 3)), x = 2.5, and x = 2.8. 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_345
|
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(2π((3x - 1)/(2x)) + 1) - 1) + 3)/(-1(3cos(2π((3x - 1)/(2x)) + 1) - 1) + 2), g(x) = 2|(3sin(3πx + 1) - 2) - 1| + 1, x = -0.1, and x = 0.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
16.0
|
math
|
train
|
math_algebra_func_area_level_2_2_346
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 1|((-3(-3|x + 1| + 1))/(3(-3|x + 1| + 1) - 2)) + 1| - 3 and g(x) = 2((1x + 2)/(-1x - 3)) + 1 from x = -1.2 to x = -1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
10.1
|
math
|
train
|
math_algebra_func_area_level_2_2_347
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -4(5((-1x - 3)/(-3x + 2)) + 1)^2 + 2 and g(x) = (3(1cos(1πx + 1)) - 1)/(-3(1cos(1πx + 1)) - 1) from x = -2.6 to x = -1.8. 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_348
|
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((-2(-1e^(-1x) + 1) - 1)/(-3(-1e^(-1x) + 1) - 3)) and g(x) = 1(-2|x + 1| + 3)^2 + 3(-2|x + 1| + 3) - 5 between the vertical lines x = 0.1 and x = 2.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
7.3
|
math
|
train
|
math_algebra_func_area_level_2_2_349
|
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(-1x + 5) - 1)/(1(-1x + 5) + 3)) - 3)/(1((-1(-1x + 5) - 1)/(1(-1x + 5) + 3)) - 3), g(x) = -3cos(3π(-3|x + 2| - 2) - 2) + 2, x = -1.6, and x = -1.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.4
|
math
|
train
|
math_algebra_func_area_level_2_2_350
|
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(1|x + 1| + 1) + 1)^2 - 3(-3(1|x + 1| + 1) + 1) + 3 and g(x) = 3(-1e^(2x) - 1)^2 + 1(-1e^(2x) - 1) - 3 between the vertical lines x = -1.1 and x = -0.9. 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_351
|
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))/(-3(1|x - 3| - 1) + 2)) + 2| + 1, g(x) = (-3(3x^2 - 5x - 1) - 2)/(3(3x^2 - 5x - 1) - 2), x = -0.3, and x = 1.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
18.9
|
math
|
train
|
math_algebra_func_area_level_2_2_352
|
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(-5(5x + 1)^2 - 5(5x + 1) + 2) - 2) - 3, g(x) = 2e^(1((3x - 1)/(2x - 1))) - 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}"
]
}
|
0.1
|
math
|
train
|
math_algebra_func_area_level_2_2_353
|
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(3e^(1(4x^2 - 3x - 2)) - 3) - 4 and g(x) = 1e^(-1(1|x + 3| - 1)) + 2 between the vertical lines x = -0.6 and x = 1.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
14.5
|
math
|
train
|
math_algebra_func_area_level_2_2_354
|
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((-1x + 2)/(3x + 3))^2 + 3((-1x + 2)/(3x + 3)) + 5) - 2 and g(x) = 5(-4x - 2)^2 + 5(-4x - 2) + 2 between the vertical lines x = -1.1 and x = -0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
-15.3
|
math
|
train
|
math_algebra_func_area_level_2_2_355
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -1e^(-1(-1(2x^2 - 3x - 4)^2 - 2(2x^2 - 3x - 4) + 1)) + 1, g(x) = -1sin(1π(-5x - 5) - 2) - 2, x = 1.8, and x = 2.5. 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_356
|
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(3π(1x^2 + 5) + 1) - 1), g(x) = (1(1cos(3πx) + 2) + 1)/(-3(1cos(3πx) + 2) + 2), x = 4.1, and x = 4.199999999999999. 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_357
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 2|(2cos(3π(-4x - 2) + 2) - 3) - 2| - 1, g(x) = 2(-3e^(1x) + 1)^2 - 2(-3e^(1x) + 1) + 4, x = -0.5, and x = -0.4. 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_358
