{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2e^(1(-1(-2|x| + 1)^2 - 5(-2|x| + 1) - 3)) - 1 and g(x) = (-3(-2x^2 - 4))/(-3(-2x^2 - 4) - 1) between the vertical lines x = -0.8 and x = 0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-1(-4(3x^2 - 4x + 1) + 3) + 3)/(2(-4(3x^2 - 4x + 1) + 3) + 1), g(x) = 5(-4x - 5) - 2, x = 0.0, and x = 1.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "54.4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 5(-2(1sin(1\u03c0x - 1) - 1)^2 + 5(1sin(1\u03c0x - 1) - 1) - 1)^2 + 5(-2(1sin(1\u03c0x - 1) - 1)^2 + 5(1sin(1\u03c0x - 1) - 1) - 1) - 4 and g(x) = 1e^(2(-3x + 2)) - 2 from x = 4.7 to x = 4.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2sin(3\u03c0((-2(1x^2 - 1x - 4) + 1)/(2(1x^2 - 1x - 4) - 1))) and g(x) = (2(-1x^2 - 3x - 2) + 1)/(1(-1x^2 - 3x - 2)) between the vertical lines x = -2.4 and x = -0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "64.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -4(-4(-3x^2 + 3x + 2) - 5)^2 - 3(-4(-3x^2 + 3x + 2) - 5) + 5 and g(x) = (2(1e^(-2x)) + 1)/(-1(1e^(-2x)) + 2) between the vertical lines x = -0.7 and x = -0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-3(1(3e^(-1x) - 1)^2 - 3(3e^(-1x) - 1) + 2) + 2)/(2(1(3e^(-1x) - 1)^2 - 3(3e^(-1x) - 1) + 2) - 1), g(x) = 2e^(2((3x + 2)/(-1x + 3))) + 1, x = -0.1, and x = 0.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -4(2(4x) - 5)^2 - 1, g(x) = 2sin(2\u03c0(4x^2 - 4x - 4) + 3) - 3, x = 0.5, and x = 0.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3(-2(3sin(1\u03c0x - 2) - 2)^2 + 3(3sin(1\u03c0x - 2) - 2) + 2)^2 + 1(-2(3sin(1\u03c0x - 2) - 2)^2 + 3(3sin(1\u03c0x - 2) - 2) + 2) - 3 and g(x) = 3((-2x + 3)/(-3x)) - 4 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}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1(-2sin(2\u03c0(3x - 1) - 3) - 2)^2 - 3(-2sin(2\u03c0(3x - 1) - 3) - 2) + 2 and g(x) = 5(5x^2 + 3x - 1) - 4 from x = -1.4 to x = -1.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.4", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2|(-2sin(3\u03c0(-1x^2 - 1x + 4) - 1) - 2) - 2| + 3, g(x) = 5((-1x + 3)/(-3x - 3)) + 1, x = -2.1, and x = -2.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2sin(3\u03c0(3|(-2|x| + 1) - 3| - 3) + 1) - 2 and g(x) = 2|(1x^2 - 2x - 3) - 2| - 3 from x = -1.6 to x = -1.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-1(-1((-2x - 3)/(-1x))^2 + 2((-2x - 3)/(-1x))) + 3)/(1(-1((-2x - 3)/(-1x))^2 + 2((-2x - 3)/(-1x))) + 3) and g(x) = -5(3|x + 3|) + 3 from x = -3.2 to x = -2.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -5(-1(3|x - 3| - 2)^2 - 4(3|x - 3| - 2) + 4) - 1, g(x) = (1(-2x - 4) + 2)/(3(-2x - 4) + 2), x = 2.0, and x = 4.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "52.9", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-3(5((3x)/(1x + 1))^2 + 1((3x)/(1x + 1))))/(3(5((3x)/(1x + 1))^2 + 1((3x)/(1x + 1))) - 1), g(x) = -1cos(3\u03c0(1x) + 2) - 1, x = 1.0, and x = 1.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2sin(1\u03c0((2(2x^2 + 3x - 2))/(2(2x^2 + 3x - 2) + 2)) - 3) - 1 and g(x) = 1cos(2\u03c0((-1x + 2)/(1x)) + 2) + 1 from x = -0.2 to x = -0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-1(-4(-1x - 2) - 2) - 3)/(2(-4(-1x - 2) - 2) + 1) and g(x) = 2sin(3\u03c0(2x - 1) + 3) + 1 from x = 2.3 to x = 2.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2(-3|(2sin(2\u03c0x - 1) - 2) + 1| + 3)^2 - 4(-3|(2sin(2\u03c0x - 1) - 2) + 1| + 3) - 4 and g(x) = 2|(-3|x - 1| + 2) + 3| - 2 between the vertical lines x = -2.9 and x = -2.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7.6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (2(-3cos(1\u03c0((-2x - 2)/(-2x + 1)) - 3)) - 1)/(-3(-3cos(1\u03c0((-2x - 2)/(-2x + 1)) - 3)) - 2) and g(x) = (-2((2x + 3)/(-2x + 3)) - 1)/(3((2x + 3)/(-2x + 3)) + 3) from x = -1.6 to x = -0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 3e^(1(-4(-1|x - 3| - 2)^2 - 5(-1|x - 3| - 2) - 3)) and g(x) = 1|(2cos(2\u03c0x - 1) + 1)| between the vertical lines x = -4.2 and x = -3.