id
string
setting_key
string
messages
list
ground_truth
string
dataset
string
algebra_func_area_train_0400
algebra_func_area
[ { "role": "user", "content": "Determine the area of the region enclosed by the graphs of f(x) = 3(-3|(-3sin(2π((-1x - 3)/(2x + 2)) - 2) - 3) - 1| + 3) + 4 and g(x) = -3sin(2π(3(-1x^2 + 3x - 1) - 3) + 1) + 3 between the vertical lines x = -3.0 and x = -2.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.2
MATH_EXPLORATIVE
algebra_func_area_train_0401
algebra_func_area
[ { "role": "user", "content": "Determine the area of the region enclosed by the graphs of f(x) = 1((2x - 3)/(2x))^2 + 1((2x - 3)/(2x)) - 2 and g(x) = (-3x + 2)/(-2x + 1) 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}" } ]
11.1
MATH_EXPLORATIVE
algebra_func_area_train_0402
algebra_func_area
[ { "role": "user", "content": "Find the area of the region bounded by the curves f(x) = 1(2|((3x + 1)/(-2x + 3)) - 2| - 2)^2 + 4(2|((3x + 1)/(-2x + 3)) - 2| - 2) + 3, g(x) = 4(2|x - 1| + 2)^2 - 5, x = 1.0, and x = 2.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
-26.6
MATH_EXPLORATIVE
algebra_func_area_train_0403
algebra_func_area
[ { "role": "user", "content": "Determine the area of the region enclosed by the graphs of f(x) = (2(5(-1(-2|x + 3| + 3) - 4)^2 - 3(-1(-2|x + 3| + 3) - 4) - 3) - 3)/(-3(5(-1(-2|x + 3| + 3) - 4)^2 - 3(-1(-2|x + 3| + 3) - 4) - 3) + 1) and g(x) = 5(-2|(1x^2) + 1| - 1) + 2 between the vertical lines x = 0.2 and x = 1.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
15.8
MATH_EXPLORATIVE
algebra_func_area_train_0404
algebra_func_area
[ { "role": "user", "content": "Determine the area of the region enclosed by the graphs of f(x) = 1|(-3cos(3πx + 3) + 3) - 3| + 1 and g(x) = 3x - 3 between the vertical lines x = 1.5 and x = 1.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.3
MATH_EXPLORATIVE
algebra_func_area_train_0405
algebra_func_area
[ { "role": "user", "content": "Calculate the area enclosed between the functions f(x) = (-3(-3|x|) + 1)/(-3(-3|x|)) and g(x) = 3x^2 - 1 from x = -0.8 to x = 0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
7.5
MATH_EXPLORATIVE
algebra_func_area_train_0406
algebra_func_area
[ { "role": "user", "content": "Calculate the area enclosed between the functions f(x) = 1sin(3π(3x^2 + 3x - 3) - 2) - 1 and g(x) = -1|x - 1| - 1 from x = 1.7 to x = 1.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.1
MATH_EXPLORATIVE
algebra_func_area_train_0407
algebra_func_area
[ { "role": "user", "content": "Calculate the area enclosed between the functions f(x) = 3((-1(-3sin(3πx + 1) + 2) + 3)/(2(-3sin(3πx + 1) + 2) + 3)) - 5 and g(x) = 1sin(2π(-4x + 4) + 3) from x = -0.0 to x = 0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.4
MATH_EXPLORATIVE
algebra_func_area_train_0408
algebra_func_area
[ { "role": "user", "content": "Determine the area of the region enclosed by the graphs of f(x) = -1cos(1π((-2x - 2)/(3x - 2)) + 3) + 1 and g(x) = -2x^2 - 5x + 5 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_EXPLORATIVE
algebra_func_area_train_0409
algebra_func_area
[ { "role": "user", "content": "Calculate the area enclosed between the functions f(x) = -2e^(-2(-1|x| + 1)) - 1 and g(x) = -3|x + 3| - 2 from x = -1.5 to x = 2.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
27.8
MATH_EXPLORATIVE
algebra_func_area_train_0410
algebra_func_area
[ { "role": "user", "content": "Calculate the area enclosed between the functions f(x) = -4(3(-1|x - 2|)^2 + 1(-1|x - 2|) + 3) - 3 and g(x) = -2|(-5x + 3) - 2| - 3 from x = 1.5 to x = 3.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
13.0
MATH_EXPLORATIVE
algebra_func_area_train_0411
algebra_func_area
[ { "role": "user", "content": "Calculate the area enclosed between the functions f(x) = -2|(-1((-1x + 3)/(2x + 3)) - 5) - 2| + 1 and g(x) = -4((-2x + 3)/(2x - 3))^2 - 1((-2x + 3)/(2x - 3)) + 3 from x = -1.9 to x = -1.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.0
MATH_EXPLORATIVE
algebra_func_area_train_0412
algebra_func_area
[ { "role": "user", "content": "Calculate the area enclosed between the functions f(x) = 3(3|((3x + 2)/(2x - 1)) - 3| + 1) - 2 and g(x) = 1sin(3π(-3|x + 2| - 2)) + 1 from x = 1.7 to x = 1.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.1