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 1e^(1((-2((1x)/(-3x + 1)))/(-1((1x)/(-3x + 1)) + 2))) + 3, g(x) = -2cos(2π(3x + 2) - 1) + 3, x = -3.2, and x = -3.1. 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_359
|
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 + 2)/(-2x + 3)) - 2)/(2((-2x + 2)/(-2x + 3)) - 1))^2 + 1((-3((-2x + 2)/(-2x + 3)) - 2)/(2((-2x + 2)/(-2x + 3)) - 1)) + 5, g(x) = -2cos(2π(-1x - 3) + 3) + 2, x = 1.1, and x = 1.3. 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_360
|
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((-3x - 2)/(-2x - 2))^2 + 4((-3x - 2)/(-2x - 2)) - 5) + 2, g(x) = (2(-5x^2 + 3x) + 1)/(-3(-5x^2 + 3x)), x = -0.4, and x = -0.0. 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_361
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (-2(-3|(3x^2 - 1x + 2) - 3| + 2) + 1)/(-2(-3|(3x^2 - 1x + 2) - 3| + 2) + 1) and g(x) = -2sin(3π(-3x - 1) + 2) from x = -4.8 to x = -4.7. 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_362
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -3e^(-1(4(1|x - 2| - 1) + 3)) - 1 and g(x) = -2cos(1π((-2x + 2)/(2x)) - 2) between the vertical lines x = 0.3 and x = 0.5. 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_363
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -4(3sin(1π(3|x - 1| - 2)) + 1) + 4 and g(x) = 3|(3sin(3πx - 1) - 2) + 1| from x = -4.8 to x = -4.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
4.9
|
math
|
train
|
math_algebra_func_area_level_2_2_364
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -2|(2cos(3π((-2x + 2)/(2x - 1)) + 3) + 3) - 2| - 2 and g(x) = -2|(5x^2 + 5x - 3) - 1| + 1 from x = 0.3 to x = 0.4. 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_365
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -1|(-2(-1cos(2πx + 1) + 1)) + 2| + 1 and g(x) = 1(-2cos(2πx + 1) + 2)^2 - 1(-2cos(2πx + 1) + 2) - 1 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_366
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (2(5(-2x + 4)^2 - 3) + 3)/(1(5(-2x + 4)^2 - 3) - 2), g(x) = 2(2|x + 1| + 1) + 3, x = 1.5, and x = 2.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
32.3
|
math
|
train
|
math_algebra_func_area_level_2_2_367
|
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(-3|x + 2| + 3)^2 - 2(-3|x + 2| + 3) - 2) - 2)/(-2(1(-3|x + 2| + 3)^2 - 2(-3|x + 2| + 3) - 2) - 1), g(x) = 2sin(2π(5x - 1) - 2) - 2, x = -3.1, and x = -3.0. 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_368
|
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(4x^2 + 2x - 5) + 1)/(-2(4x^2 + 2x - 5) + 3)) + 2, g(x) = 1(-1cos(2πx - 3)) + 2, x = -1.4, and x = 0.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
5.0
|
math
|
train
|
math_algebra_func_area_level_2_2_369
|
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) - 1)/(-1(-2x - 1) - 2))^2 + 4((-1(-2x - 1) - 1)/(-1(-2x - 1) - 2)) + 5 and g(x) = (-3(-1sin(1πx + 3) - 2) + 2)/(-2(-1sin(1πx + 3) - 2) - 3) between the vertical lines x = 2.0 and x = 3.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
66.9
|
math
|
train
|
math_algebra_func_area_level_2_2_370
|
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((-1x)/(-2x + 3)) + 2)/(-2((-1x)/(-2x + 3)) - 2)) - 1| + 3 and g(x) = (1(-2sin(1πx - 1)) + 3)/(2(-2sin(1πx - 1)) + 1) between the vertical lines x = 3.3 and x = 4.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
6.0
|
math
|
train
|
math_algebra_func_area_level_2_2_371
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 2(-1(1x^2 + 1x - 1)) - 2 and g(x) = 2(3sin(3πx + 3) - 2)^2 + 4(3sin(3πx + 3) - 2) - 3 from x = -0.6 to x = -0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