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.4", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 4((2((-1x + 1)/(-2x - 1)) - 3)/(-3((-1x + 1)/(-2x - 1)) + 2)) - 2, g(x) = -3cos(1\u03c0(3x + 1) + 3) - 3, x = -0.8, and x = -0.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2(2(1cos(3\u03c0x - 1))^2 + 2(1cos(3\u03c0x - 1)) - 2)^2 + 3(2(1cos(3\u03c0x - 1))^2 + 2(1cos(3\u03c0x - 1)) - 2) - 3 and g(x) = -4(4x^2 + 3x - 3) - 1 from x = 0.6 to x = 0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 5(-3((-3x + 1)/(-2x + 3)) + 1) - 3 and g(x) = 5(-1cos(3\u03c0x + 2)) - 4 between the vertical lines x = -0.0 and x = 0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-2(1|(1cos(3\u03c0x - 3) + 3) - 2| + 1) - 3)/(1(1|(1cos(3\u03c0x - 3) + 3) - 2| + 1) + 1) and g(x) = -1(2|x + 1|) - 2 from x = -1.2 to x = -0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-3(-3|(3e^(2x) - 1) - 3|) - 1)/(1(-3|(3e^(2x) - 1) - 3|) - 3), g(x) = -1|(5x + 5) - 1|, x = -1.3, and x = -0.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2cos(2\u03c0(5((1x - 2)/(2x - 3))^2 + 2((1x - 2)/(2x - 3)) - 1) - 3) - 2 and g(x) = -3(-2sin(1\u03c0x - 2) + 1)^2 + 1(-2sin(1\u03c0x - 2) + 1) + 2 between the vertical lines x = 1.2 and x = 1.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -5(1|(-2|x - 3|)| - 1), g(x) = -1|(-2cos(2\u03c0x - 3) + 2) - 1| + 2, x = 2.7, and x = 3.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-3(2|(2cos(2\u03c0x - 1) - 2)| - 3) + 3)/(-3(2|(2cos(2\u03c0x - 1) - 2)| - 3) - 3) and g(x) = -5(-1x + 3)^2 + 4(-1x + 3) + 3 from x = 4.0 to x = 4.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 4((1(3cos(3\u03c0x - 3) - 1) - 1)/(-1(3cos(3\u03c0x - 3) - 1) - 3)) + 3 and g(x) = (1(-2sin(1\u03c0x - 1) + 3) - 1)/(-3(-2sin(1\u03c0x - 1) + 3) + 4) 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}", "role": "user"}], "ground_truth": "18.8", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1(-1cos(1\u03c0((1x + 2)/(3x + 2)) - 2) - 1)^2 and g(x) = 2sin(3\u03c0((1x + 2)/(-2x - 2)) - 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}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2|(-1(-1cos(1\u03c0x - 1) - 1) - 5) + 2| + 3 and g(x) = 2e^(1(-1x + 2)) from x = 4.0 to x = 4.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (1((2((-1x)/(-3x - 1)) + 2)/(1((-1x)/(-3x - 1)))) + 2)/(-1((2((-1x)/(-3x - 1)) + 2)/(1((-1x)/(-3x - 1)))) - 3) and g(x) = 3cos(1\u03c0((-3x - 2)/(-1x - 2)) + 3) - 1 from x = -2.0 to x = -1.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1(1((1x)/(2x + 2))^2 - 1((1x)/(2x + 2)) - 4)^2 - 5(1((1x)/(2x + 2))^2 - 1((1x)/(2x + 2)) - 4) and g(x) = 3|(3e^(-1x)) + 3| - 2 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}", "role": "user"}], "ground_truth": "8.9", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3|(-2(1x^2 - 1x)) + 2| - 3, g(x) = 3e^(-1((3x - 1)/(-1x + 2))) - 2, x = -1.4, and x = -0.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (3((-1(-1|x + 1| + 1) - 3)/(-2(-1|x + 1| + 1) + 3)) - 1)/(2((-1(-1|x + 1| + 1) - 3)/(-2(-1|x + 1| + 1) + 3)) - 3) and g(x) = -1sin(2\u03c0((2x)/(-1x - 1))) from x = 0.1 to x = 0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1(5(-3e^(-1x) + 1) + 1) - 1, g(x) = -2cos(2\u03c0(4x + 5) - 1) + 2, x = 0.5, and x = 0.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 3sin(3\u03c0(3(-1x - 4) + 3) + 1) - 3 and g(x) = -3(1|x| - 2)^2 - 3(1|x| - 2) + 4 between the vertical lines x = -2.8 and x = -2.6999999999999997. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-3(2cos(1\u03c0((2x)/(-1x - 1)) - 1) + 3) - 1)/(-2(2cos(1\u03c0((2x)/(-1x - 1)) - 1) + 3) + 3), g(x) = 3(-2e^(-2x) - 1), x = -0.4, and x = 0.