MATH_EXPLORATIVE
algebra_func_area_train_0413
algebra_func_area
[ { "role": "user", "content": "Find the area of the region bounded by the curves f(x) = 1sin(3π((3(-1|x + 1| - 2) + 3)/(-3(-1|x + 1| - 2) + 1)) - 3), g(x) = (-2(2|x| - 3))/(3(2|x| - 3) - 1), x = 0.1, and x = 1.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.6
MATH_EXPLORATIVE
algebra_func_area_train_0414
algebra_func_area
[ { "role": "user", "content": "Calculate the area enclosed between the functions f(x) = (1(2|(-2(1sin(2πx) - 3) - 5)| - 2))/(2(2|(-2(1sin(2πx) - 3) - 5)| - 2) + 3) and g(x) = -1|(-4(3x + 2)^2 - 2) + 1| - 3 from x = 0.4 to x = 0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
5.8
MATH_EXPLORATIVE
algebra_func_area_train_0415
algebra_func_area
[ { "role": "user", "content": "Calculate the area enclosed between the functions f(x) = (1(-2|x + 3| + 2))/(1(-2|x + 3| + 2) - 3) and g(x) = -4x^2 + 3x + 5 from x = -0.8 to x = 1.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
7.4
MATH_EXPLORATIVE
algebra_func_area_train_0416
algebra_func_area
[ { "role": "user", "content": "Find the area of the region bounded by the curves f(x) = 3cos(1π(2|(-4x^2 - 1x - 4) - 1| + 1) + 1) + 1, g(x) = -5(-1|x|) + 2, x = 0.1, and x = 0.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.1
MATH_EXPLORATIVE
algebra_func_area_train_0417
algebra_func_area
[ { "role": "user", "content": "Find the area of the region bounded by the curves f(x) = 1cos(2π(1|(1x + 5) - 1| - 2) - 2) + 1, g(x) = 2cos(3π(1x^2 + 4x + 4) + 1) - 1, x = 3.8, and x = 3.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.1
MATH_EXPLORATIVE
algebra_func_area_train_0418
algebra_func_area
[ { "role": "user", "content": "Find the area of the region bounded by the curves f(x) = (2(-2cos(2πx - 2) + 1) - 2)/(-1(-2cos(2πx - 2) + 1) + 3), g(x) = 5x^2 + 5x + 3, x = 0.9, and x = 1.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
17.6
MATH_EXPLORATIVE
algebra_func_area_train_0419
algebra_func_area
[ { "role": "user", "content": "Determine the area of the region enclosed by the graphs of f(x) = -5(4(-1cos(3π(-2|x + 1| - 2) - 2) + 1)^2 - 4(-1cos(3π(-2|x + 1| - 2) - 2) + 1) + 1) - 4 and g(x) = 3((3(-1|x + 1| + 3) - 2)/(-3(-1|x + 1| + 3))) - 2 between the vertical lines x = -4.5 and x = -4.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
3.7
MATH_EXPLORATIVE
algebra_func_area_train_0420
algebra_func_area
[ { "role": "user", "content": "Calculate the area enclosed between the functions f(x) = 1cos(1π(5x + 3) - 3) + 3 and g(x) = -5x - 4 from x = -1.6 to x = -1.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.2
MATH_EXPLORATIVE
algebra_func_area_train_0421
algebra_func_area
[ { "role": "user", "content": "Find the area of the region bounded by the curves f(x) = -2cos(1π(3|(-2(5x + 3)^2 - 3(5x + 3) + 1) + 2| - 3) + 1), g(x) = -1|(5(-4x^2 - 5x + 5) - 3)| + 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}" } ]
0.2
MATH_EXPLORATIVE
algebra_func_area_train_0422
algebra_func_area
[ { "role": "user", "content": "Find the area of the region bounded by the curves f(x) = -1(-1sin(1π((-2x)/(-2x - 3)) - 3) - 1) - 5, g(x) = -3(5x^2 - 2x + 2) + 2, x = -0.0, and x = 0.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.4
MATH_EXPLORATIVE
algebra_func_area_train_0423
algebra_func_area
[ { "role": "user", "content": "Calculate the area enclosed between the functions f(x) = 1cos(1π(-4(-1|x - 3| - 1) - 4)) - 2 and g(x) = (-3(-4x + 5))/(3(-4x + 5) - 2) from x = -4.5 to x = -4.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.5
MATH_EXPLORATIVE
algebra_func_area_train_0424
algebra_func_area
[ { "role": "user", "content": "Determine the area of the region enclosed by the graphs of f(x) = 3e^(1(-3x - 1)) - 2 and g(x) = -3x^2 + 5x + 5 between the vertical lines x = -0.4 and x = 2.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
18.6
MATH_EXPLORATIVE
algebra_func_area_train_0425
algebra_func_area
[ { "role": "user", "content": "Calculate the area enclosed between the functions f(x) = -2((2(1x - 1) - 2)/(-1(1x - 1) - 2))^2 - 5((2(1x - 1) - 2)/(-1(1x - 1) - 2)) and g(x) = 3|(-3cos(2πx - 1) - 2) + 1| - 3 from x = 2.8 to x = 2.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.3