4.5
|
math
|
train
|
math_algebra_func_area_level_2_2_372
|
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(1x^2 + 1x + 5)^2 - 4(1x^2 + 1x + 5) + 4) - 1)/(3(1(1x^2 + 1x + 5)^2 - 4(1x^2 + 1x + 5) + 4) + 1), g(x) = -1(2x^2 - 4x) - 1, x = 0.2, and x = 1.8. 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_373
|
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(-3sin(1πx + 1) - 2) + 3) + 2, g(x) = (-1(4x + 2) + 1)/(-1(4x + 2) - 1), x = -0.6, and x = 0.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
20.0
|
math
|
train
|
math_algebra_func_area_level_2_2_374
|
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(1|x + 2| + 2) + 3)/(2(1|x + 2| + 2) + 1)) - 2| - 1 and g(x) = -1sin(2π(1x + 2) + 1) - 1 between the vertical lines x = 2.7 and x = 3.5. 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_375
|
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| - 1) + 3)/(-2(3|x - 3| - 1) + 1)) - 2 and g(x) = -1cos(2π(-4x^2 + 3x + 3) + 2) between the vertical lines x = 3.6 and x = 3.7. 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_376
|
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((-2x - 2)/(1x)) - 4)^2 + 1(5((-2x - 2)/(1x)) - 4) + 1, g(x) = -5(1x + 2), x = -0.8, and x = -0.6. 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_377
|
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 + 1) + 2|)^2 - 2(1|(2x + 1) + 2|) - 1, g(x) = 1e^(1(-1x^2 + 4x)) + 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}"
]
}
|
42.3
|
math
|
train
|
math_algebra_func_area_level_2_2_378
|
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(-2sin(3π(-2|x - 1|) + 2) - 2)^2 - 5(-2sin(3π(-2|x - 1|) + 2) - 2) + 2 and g(x) = 2sin(3π(-1|x - 3| - 1) + 3) + 2 between the vertical lines x = -1.1 and x = -0.6. 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_379
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 1sin(1π(-4(-1x^2 - 5x + 4) - 5) + 3) - 2, g(x) = 4(-3cos(2πx + 1) - 1)^2 + 3(-3cos(2πx + 1) - 1) - 4, x = -0.5, and x = -0.4. 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_380
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 4(3(-2cos(3πx + 3) + 2)^2 - 4(-2cos(3πx + 3) + 2) + 2)^2 - 2(3(-2cos(3πx + 3) + 2)^2 - 4(-2cos(3πx + 3) + 2) + 2) - 1 and g(x) = 3|(2cos(1πx + 2))| - 1 from x = 0.4 to x = 0.5. 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_381
|
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 - 2x - 1) + 1| - 2))/(-2(2|(1x^2 - 2x - 1) + 1| - 2) + 3), g(x) = -3sin(1π(-5x + 4) - 3), x = -3.4, and x = -3.2. 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_382
|
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(1cos(1πx + 2)) + 1) - 2| + 2, g(x) = -2((-2x - 1)/(-2x)), x = -3.2, and x = -2.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
2.6
|
math
|
train
|
math_algebra_func_area_level_2_2_383
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 2(-2cos(1π(1|x + 2| - 3) + 1) + 1)^2 - 1(-2cos(1π(1|x + 2| - 3) + 1) + 1) - 2 and g(x) = -1cos(3π(3|x + 3| + 2) - 1) + 3 from x = 0.0 to x = 1.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
4.4
|
math
|
train
|
math_algebra_func_area_level_2_2_384
|
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(3π(-2x - 3) + 2) + 3) - 1 and g(x) = 4(-2|x| + 2) + 3 between the vertical lines x = -0.2 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_385
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 2(5(-1x^2 + 1x + 4) - 4)^2 + 1(5(-1x^2 + 1x + 4) - 4) + 2 and g(x) = -3cos(1π((1x - 1)/(2x + 3)) + 2) + 1 from x = -1.4 to x = -1.2999999999999998. 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_386