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16.9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2(-3|((2x - 2)/(3x - 2)) - 2| + 3)^2 - 5(-3|((2x - 2)/(3x - 2)) - 2| + 3) - 1 and g(x) = 1sin(2\u03c0(-5x^2 - 1) + 3) + 1 from x = -0.5 to x = -0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3e^(1(-1|(-1x + 5) + 1| - 3)), g(x) = 2|(-1x + 2)| - 1, x = 1.5, and x = 2.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-1(3|(-3sin(1\u03c0x - 3) - 2) - 2| - 1))/(1(3|(-3sin(1\u03c0x - 3) - 2) - 2| - 1) - 3) and g(x) = -4(-1e^(1x) + 3)^2 + 4(-1e^(1x) + 3) - 3 from x = 0.3 to x = 0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -3|((2(-2x^2 - 4x - 5) - 2)/(2(-2x^2 - 4x - 5) + 1)) + 1| + 3, g(x) = (2(-2x^2 + 4x - 1))/(-2(-2x^2 + 4x - 1) - 3), x = -0.2, and x = 2.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3(5(-4x^2 + 5x)^2 - 4)^2 + 3(5(-4x^2 + 5x)^2 - 4) - 1, g(x) = -3((2x + 2)/(2x + 2))^2 + 3, x = -0.1, and x = 0.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1sin(1\u03c0(1((-3x - 1)/(1x + 1))^2 + 3((-3x - 1)/(1x + 1)) - 3) - 3) - 1 and g(x) = 3|((1x)/(3x)) - 1| - 3 from x = -1.7 to x = -1.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 3((-2(-2cos(3\u03c0x + 2) + 1) + 3)/(-2(-2cos(3\u03c0x + 2) + 1)))^2 - 5((-2(-2cos(3\u03c0x + 2) + 1) + 3)/(-2(-2cos(3\u03c0x + 2) + 1))) - 4 and g(x) = 2cos(1\u03c0(-3x) - 1) + 1 from x = 4.6 to x = 5.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3cos(3\u03c0(-1|(-3x + 5) - 1| + 1) + 2) - 2 and g(x) = (3(3sin(3\u03c0x - 3) + 3) - 3)/(-3(3sin(3\u03c0x - 3) + 3) - 3) from x = 4.6 to x = 4.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2|(-2e^(1((1x + 2)/(-1x))) - 1) - 2| - 3 and g(x) = (-2(2cos(1\u03c0x - 1) + 1) - 1)/(3(2cos(1\u03c0x - 1) + 1) + 2) between the vertical lines x = 1.1 and x = 1.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-2((1(3|x + 1| + 1) - 3)/(-1(3|x + 1| + 1) - 2)) - 1)/(-1((1(3|x + 1| + 1) - 3)/(-1(3|x + 1| + 1) - 2)) - 2) and g(x) = 1(2sin(1\u03c0x + 3) - 2)^2 - 2(2sin(1\u03c0x + 3) - 2) - 3 between the vertical lines x = 1.9 and x = 3.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15.6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1|(-3|(2x - 5)| + 1) + 2| + 1 and g(x) = 4(-5x^2 - 1x + 2) + 5 from x = -1.4 to x = 0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37.9", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1(3sin(2\u03c0(-1x) - 1) - 3)^2 - 5(3sin(2\u03c0(-1x) - 1) - 3) + 4, g(x) = 3(-3cos(2\u03c0x + 1))^2 - 1(-3cos(2\u03c0x + 1)) + 4, x = -3.1, and x = -2.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17.7", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1((2(-2|x| + 1) + 3)/(-1(-2|x| + 1) + 2))^2 + 4((2(-2|x| + 1) + 3)/(-1(-2|x| + 1) + 2)) - 1 and g(x) = -3|(-1|x + 1| + 2)| + 1 between the vertical lines x = -1.8 and x = 1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28.6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 3(-2(4x^2 + 2x - 2) - 1) - 1 and g(x) = 1|(2cos(1\u03c0x + 2) + 2)| - 1 from x = -0.8 to x = 0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6.4", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3(2|(5x^2 - 5x - 4) - 1| - 2)^2 - 5(2|(5x^2 - 5x - 4) - 1| - 2) - 3, g(x) = 3|(-5x + 1)| - 2, x = -0.6, and x = -0.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.9", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-2(2cos(3\u03c0(1x + 2) + 1)) + 3)/(1(2cos(3\u03c0(1x + 2) + 1))), g(x) = 2(-4x^2 - 3)^2 + 5(-4x^2 - 3) - 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}", "role": "user"}], "ground_truth": "8.6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1(5(-2|x - 1| + 3) + 1)^2 + 3(5(-2|x - 1| + 3) + 1) and g(x) = -3cos(2\u03c0((-2x - 2)/(1x - 2))) - 2 from x = 2.9 to x = 3.