MATH_EXPLORATIVE
algebra_func_area_train_0426
algebra_func_area
[ { "role": "user", "content": "Calculate the area enclosed between the functions f(x) = 1|((-3(-5(-5x - 5)^2 + 3(-5x - 5) - 2) - 2)/(3(-5(-5x - 5)^2 + 3(-5x - 5) - 2) + 1)) + 1| + 2 and g(x) = 3|(-1(-1x + 2)^2 - 4(-1x + 2) + 5)| - 2 from x = 0.8 to x = 1.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.9
MATH_EXPLORATIVE
algebra_func_area_train_0427
algebra_func_area
[ { "role": "user", "content": "Calculate the area enclosed between the functions f(x) = 3|(-3sin(1πx + 3) + 1) + 2| - 1 and g(x) = 4x + 4 from x = -0.7 to x = -0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
1.2
MATH_EXPLORATIVE
algebra_func_area_train_0428
algebra_func_area
[ { "role": "user", "content": "Find the area of the region bounded by the curves f(x) = 5(-2sin(3π(-4x - 1) - 3) + 1)^2 + 3(-2sin(3π(-4x - 1) - 3) + 1) + 5, g(x) = 1((-1x + 2)/(-3x - 2)) + 5, x = -4.7, and x = -4.6000000000000005. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
2.5
MATH_EXPLORATIVE
algebra_func_area_train_0429
algebra_func_area
[ { "role": "user", "content": "Determine the area of the region enclosed by the graphs of f(x) = -2((1x + 3)/(-1x - 2)) - 1 and g(x) = -4x^2 + 5x + 5 between the vertical lines x = -0.4 and x = 1.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
6.9
MATH_EXPLORATIVE
algebra_func_area_train_0430
algebra_func_area
[ { "role": "user", "content": "Determine the area of the region enclosed by the graphs of f(x) = 1cos(2π(-1x + 5)) and g(x) = (3x + 2)/(2x + 2) between the vertical lines x = -0.7 and x = -0.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.6
MATH_EXPLORATIVE
algebra_func_area_train_0431
algebra_func_area
[ { "role": "user", "content": "Determine the area of the region enclosed by the graphs of f(x) = -1|(-4((3x + 1)/(-1x + 3)) + 4) + 2| - 2 and g(x) = -3|(5x) - 3| between the vertical lines x = 0.2 and x = 0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.9
MATH_EXPLORATIVE
algebra_func_area_train_0432
algebra_func_area
[ { "role": "user", "content": "Calculate the area enclosed between the functions f(x) = 1cos(2π((2x + 3)/(-2x + 3)) + 1) - 3 and g(x) = -3x^2 + 2x - 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_EXPLORATIVE
algebra_func_area_train_0433
algebra_func_area
[ { "role": "user", "content": "Calculate the area enclosed between the functions f(x) = 3|(-4(3cos(3π(-2x^2 + 1x - 1) + 2) + 2) + 1)| - 1 and g(x) = 1|((-3(-1cos(2πx + 2) + 2) - 3)/(2(-1cos(2πx + 2) + 2) + 2)) + 2| from x = 2.1 to x = 2.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
2.3
MATH_EXPLORATIVE
algebra_func_area_train_0434
algebra_func_area
[ { "role": "user", "content": "Determine the area of the region enclosed by the graphs of f(x) = -4((-2(-3(-3|x| + 2) + 4) - 3)/(2(-3(-3|x| + 2) + 4) + 2))^2 - 3((-2(-3(-3|x| + 2) + 4) - 3)/(2(-3(-3|x| + 2) + 4) + 2)) - 5 and g(x) = 1(-5((-2x + 1)/(-3x + 2))^2 - 4) + 3 between the vertical lines x = 0.6 and x = 1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
-1.2
MATH_EXPLORATIVE
algebra_func_area_train_0435
algebra_func_area
[ { "role": "user", "content": "Calculate the area enclosed between the functions f(x) = 3sin(1π(1x^2 + 5x + 3) + 1) + 1 and g(x) = (3x + 1)/(3x + 2) from x = 1.8 to x = 2.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.4
MATH_EXPLORATIVE
algebra_func_area_train_0436
algebra_func_area
[ { "role": "user", "content": "Calculate the area enclosed between the functions f(x) = -3((-1(-3sin(2π(1|x + 1| + 2) + 2)))/(-3(-3sin(2π(1|x + 1| + 2) + 2)) - 2)) + 5 and g(x) = (-2(-2|(-1x^2 - 2x + 1) + 3| - 1) + 2)/(-1(-2|(-1x^2 - 2x + 1) + 3| - 1)) from x = 1.1 to x = 1.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
1.5
MATH_EXPLORATIVE
algebra_func_area_train_0437
algebra_func_area
[ { "role": "user", "content": "Find the area of the region bounded by the curves f(x) = 1|(-1cos(1π(3x - 2) + 3) - 2) - 3| + 2, g(x) = 1(2sin(2πx) - 3)^2 - 2(2sin(2πx) - 3) - 2, x = 0.1, and x = 0.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
1.5
MATH_EXPLORATIVE
algebra_func_area_train_0438
algebra_func_area