|
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((1x + 2)/(1x)) + 3) - 2) + 3, g(x) = (-3(3x^2 + 5x - 2) + 2)/(-2(3x^2 + 5x - 2) - 1), x = 0.1, and x = 0.2. 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_387
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 3sin(3π(3((-1x - 2)/(1x + 3))^2 - 2((-1x - 2)/(1x + 3)) + 2) - 1) - 3, g(x) = 3((3x + 3)/(-2x + 3)) + 1, x = -3.5, 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_388
|
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(3πx - 1) + 2) - 5)^2 - 4(1(-3sin(3πx - 1) + 2) - 5) - 3, g(x) = 1e^(-2(4x^2 - 3x + 2)) + 1, x = 3.4, and x = 3.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
14.7
|
math
|
train
|
math_algebra_func_area_level_2_2_389
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 5(-4((1x + 3)/(1x - 3))^2 - 5((1x + 3)/(1x - 3)) - 1)^2 - 3(-4((1x + 3)/(1x - 3))^2 - 5((1x + 3)/(1x - 3)) - 1) - 1 and g(x) = -3|((-1x - 1)/(3x)) - 1| - 1 from x = -0.3 to x = -0.2. 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_390
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 3e^(2(3((-2x - 3)/(-1x - 1))^2 + 3((-2x - 3)/(-1x - 1)) - 4)) + 1 and g(x) = -1(-4x^2 + 1x - 5) + 1 between the vertical lines x = -1.9 and x = -1.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
9.1
|
math
|
train
|
math_algebra_func_area_level_2_2_391
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 2((-3(-3x - 4) + 1)/(-3(-3x - 4) - 3)) - 5, g(x) = -1(1x^2 + 3x - 4) - 3, x = -4.1, and x = -0.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
27.3
|
math
|
train
|
math_algebra_func_area_level_2_2_392
|
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(-2cos(3π(-5x + 1) + 2)) + 3)/(1(-2cos(3π(-5x + 1) + 2))) and g(x) = -2((2x + 1)/(-1x - 1)) + 4 between the vertical lines x = -2.9 and x = -2.8. Round 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_393
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -1(3(1x + 5) + 5) + 2 and g(x) = -2e^(-1(-2x^2 + 1x)) from x = -0.8 to x = 1.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
29.9
|
math
|
train
|
math_algebra_func_area_level_2_2_394
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -2|(-1cos(3π(1|x| - 1) - 2)) - 2| + 3, g(x) = -3(1x - 1)^2 + 2(1x - 1) - 2, x = 1.3, and x = 1.8. 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_2_2_395
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 4(2|(1x^2 + 3x - 5) + 3| - 3) - 3 and g(x) = 1cos(3π(-2x^2 + 2x + 1) - 3) - 3 from x = 0.2 to x = 0.9. 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_396
|
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(-1cos(2πx + 1) + 2) - 5) - 3)/(2(-3(-1cos(2πx + 1) + 2) - 5) + 1) and g(x) = -2|(-2e^(-1x) + 3) + 2| + 2 between the vertical lines x = -1.0 and x = -0.8. 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_397
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 1sin(1π(2((-2x - 1)/(-2x + 3)) - 2) - 3) - 3, g(x) = -4(3cos(3πx) - 2)^2 - 3(3cos(3πx) - 2) + 2, x = -0.8, and x = -0.7. 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_398
|
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|(5x^2 + 1x - 4) - 3| - 2) - 2) and g(x) = 2cos(3π(-3x^2 - 1x + 3) + 2) + 1 between the vertical lines x = 4.8 and x = 4.8999999999999995. 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_399
|
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(2sin(1πx + 3) + 1) - 3) - 2, g(x) = -2|(-1e^(-2x) + 1) - 1| - 2, x = 0.7, and x = 2.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
71.3
|
math
|
train
|
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