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-1(3sin(1\u03c0((2x - 2)/(1x - 2)) - 2) + 1) - 2)/(3(3sin(1\u03c0((2x - 2)/(1x - 2)) - 2) + 1) + 2) and g(x) = 1|((-2x - 1)/(-2x + 3)) + 2| from x = 2.2 to x = 2.3000000000000003. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1|(1e^(1(2|x - 2|)) - 3) - 2| + 2, g(x) = (-1((2x)/(-1x - 1)) + 3)/(1((2x)/(-1x - 1))), x = 0.0, and x = 0.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (3(3|(2sin(3\u03c0x + 1) - 3) + 3| - 2) + 3)/(1(3|(2sin(3\u03c0x + 1) - 3) + 3| - 2) + 2) and g(x) = -2cos(1\u03c0(1x - 5) + 2) - 3 from x = 2.9 to x = 3.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-1(-3(-5x^2 + 4x - 2) - 5) + 1)/(1(-3(-5x^2 + 4x - 2) - 5) + 1) and g(x) = -2(-3x^2 - 2x) + 1 from x = 0.1 to x = 0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "23.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-1(-1|(5x + 2) - 2| + 3) - 2)/(-2(-1|(5x + 2) - 2| + 3) + 3) and g(x) = 3(3x^2 + 5x - 5) - 5 between the vertical lines x = -2.6 and x = -0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "49.8", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (2(-2|(1cos(1\u03c0x + 1) - 3) + 2| + 3) + 1)/(1(-2|(1cos(1\u03c0x + 1) - 3) + 2| + 3) - 3), g(x) = -3|(1e^(2x) + 2) + 2| + 3, x = -0.1, and x = 1.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42.8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1|((-3(3e^(1x) - 3) - 3)/(-1(3e^(1x) - 3) - 2)) - 2| + 1 and g(x) = 3(2cos(3\u03c0x + 1) + 2)^2 - 3(2cos(3\u03c0x + 1) + 2) from x = -5.0 to x = -4.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3|(-1cos(2\u03c0(-4x - 3) - 1)) + 2| + 1, g(x) = 2(2x - 4) + 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}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-2(-3|((-3x + 3)/(-1x + 2)) - 2| + 3) + 2)/(-2(-3|((-3x + 3)/(-1x + 2)) - 2| + 3) + 1), g(x) = -2e^(1(1x + 2)) + 2, x = -2.4, and x = 0.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22.8", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1cos(2\u03c0(-3(-1x - 4)^2 - 3)) + 1, g(x) = 3(-1e^(1x) + 2)^2 + 5(-1e^(1x) + 2) - 3, x = 0.4, and x = 1.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-1(1|((-2x - 1)/(3x)) + 3| + 3) - 3)/(-1(1|((-2x - 1)/(3x)) + 3| + 3) - 2), g(x) = 1(1x^2 + 5x + 2) + 2, x = -4.3, and x = -0.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2e^(1((-1(-1x - 5) - 2)/(1(-1x - 5)))) + 1 and g(x) = 3(4x^2 - 4x - 1) between the vertical lines x = -0.2 and x = 1.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.6", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -5(-2(1x^2 - 4x + 5) - 1) + 2 and g(x) = 2(3|x - 3| - 3)^2 - 4(3|x - 3| - 3) - 2 between the vertical lines x = -0.5 and x = 3.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "53.7", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (3(-2|(-3x + 4) - 3| - 2) - 2)/(3(-2|(-3x + 4) - 3| - 2) - 2) and g(x) = -1((1x + 1)/(-2x - 1))^2 - 1((1x + 1)/(-2x - 1)) + 4 between the vertical lines x = -0.6 and x = -0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.8", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1(1|(5x^2 - 4x + 1) - 2| - 1)^2 + 2(1|(5x^2 - 4x + 1) - 2| - 1), g(x) = 2e^(-1(2x^2 + 5x + 5)) + 3, x = -0.5, and x = 1.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3(-1(-1x)) + 4, g(x) = -4(3e^(-1x) - 3)^2 + 5(3e^(-1x) - 3) + 2, x = -0.3, and x = -0.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-1(2cos(2\u03c0(1x^2 - 2x - 3) - 2) + 3) - 3)/(2(2cos(2\u03c0(1x^2 - 2x - 3) - 2) + 3) - 1) and g(x) = -5((-1x + 2)/(2x - 1))^2 + 1((-1x + 2)/(2x - 1)) + 5 between the vertical lines x = -0.7 and x = -0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3cos(2\u03c0(2|(1x - 4) - 3| - 3) - 1) - 1 and g(x) = -3cos(3\u03c0(2|x - 2| - 2) + 1) - 3 from x = -2.2 to x = -2.