[ { "role": "user", "content": "Find the area of the region bounded by the curves f(x) = 3|(-5(-1((-1x + 3)/(-2x + 3))^2 + 1((-1x + 3)/(-2x + 3)) - 1) + 3)| - 3, g(x) = 1|(-1((1x)/(3x + 3))^2 - 1((1x)/(3x + 3)) + 5) + 1| + 3, x = -1.1, and x = -0.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
10.3
MATH_EXPLORATIVE
algebra_func_area_train_0439
algebra_func_area
[ { "role": "user", "content": "Determine the area of the region enclosed by the graphs of f(x) = 3(-3|x| + 2) + 4 and g(x) = (-1x + 3)/(1x + 1) between the vertical lines x = -0.4 and x = 1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
5.4
MATH_EXPLORATIVE
algebra_func_area_train_0440
algebra_func_area
[ { "role": "user", "content": "Find the area of the region bounded by the curves f(x) = -1cos(1π(2x + 1) + 3), g(x) = (3x - 1)/(-3x - 2), x = 3.1, and x = 3.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.8
MATH_EXPLORATIVE
algebra_func_area_train_0441
algebra_func_area
[ { "role": "user", "content": "Find the area of the region bounded by the curves f(x) = (-2(-3(3|x - 1| + 1)^2 + 2(3|x - 1| + 1) + 4) - 1)/(-1(-3(3|x - 1| + 1)^2 + 2(3|x - 1| + 1) + 4) + 3), g(x) = (-1(-4x^2 - 1x) - 3)/(-1(-4x^2 - 1x) - 3), x = 0.7, and x = 1.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
25.7
MATH_EXPLORATIVE
algebra_func_area_train_0442
algebra_func_area
[ { "role": "user", "content": "Determine the area of the region enclosed by the graphs of f(x) = (2(-3|x - 1| - 3) - 1)/(1(-3|x - 1| - 3) + 1) and g(x) = -3x^2 + 1x + 5 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}" } ]
2.8
MATH_EXPLORATIVE
algebra_func_area_train_0443
algebra_func_area
[ { "role": "user", "content": "Determine the area of the region enclosed by the graphs of f(x) = -2sin(3π(3|x| - 1) + 3) + 2 and g(x) = -5x^2 - 5x + 4 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}" } ]
0.1
MATH_EXPLORATIVE
algebra_func_area_train_0444
algebra_func_area
[ { "role": "user", "content": "Find the area of the region bounded by the curves f(x) = -1(1|((-1(4x - 3) + 1)/(2(4x - 3) + 3)) - 2| - 1)^2 - 5(1|((-1(4x - 3) + 1)/(2(4x - 3) + 3)) - 2| - 1) + 1, g(x) = -3sin(1π((3(1x^2 - 3x) + 2)/(3(1x^2 - 3x) - 2)) + 1) - 3, x = 0.4, and x = 1.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
3.3
MATH_EXPLORATIVE
algebra_func_area_train_0445
algebra_func_area
[ { "role": "user", "content": "Find the area of the region bounded by the curves f(x) = 1|(4(-2((2x - 1)/(2x - 3))^2 - 4((2x - 1)/(2x - 3)) + 5) - 4)|, g(x) = (2(4(1|x + 3| - 2)^2 - 1(1|x + 3| - 2) + 1) - 3)/(2(4(1|x + 3| - 2)^2 - 1(1|x + 3| - 2) + 1) - 1), x = -1.9, and x = 1.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
27.5
MATH_EXPLORATIVE
algebra_func_area_train_0446
algebra_func_area
[ { "role": "user", "content": "Determine the area of the region enclosed by the graphs of f(x) = 1sin(3π(-3|(-1(5x - 5)^2 + 2) - 2|)) + 3 and g(x) = (3(-3(1|x + 2|)) + 3)/(-2(-3(1|x + 2|)) - 1) between the vertical lines x = -1.8 and x = -1.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.2
MATH_EXPLORATIVE
algebra_func_area_train_0447
algebra_func_area
[ { "role": "user", "content": "Determine the area of the region enclosed by the graphs of f(x) = (1(5(1|x| - 3)^2 + 3(1|x| - 3) + 5))/(2(5(1|x| - 3)^2 + 3(1|x| - 3) + 5) - 3) and g(x) = (2(-2x - 3) + 1)/(3(-2x - 3) + 1) between the vertical lines x = 2.1 and x = 3.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.1
MATH_EXPLORATIVE
algebra_func_area_train_0448
algebra_func_area
[ { "role": "user", "content": "Determine the area of the region enclosed by the graphs of f(x) = 1(2(1|((1x + 3)/(2x - 1)) - 3| - 1)^2 + 2(1|((1x + 3)/(2x - 1)) - 3| - 1)) - 2 and g(x) = (2(2|(4x^2 - 2x + 1) + 3|) - 1)/(1(2|(4x^2 - 2x + 1) + 3|) + 1) between the vertical lines x = 0.9 and x = 4.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
6.6
MATH_EXPLORATIVE
algebra_func_area_train_0449
algebra_func_area
[ { "role": "user", "content": "Determine the area of the region enclosed by the graphs of f(x) = -5(-5x - 3)^2 + 4 and g(x) = 2x + 3 between the vertical lines x = -0.7 and x = -0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.4
MATH_EXPLORATIVE
algebra_func_area_train_0450
algebra_func_area
[ { "role": "user", "content": "Calculate the area enclosed between the functions f(x) = 4(-3|x - 2| + 2) - 3 and g(x) = (2x - 2)/(2x + 1) from x = 1.6 to x = 2.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
1.8
MATH_EXPLORATIVE
algebra_func_area_train_0451
algebra_func_area
[ { "role": "user", "content": "Determine the area of the region enclosed by the graphs of f(x) = (-2(-3(-2|(3x + 3) + 2| + 1)^2 + 4(-2|(3x + 3) + 2| + 1) - 2) - 1)/(-1(-3(-2|(3x + 3) + 2| + 1)^2 + 4(-2|(3x + 3) + 2| + 1) - 2) - 2) and g(x) = 2sin(1π((1(5x - 4) + 3)/(-3(5x - 4) - 3)) + 2) + 1 between the vertical lines x = 0.7 and x = 1.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.9
MATH_EXPLORATIVE
algebra_func_area_train_0452
algebra_func_area
[ { "role": "user", "content": "Determine the area of the region enclosed by the graphs of f(x) = -5(1(2|x + 2| - 2)^2 - 3) - 2 and g(x) = -4(1x + 2)^2 - 1(1x + 2) - 2 between the vertical lines x = -1.9 and x = 0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
32.7
MATH_EXPLORATIVE
algebra_func_area_train_0453
algebra_func_area
[ { "role": "user", "content": "Calculate the area enclosed between the functions f(x) = -2|(-2(4(-1cos(1πx + 1) - 1)^2 + 3(-1cos(1πx + 1) - 1) - 3) + 3) + 3| - 1 and g(x) = 5((-1(-2|x + 3| + 2) + 3)/(-3(-2|x + 3| + 2) - 1)) + 2 from x = -4.0 to x = -2.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
34.6
MATH_EXPLORATIVE
algebra_func_area_train_0454
algebra_func_area
[ { "role": "user", "content": "Determine the area of the region enclosed by the graphs of f(x) = 1(2|x + 1| - 1)^2 + 2(2|x + 1| - 1) + 3 and g(x) = 2x + 5 between the vertical lines x = -1.3 and x = -0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.9
MATH_EXPLORATIVE
algebra_func_area_train_0455
algebra_func_area
[ { "role": "user", "content": "Calculate the area enclosed between the functions f(x) = -2(-2sin(3πx - 1) + 3) + 5 and g(x) = 5x + 5 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_EXPLORATIVE
algebra_func_area_train_0456
algebra_func_area
[ { "role": "user", "content": "Calculate the area enclosed between the functions f(x) = 2(-1|(2((1x - 1)/(3x - 1))^2 - 4((1x - 1)/(3x - 1)) + 1) - 1| - 1) and g(x) = (-1(-1(-2x + 3)^2 + 4) - 3)/(3(-1(-2x + 3)^2 + 4) + 2) from x = 0.4 to x = 2.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
11.1
MATH_EXPLORATIVE
algebra_func_area_train_0457
algebra_func_area
[ { "role": "user", "content": "Find the area of the region bounded by the curves f(x) = 3sin(1π(5x) + 1) - 2, g(x) = 1|x - 1| - 1, x = 1.2, and x = 1.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.1
MATH_EXPLORATIVE
algebra_func_area_train_0458
algebra_func_area
[ { "role": "user", "content": "Find the area of the region bounded by the curves f(x) = -1|((-3(1cos(3π(-1x^2 + 2x - 4)) - 3) - 3)/(-1(1cos(3π(-1x^2 + 2x - 4)) - 3) + 3))| + 1, g(x) = 2|(-5((2x - 3)/(-2x - 2)) - 2) - 2| - 2, x = 4.9, and x = 5.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.0
MATH_EXPLORATIVE
algebra_func_area_train_0459
algebra_func_area
[ { "role": "user", "content": "Determine the area of the region enclosed by the graphs of f(x) = 2(1|(-2sin(1πx + 2) + 1) - 2| - 1) - 5 and g(x) = 3(1cos(1πx - 1) - 3) between the vertical lines x = 2.6 and x = 4.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
9.7
MATH_EXPLORATIVE
algebra_func_area_train_0460
algebra_func_area
[ { "role": "user", "content": "Calculate the area enclosed between the functions f(x) = -1(2|(-4((-2x - 2)/(2x - 3))^2 - 2((-2x - 2)/(2x - 3)) + 4)|) - 2 and g(x) = -5(-2cos(3π((1x)/(-3x - 2)) - 3) - 2) - 4 from x = -0.0 to x = 0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.2
MATH_EXPLORATIVE
algebra_func_area_train_0461
algebra_func_area
[ { "role": "user", "content": "Determine the area of the region enclosed by the graphs of f(x) = 3|((2(4(-2x^2 + 2) - 4))/(3(4(-2x^2 + 2) - 4) - 2)) - 2| + 2 and g(x) = (-3(-3|(3x^2 - 5x + 2) - 3| + 3) - 2)/(-1(-3|(3x^2 - 5x + 2) - 3| + 3) - 3) between the vertical lines x = 0.6 and x = 1.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
4.2
MATH_EXPLORATIVE
algebra_func_area_train_0462
algebra_func_area