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 4(-2sin(2\u03c0((1x - 3)/(-1x - 1)) + 3) + 3) + 1, g(x) = (1(2x^2 - 4x - 5) - 3)/(-3(2x^2 - 4x - 5) - 1), x = -0.8, and x = -0.7000000000000001. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.6", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-3(2|(2cos(3\u03c0x + 1) + 3) - 2|) + 2)/(1(2|(2cos(3\u03c0x + 1) + 3) - 2|) + 1) and g(x) = 3cos(1\u03c0((-1x - 3)/(1x - 2)) + 1) - 1 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}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-2(-4(2cos(1\u03c0x - 3) - 2)^2 + 1(2cos(1\u03c0x - 3) - 2) - 4) - 1)/(2(-4(2cos(1\u03c0x - 3) - 2)^2 + 1(2cos(1\u03c0x - 3) - 2) - 4) + 2) and g(x) = -3sin(1\u03c0(2|x + 2| + 2)) - 1 between the vertical lines x = 4.0 and x = 4.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3sin(3\u03c0(3|(1x^2 - 3x - 3) + 3| + 1) + 2) + 2, g(x) = 1(-1|x + 2|)^2 - 4(-1|x + 2|) + 4, x = -2.0, and x = -1.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3sin(2\u03c0(2(1x - 4) - 1) - 1) - 3, g(x) = (1(-1|x + 2| - 1) + 3)/(-1(-1|x + 2| - 1) + 2), x = 3.8, and x = 4.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -5(3(3|x - 3| - 2)^2 - 2(3|x - 3| - 2) - 3) + 1 and g(x) = -5(2sin(3\u03c0x - 3) - 1)^2 + 5(2sin(3\u03c0x - 3) - 1) + 1 between the vertical lines x = 3.3 and x = 4.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31.9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1(-3(-2|x - 1| + 2)^2 - 4(-2|x - 1| + 2) + 3)^2 + 5 and g(x) = (-2(1x) - 2)/(2(1x)) from x = 2.7 to x = 3.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-1(-2(-1x - 2)^2 - 4(-1x - 2)) + 3)/(-3(-2(-1x - 2)^2 - 4(-1x - 2)) + 2) and g(x) = (1(2sin(1\u03c0x)) + 1)/(-2(2sin(1\u03c0x)) + 3) between the vertical lines x = 1.0 and x = 2.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3|(-3sin(2\u03c0(-5x - 1) - 1) - 3) + 1| - 2 and g(x) = -1|((2x - 3)/(1x - 3)) - 1| + 1 between the vertical lines x = 3.8 and x = 3.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2|(-3cos(1\u03c0(4x^2 + 1x - 3) - 1) - 2)| + 2 and g(x) = (-3(-1x - 2) - 3)/(2(-1x - 2) - 1) from x = -4.6 to x = -4.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2|((-1(-3x^2 + 1) - 2)/(-2(-3x^2 + 1) - 1)) + 1| - 2 and g(x) = (-3(-3x^2 + 5x - 4) + 2)/(-1(-3x^2 + 5x - 4) + 3) from x = 0.0 to x = 0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6.4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-3(-2sin(1\u03c0(-2|x + 2| + 3) - 3)) + 2)/(-1(-2sin(1\u03c0(-2|x + 2| + 3) - 3)) + 3) and g(x) = 1(-1e^(-2x) - 3)^2 + 3(-1e^(-2x) - 3) + 1 from x = 3.6 to x = 4.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2|(3(-4x - 1) + 1) - 3| + 3 and g(x) = -2sin(1\u03c0(-2x - 5)) - 3 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}", "role": "user"}], "ground_truth": "1.4", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2cos(1\u03c0(3(3|x - 2|) - 1) - 2) - 2, g(x) = -3(4x + 2), x = -0.4, and x = -0.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 3(-2sin(3\u03c0((-2x - 2)/(2x - 1)) - 3) + 1)^2 - 3(-2sin(3\u03c0((-2x - 2)/(2x - 1)) - 3) + 1) - 4 and g(x) = 1|(1|x - 3| + 1) + 3| + 1 between the vertical lines x = -0.1 and x = 0.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-1(-2(-5x^2 + 3x + 2) + 2) - 2)/(-3(-2(-5x^2 + 3x + 2) + 2) - 3) and g(x) = (-3(-2sin(1\u03c0x + 3) + 1) + 2)/(2(-2sin(1\u03c0x + 3) + 1) - 3) between the vertical lines x = -0.9 and x = -0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1(-5(-2cos(1\u03c0x + 3) - 2) - 1) + 1 and g(x) = 2sin(3\u03c0(-3|x - 3| - 2) - 2) - 1 from x = 0.0 to x = 2.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1((-2(-1|x - 3| - 1) - 3)/(2(-1|x - 3| - 1))) + 1, g(x) = -3(5x^2 - 3x - 4) - 5, x = -0.4, and x = 1.