[ { "role": "user", "content": "Find the area of the region bounded by the curves f(x) = -1|(-1(1x^2 + 5x + 4) + 4) - 2| + 2, g(x) = 1|(2x^2 - 2x + 2) - 2| - 1, x = -0.6, and x = 0.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.9
MATH_EXPLORATIVE
algebra_func_area_train_0463
algebra_func_area
[ { "role": "user", "content": "Calculate the area enclosed between the functions f(x) = -5((1x - 1)/(1x - 3)) - 3 and g(x) = 3x^2 + 4x - 4 from x = -0.7 to x = -0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.0
MATH_EXPLORATIVE
algebra_func_area_train_0464
algebra_func_area
[ { "role": "user", "content": "Find the area of the region bounded by the curves f(x) = 1cos(3π(-2|(4x^2 - 4x - 5) - 2| + 2) - 1) + 1, g(x) = (-1(-3cos(3πx - 2)) + 3)/(3(-3cos(3πx - 2)) - 2), x = 3.3, and x = 3.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.4
MATH_EXPLORATIVE
algebra_func_area_train_0465
algebra_func_area
[ { "role": "user", "content": "Determine the area of the region enclosed by the graphs of f(x) = 4(-2cos(1πx - 2) - 2) and g(x) = (3x - 1)/(-2x + 1) between the vertical lines x = 0.5 and x = 1.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
12.3
MATH_EXPLORATIVE
algebra_func_area_train_0466
algebra_func_area
[ { "role": "user", "content": "Calculate the area enclosed between the functions f(x) = (-2(-3x^2 - 2x - 2) - 1)/(-2(-3x^2 - 2x - 2)) and g(x) = 1|x + 3| - 1 from x = -5.0 to x = -1.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
3.9
MATH_EXPLORATIVE
algebra_func_area_train_0467
algebra_func_area
[ { "role": "user", "content": "Determine the area of the region enclosed by the graphs of f(x) = -5((-1(-3|(1x^2 + 4x + 2)| + 1))/(2(-3|(1x^2 + 4x + 2)| + 1))) + 3 and g(x) = (1(-5(2|x| - 3) - 4) + 3)/(1(-5(2|x| - 3) - 4) + 2) between the vertical lines x = -1.3 and x = 1.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
13.7
MATH_EXPLORATIVE
algebra_func_area_train_0468
algebra_func_area
[ { "role": "user", "content": "Determine the area of the region enclosed by the graphs of f(x) = -2|(-1sin(1πx) + 1) - 2| + 3 and g(x) = 1x^2 - 4 between the vertical lines x = -2.6 and x = 2.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
15.4
MATH_EXPLORATIVE
algebra_func_area_train_0469
algebra_func_area
[ { "role": "user", "content": "Determine the area of the region enclosed by the graphs of f(x) = 3sin(2π(-3|x - 2| + 3) - 2) + 1 and g(x) = (1x - 1)/(1x + 1) between the vertical lines x = 4.6 and x = 4.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.2
MATH_EXPLORATIVE
algebra_func_area_train_0470
algebra_func_area
[ { "role": "user", "content": "Determine the area of the region enclosed by the graphs of f(x) = -2sin(1π(-1(1|(1x - 2) - 1| + 1)^2 - 5) + 1) - 1 and g(x) = (3(2|(3x^2 + 4x - 2) + 3|) - 2)/(-3(2|(3x^2 + 4x - 2) + 3|)) between the vertical lines x = -3.6 and x = -3.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.1
MATH_EXPLORATIVE
algebra_func_area_train_0471
algebra_func_area
[ { "role": "user", "content": "Calculate the area enclosed between the functions f(x) = -2|(1(-2((1x - 1)/(-3x + 1))^2 + 2) + 4)| + 1 and g(x) = 2|(-4((-1x - 2)/(-3x + 4))^2 - 5((-1x - 2)/(-3x + 4)) - 2) + 2| - 3 from x = 0.2 to x = 0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
-6.5
MATH_EXPLORATIVE
algebra_func_area_train_0472
algebra_func_area
[ { "role": "user", "content": "Calculate the area enclosed between the functions f(x) = (3(3|x - 3| + 1) - 3)/(1(3|x - 3| + 1) + 2) and g(x) = -3x^2 - 3x + 3 from x = -1.2 to x = 0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
1.3
MATH_EXPLORATIVE
algebra_func_area_train_0473
algebra_func_area
[ { "role": "user", "content": "Determine the area of the region enclosed by the graphs of f(x) = -1(2sin(2π(-1|x + 2| - 1)) + 2) and g(x) = -3|(2e^(-2x))| - 2 between the vertical lines x = 3.5 and x = 4.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.6
MATH_EXPLORATIVE
algebra_func_area_train_0474
algebra_func_area
[ { "role": "user", "content": "Calculate the area enclosed between the functions f(x) = 1(-3|(-1(-1sin(3πx - 2))^2 - 4) + 3| - 1) - 2 and g(x) = -1|(1e^(1(3x^2 - 3x + 1)) + 3) - 1| from x = -0.1 to x = 1.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
4.5
MATH_EXPLORATIVE
algebra_func_area_train_0475
algebra_func_area
[ { "role": "user", "content": "Determine the area of the region enclosed by the graphs of f(x) = (1(-1|(-4(5x)^2 - 4(5x) + 4)| + 3) - 3)/(-1(-1|(-4(5x)^2 - 4(5x) + 4)| + 3) - 3) and g(x) = 1e^(1(2|(-4x^2 + 3x + 1) - 1| - 2)) 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}" } ]
0.0
MATH_EXPLORATIVE
algebra_func_area_train_0476
algebra_func_area
[ { "role": "user", "content": "Find the area of the region bounded by the curves f(x) = 1sin(2π(-1x^2 + 5x + 4) - 2) + 2, g(x) = (3x + 2)/(-1x - 2), x = -1.2, and x = -1.0999999999999999. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.0
MATH_EXPLORATIVE
algebra_func_area_train_0477
algebra_func_area
[ { "role": "user", "content": "Determine the area of the region enclosed by the graphs of f(x) = -5(4((-2(2|x + 1|) + 2)/(3(2|x + 1|) - 1)) - 4)^2 - 2(4((-2(2|x + 1|) + 2)/(3(2|x + 1|) - 1)) - 4) + 4 and g(x) = 1cos(3π((-1(-1|x - 2| + 3) + 3)/(3(-1|x - 2| + 3) + 3)) + 3) - 3 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}" } ]
29.5
MATH_EXPLORATIVE
algebra_func_area_train_0478
algebra_func_area
[ { "role": "user", "content": "Calculate the area enclosed between the functions f(x) = 4((1(1|(-1x^2 + 3) + 1| + 3) - 3)/(1(1|(-1x^2 + 3) + 1| + 3))) - 2 and g(x) = -1e^(1((2(-2x - 2))/(2(-2x - 2) - 1))) + 3 from x = -2.5 to x = -1.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.4
MATH_EXPLORATIVE
algebra_func_area_train_0479
algebra_func_area
[ { "role": "user", "content": "Calculate the area enclosed between the functions f(x) = 3(1sin(1πx)) - 5 and g(x) = -2|x - 2| + 3 from x = -2.0 to x = -1.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
1.1
MATH_EXPLORATIVE
algebra_func_area_train_0480
algebra_func_area
[ { "role": "user", "content": "Calculate the area enclosed between the functions f(x) = (-1(-5x^2 + 3x + 5) + 2)/(2(-5x^2 + 3x + 5) + 2) and g(x) = 2|x - 3| - 1 from x = 1.4 to x = 2.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
3.2
MATH_EXPLORATIVE
algebra_func_area_train_0481
algebra_func_area
[ { "role": "user", "content": "Calculate the area enclosed between the functions f(x) = -3(2x - 1)^2 + 2(2x - 1) + 5 and g(x) = (1x + 2)/(1x + 2) from x = 0.1 to x = 1.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
3.5
MATH_EXPLORATIVE
algebra_func_area_train_0482
algebra_func_area
[ { "role": "user", "content": "Determine the area of the region enclosed by the graphs of f(x) = (1(-4(2|(-1x^2 + 5x - 5) + 2| - 3) - 3))/(2(-4(2|(-1x^2 + 5x - 5) + 2| - 3) - 3) - 3) and g(x) = -1((-1(3|x - 1| - 1))/(2(3|x - 1| - 1) + 1))^2 + 1((-1(3|x - 1| - 1))/(2(3|x - 1| - 1) + 1)) - 1 between the vertical lines x = 0.4 and x = 1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
11.5
MATH_EXPLORATIVE
algebra_func_area_train_0483
algebra_func_area
[ { "role": "user", "content": "Find the area of the region bounded by the curves f(x) = 3sin(2π(-1x - 5) + 2) + 2, g(x) = (3x - 3)/(-2x + 3), x = 0.5, and x = 0.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.0
MATH_EXPLORATIVE
algebra_func_area_train_0484
algebra_func_area
[ { "role": "user", "content": "Find the area of the region bounded by the curves f(x) = (3(-1(3|x - 2|) - 2) - 1)/(3(-1(3|x - 2|) - 2) - 2), g(x) = (-3(3cos(2πx - 2) + 3) + 2)/(-2(3cos(2πx - 2) + 3) + 1), x = 2.0, and x = 2.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.3
MATH_EXPLORATIVE
algebra_func_area_train_0485
algebra_func_area
[ { "role": "user", "content": "Determine the area of the region enclosed by the graphs of f(x) = -2((-2(-3e^(1x) - 3) - 3)/(-3(-3e^(1x) - 3) - 1))^2 + 3 and g(x) = -4(-1|x - 1| - 1)^2 - 5(-1|x - 1| - 1) + 3 between the vertical lines x = 0.6 and x = 1.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.7
MATH_EXPLORATIVE
algebra_func_area_train_0486
algebra_func_area
[ { "role": "user", "content": "Calculate the area enclosed between the functions f(x) = (1(1cos(1πx - 1)))/(3(1cos(1πx - 1)) - 2) and g(x) = 3x^2 - 2x - 3 from x = 1.4 to x = 2.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
2.6
MATH_EXPLORATIVE
algebra_func_area_train_0487
algebra_func_area
[ { "role": "user", "content": "Calculate the area enclosed between the functions f(x) = (3(-2|x - 3| + 2))/(2(-2|x - 3| + 2) - 3) and g(x) = 3|x + 3| + 3 from x = 2.8 to x = 3.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