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1(-3((3x + 1)/(2x))^2 + 4((3x + 1)/(2x)) + 1)^2 + 5(-3((3x + 1)/(2x))^2 + 4((3x + 1)/(2x)) + 1) - 3 and g(x) = -5(-3|x|) - 4 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}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-3(4(-4x^2 + 2x + 2) + 2) + 3)/(2(4(-4x^2 + 2x + 2) + 2) - 1), g(x) = -2cos(3\u03c0(-4x + 1) + 1) - 3, x = 3.7, and x = 3.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-3(-1|(2|x - 2|) + 1| + 3) + 3)/(-2(-1|(2|x - 2|) + 1| + 3) + 3) and g(x) = 2(3x^2 + 4x + 4) + 5 between the vertical lines x = 1.8 and x = 2.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19.4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-1(-2|(4x - 2) + 3| + 3))/(3(-2|(4x - 2) + 3| + 3) + 3) and g(x) = 2|(-3e^(1x) - 3) - 3| + 2 from x = -0.8 to x = 0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 4(1|((-2x + 1)/(2x - 3))| + 3)^2 + 2(1|((-2x + 1)/(2x - 3))| + 3) + 3 and g(x) = 2e^(2(-3x^2 - 4x + 1)) + 1 between the vertical lines x = -1.1 and x = -0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "82.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1(-5(3cos(3\u03c0x - 1) + 1) - 5)^2 - 2(-5(3cos(3\u03c0x - 1) + 1) - 5) + 4 and g(x) = (-1((2x + 2)/(2x + 2)) + 3)/(1((2x + 2)/(2x + 2)) + 1) between the vertical lines x = 3.0 and x = 3.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.4", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1(1sin(3\u03c0(3x^2 - 3x + 1)) - 3)^2 - 2(1sin(3\u03c0(3x^2 - 3x + 1)) - 3) + 5 and g(x) = 4(1x - 2)^2 + 3(1x - 2) + 2 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}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2|((-1(1|x - 3| - 2))/(2(1|x - 3| - 2) + 2)) + 1| - 3 and g(x) = (2(3x - 5) + 2)/(1(3x - 5) - 3) between the vertical lines x = 1.4 and x = 3.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "87.7", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2|(-1|(4x^2 + 2x) + 2| + 2) + 2| - 3 and g(x) = (1(-2|x + 1|) + 1)/(2(-2|x + 1|) - 1) between the vertical lines x = 0.2 and x = 0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (3((1(-2|x + 2| + 2) - 3)/(3(-2|x + 2| + 2) - 1)) + 3)/(-2((1(-2|x + 2| + 2) - 3)/(3(-2|x + 2| + 2) - 1)) + 1) and g(x) = 3cos(3\u03c0(-4x - 5) + 2) - 3 between the vertical lines x = -1.0 and x = -0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (3(4(2|x + 2| + 3)^2 + 5(2|x + 2| + 3) - 3) + 1)/(-2(4(2|x + 2| + 3)^2 + 5(2|x + 2| + 3) - 3)) and g(x) = -2sin(2\u03c0(2x^2 - 5) - 2) - 3 from x = -2.8 to x = -2.6999999999999997. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2(1(-2e^(2x)) + 2)^2 + 4(1(-2e^(2x)) + 2) - 5, g(x) = 2cos(2\u03c0(-2x^2 - 4x + 3) - 2) - 2, x = -0.2, and x = 0.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 4(-1sin(1\u03c0((1x - 2)/(-3x - 2)) + 1)) + 4, g(x) = 4(-3e^(-1x)) + 2, x = 2.6, and x = 3.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1(-2cos(3\u03c0((3x + 1)/(3x + 3)) + 2) + 1)^2 - 3(-2cos(3\u03c0((3x + 1)/(3x + 3)) + 2) + 1) + 5, g(x) = -2|(4x^2 + 4x - 4)|, x = -1.2, and x = -1.0999999999999999. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1|(-3(3sin(1\u03c0x + 1) - 3) + 2) - 1| - 3 and g(x) = (3(2sin(1\u03c0x + 1) + 1) - 3)/(3(2sin(1\u03c0x + 1) + 1) + 2) between the vertical lines x = 1.3 and x = 1.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16.7", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2e^(-2((1((-1x - 3)/(-2x + 1)) + 3)/(1((-1x - 3)/(-2x + 1)) + 1))) - 2, g(x) = (1(-4x^2 - 3x + 2))/(-3(-4x^2 - 3x + 2) - 3), x = 0.0, and x = 0.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-2(-1sin(1\u03c0((1x - 2)/(2x - 3)) + 2) - 3) - 3)/(-1(-1sin(1\u03c0((1x - 2)/(2x - 3)) + 2) - 3) + 3), g(x) = -3|((2x)/(-1x + 2)) - 2| + 2, x = 0.8, and x = 1.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-1((3(-3x^2 - 3x + 2) - 3)/(-2(-3x^2 - 3x + 2))) + 3)/(2((3(-3x^2 - 3x + 2) - 3)/(-2(-3x^2 - 3x + 2))) + 1), g(x) = 3|(-1|x + 1| + 1) - 1| - 3, x = -1.6, and x = 0.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3|(-2sin(1\u03c0(5x^2 - 1x - 4)) - 3) + 3| and g(x) = 4(1sin(1\u03c0x - 3) - 1)^2 - 3(1sin(1\u03c0x - 3) - 1) - 4 from x = 3.7 to x = 3.8000000000000003. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1|(5(2|x + 1|)^2 - 3(2|x + 1|) - 3) - 3| - 2 and g(x) = 1|(3sin(2\u03c0x + 3)) - 1| between the vertical lines x = -1.5 and x = -0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.8", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 5((-1(-2sin(2\u03c0x + 1)) - 2)/(2(-2sin(2\u03c0x + 1)) + 2)) + 1 and g(x) = (2(-1x^2 - 4x + 1) - 2)/(1(-1x^2 - 4x + 1) + 3) between the vertical lines x = 4.0 and x = 4.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-2((2(3x^2 + 5x - 2) + 2)/(-1(3x^2 + 5x - 2) - 1)) + 2)/(2((2(3x^2 + 5x - 2) + 2)/(-1(3x^2 + 5x - 2) - 1)) - 3), g(x) = -5(2cos(2\u03c0x - 2) - 1)^2 + 5(2cos(2\u03c0x - 2) - 1) - 2, x = -3.6, and x = -2.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2(-3|((-2x + 3)/(-1x + 2))| + 3)^2 - 5(-3|((-2x + 3)/(-1x + 2))| + 3) - 5 and g(x) = -2(-1|x - 3| - 3)^2 - 3(-1|x - 3| - 3) + 2 between the vertical lines x = 1.4 and x = 1.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-3(2|((-3x - 1)/(2x - 1)) - 1| + 3) - 2)/(-1(2|((-3x - 1)/(2x - 1)) - 1| + 3) - 1) and g(x) = 1(2|x + 2| - 3) from x = -4.9 to x = 1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-3((-1(4x - 1))/(2(4x - 1) - 1)) - 3)/(1((-1(4x - 1))/(2(4x - 1) - 1)) + 2), g(x) = -2sin(1\u03c0(-3x - 5)) - 2, x = -4.0, and x = -3.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 3sin(2\u03c0(-1(-1x^2 - 3x - 1)^2 - 2(-1x^2 - 3x - 1) - 1) - 3) + 1 and g(x) = 3|(-4x)| - 2 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}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-1(3(-3e^(-1x) - 1)^2 + 4(-3e^(-1x) - 1) - 3) + 1)/(2(3(-3e^(-1x) - 1)^2 + 4(-3e^(-1x) - 1) - 3) - 1), g(x) = (3(-2sin(1\u03c0x) - 1))/(-2(-2sin(1\u03c0x) - 1) - 2), x = -0.3, and x = 1.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14.6", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -3((-3(3x^2 + 1x - 1))/(1(3x^2 + 1x - 1)))^2 - 3((-3(3x^2 + 1x - 1))/(1(3x^2 + 1x - 1))) + 2, g(x) = (1(2cos(3\u03c0x - 2) + 1) + 2)/(1(2cos(3\u03c0x - 2) + 1) - 2), x = -2.6, and x = -2.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11.8", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 5(1(-3x - 5))^2 - 1(1(-3x - 5)) - 2, g(x) = 3|(2|x + 1|) + 3| + 1, x = -2.4, and x = -1.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1(-2cos(3\u03c0((-3x + 2)/(-1x)) - 2)) + 4 and g(x) = 5(1|x + 2| - 2)^2 - 3(1|x + 2| - 2) + 4 between the vertical lines x = 0.4 and x = 0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -4(2sin(3\u03c0(1x - 3) - 2) - 1)^2 + 3(2sin(3\u03c0(1x - 3) - 2) - 1) + 3 and g(x) = (3(3sin(1\u03c0x + 2) - 3) - 1)/(2(3sin(1\u03c0x + 2) - 3) - 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}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2(-2|(5x) - 3|)^2 + 2(-2|(5x) - 3|) - 3, g(x) = -1sin(2\u03c0((-3x)/(3x - 2)) - 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}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -5(-2|(2sin(2\u03c0x + 3))|) + 4, g(x) = 2|(-2|x - 1| - 3) - 3| - 3, x = 4.2, and x = 4.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1sin(3\u03c0(1(3|x - 2| - 3) - 1) + 3) and g(x) = (-3(-3|x + 2| - 2) + 1)/(3(-3|x + 2| - 2) - 1) from x = -4.8 to x = -4.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3sin(1\u03c0(-5(-3|x - 2| - 1) - 3) + 2) + 1, g(x) = -4(-4x - 5) + 1, x = -1.4, and x = -1.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-2(2(3x^2 + 5x + 2)^2 - 3(3x^2 + 5x + 2) + 4) + 2)/(-1(2(3x^2 + 5x + 2)^2 - 3(3x^2 + 5x + 2) + 4) - 2) and g(x) = -2sin(3\u03c0(-2|x - 2| + 3)) from x = -4.6 to x = -4.