4.2
MATH_EXPLORATIVE
algebra_func_area_train_0488
algebra_func_area
[ { "role": "user", "content": "Calculate the area enclosed between the functions f(x) = (3(1(-3(-3cos(3πx - 3) - 2)^2 + 4(-3cos(3πx - 3) - 2) + 3) - 3) - 2)/(-2(1(-3(-3cos(3πx - 3) - 2)^2 + 4(-3cos(3πx - 3) - 2) + 3) - 3) - 2) and g(x) = -3|(-5((2x - 2)/(-3x - 2)) - 3) + 2| - 2 from x = -4.6 to x = -4.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
6.3
MATH_EXPLORATIVE
algebra_func_area_train_0489
algebra_func_area
[ { "role": "user", "content": "Calculate the area enclosed between the functions f(x) = (1(2cos(3π(2|(5x) + 1| + 2) - 2) + 1) + 2)/(-2(2cos(3π(2|(5x) + 1| + 2) - 2) + 1) - 2) and g(x) = -1|(3cos(3π((-3x + 2)/(-3x + 2)) + 3) + 1)| - 3 from x = -1.4 to x = -1.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
15.7
MATH_EXPLORATIVE
algebra_func_area_train_0490
algebra_func_area
[ { "role": "user", "content": "Find the area of the region bounded by the curves f(x) = 3|(3sin(1πx) - 3) - 2| - 2, g(x) = -3x^2 + 4x + 4, x = 0.4, and x = 0.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.3
MATH_EXPLORATIVE
algebra_func_area_train_0491
algebra_func_area
[ { "role": "user", "content": "Determine the area of the region enclosed by the graphs of f(x) = (3(1e^(2x) - 2) - 3)/(-1(1e^(2x) - 2) + 2) and g(x) = -1|x + 1| + 2 between the vertical lines x = 0.6 and x = 4.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
17.4
MATH_EXPLORATIVE
algebra_func_area_train_0492
algebra_func_area
[ { "role": "user", "content": "Determine the area of the region enclosed by the graphs of f(x) = 2sin(2π(-2|x| + 1) - 3) + 1 and g(x) = -3x - 1 between the vertical lines x = -0.5 and x = -0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.1
MATH_EXPLORATIVE
algebra_func_area_train_0493
algebra_func_area
[ { "role": "user", "content": "Find the area of the region bounded by the curves f(x) = 2sin(2π(4(-5x + 3)^2 - 2) + 3) - 2, g(x) = 1sin(3π(1x^2 + 4x) + 2) - 1, x = 0.9, and x = 1.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.2
MATH_EXPLORATIVE
algebra_func_area_train_0494
algebra_func_area
[ { "role": "user", "content": "Calculate the area enclosed between the functions f(x) = -2(-2e^(-2((3x - 2)/(-2x - 2))) + 3)^2 + 1(-2e^(-2((3x - 2)/(-2x - 2))) + 3) - 1 and g(x) = -1e^(1(1x - 1)) - 2 from x = 0.6 to x = 1.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.7
MATH_EXPLORATIVE
algebra_func_area_train_0495
algebra_func_area
[ { "role": "user", "content": "Determine the area of the region enclosed by the graphs of f(x) = (-3(-3e^(1(3|(-1x^2 - 5x + 3) + 3| - 2)) - 1))/(-2(-3e^(1(3|(-1x^2 - 5x + 3) + 3| - 2)) - 1) + 3) and g(x) = -3sin(3π(-4((-1x - 3)/(-3x + 2)) + 4) - 1) between the vertical lines x = 0.2 and x = 0.30000000000000004. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.2
MATH_EXPLORATIVE
algebra_func_area_train_0496
algebra_func_area
[ { "role": "user", "content": "Calculate the area enclosed between the functions f(x) = -3sin(2π(-1|x - 3| - 2) - 3) + 2 and g(x) = 1x^2 + 2x - 5 from x = 2.0 to x = 2.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.1
MATH_EXPLORATIVE
algebra_func_area_train_0497
algebra_func_area
[ { "role": "user", "content": "Determine the area of the region enclosed by the graphs of f(x) = 1(3cos(3π(3(-2|x + 2| + 2)^2 + 4(-2|x + 2| + 2) + 2)) - 3) + 1 and g(x) = 3sin(2π(4((-1x - 3)/(-2x - 1)) - 1) - 2) + 2 between the vertical lines x = -5.0 and x = -4.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.3
MATH_EXPLORATIVE
algebra_func_area_train_0498
algebra_func_area
[ { "role": "user", "content": "Calculate the area enclosed between the functions f(x) = -5(-1cos(3πx + 2) + 1) + 3 and g(x) = (2x - 3)/(-3x - 2) from x = 1.0 to x = 1.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.4
MATH_EXPLORATIVE
algebra_func_area_train_0499
algebra_func_area
[ { "role": "user", "content": "Determine the area of the region enclosed by the graphs of f(x) = (-3(3sin(2πx + 2) + 3))/(2(3sin(2πx + 2) + 3) - 3) and g(x) = 2x - 3 between the vertical lines x = 0.2 and x = 2.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
14.1
MATH_EXPLORATIVE