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1sin(3\u03c0(-2|((3x - 1)/(2x)) - 2| - 2)) + 3 and g(x) = -1(1x^2 - 5x + 3)^2 + 4(1x^2 - 5x + 3) + 5 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}", "role": "user"}], "ground_truth": "4.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2sin(1\u03c0(3|(3x - 5)| + 1) - 1) and g(x) = (3(-3x - 4) + 1)/(2(-3x - 4) - 1) between the vertical lines x = -1.0 and x = -0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -4(-3cos(3\u03c0(-5x - 1) + 3) + 1)^2 + 2, g(x) = 5(-3sin(3\u03c0x + 3) - 1) - 2, x = -0.2, and x = -0.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.8", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2sin(1\u03c0(2(4x^2 + 3) - 5)) + 2 and g(x) = -3(-3sin(1\u03c0x))^2 + 4(-3sin(1\u03c0x)) + 4 between the vertical lines x = 3.0 and x = 3.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2|(-2|(-1|x + 1| + 3) - 2| + 3) - 3| + 1 and g(x) = -2cos(2\u03c0((-3x + 3)/(3x + 2)) - 1) + 2 from x = -0.4 to x = -0.30000000000000004. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2sin(1\u03c0(5(-1|x| - 2)^2) - 3), g(x) = 1|(-1cos(2\u03c0x + 3) - 1) - 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}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2cos(1\u03c0(-1|((3x)/(1x + 3)) - 1| + 2) + 2) + 2, g(x) = 2(-3e^(2x) + 1), x = -2.8, and x = -2.6999999999999997. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2|(-2|(2sin(2\u03c0x - 2) - 3) - 2| + 3) - 3| + 2, g(x) = 3(2x^2 + 3x + 1)^2 + 2(2x^2 + 3x + 1) + 1, x = -2.0, and x = 0.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37.8", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3(2cos(3\u03c0(4x^2 + 2x - 2) - 1)) + 4, g(x) = -1(-5x^2 + 4x + 2)^2 + 4(-5x^2 + 4x + 2) + 2, x = 1.1, and x = 1.2000000000000002. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2|((-3(-2e^(2x) + 1) - 2)/(-2(-2e^(2x) + 1) + 3)) - 1| + 3 and g(x) = 1|(-1x^2 + 2x + 2)| + 1 from x = 1.4 to x = 3.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.7", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 4(3cos(2\u03c0((-2x + 1)/(-3x + 4)) - 1) - 2) - 1 and g(x) = -2|((-3x + 2)/(-3x + 1)) - 1| + 2 between the vertical lines x = 1.2 and x = 1.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3|((-1(2x^2 + 1x + 5) + 1)/(2(2x^2 + 1x + 5) - 3)) - 1| + 2 and g(x) = 1(4x^2 + 5x - 1) - 1 from x = -1.1 to x = -0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3((1(5x^2 + 4x - 2) - 1)/(2(5x^2 + 4x - 2) + 2))^2 + 3 and g(x) = -2e^(2(-4x - 5)) - 3 from x = -0.0 to x = 0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -4(-3|(-1x - 2) + 3| + 1) - 5, g(x) = -2e^(1(-4x^2 - 4x + 4)) + 2, x = 0.5, and x = 1.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8.4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (3(4(-3cos(1\u03c0x - 3) - 3) - 1))/(-3(4(-3cos(1\u03c0x - 3) - 3) - 1)) and g(x) = -1e^(-1(-5x^2 + 5x + 1)) + 2 from x = -0.3 to x = 1.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (3(-3|(-2|x - 2| + 2) + 1| + 1) - 1)/(-3(-3|(-2|x - 2| + 2) + 1| + 1) + 4), g(x) = 3(5x^2 - 2x - 3)^2 - 5(5x^2 - 2x - 3) + 1, x = 1.1, and x = 1.2000000000000002. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (3(-1(-5x - 5)) + 2)/(-3(-1(-5x - 5))), g(x) = 4(2sin(3\u03c0x - 2) + 2) - 2, x = 4.7, and x = 4.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -3(-1sin(1\u03c0(-1x - 4) + 3))^2 + 3, g(x) = -3cos(3\u03c0(4x^2 - 5x - 3) + 1), x = 3.6, and x = 3.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1cos(2\u03c0(-3|(-5x - 3) - 2| + 2)) + 2, g(x) = -1(-2x^2 - 3x + 5)^2 + 3(-2x^2 - 3x + 5) + 2, x = -2.0, and x = -1.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2|(-5(-3|x + 3| + 2) + 3) + 2| + 3 and g(x) = 2cos(2\u03c0(-4x - 2) + 1) + 1 from x = -3.3 to x = -2.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2|(-3(-2x^2 - 1x + 4)^2 + 5(-2x^2 - 1x + 4) + 4) - 1| + 1 and g(x) = -2(3sin(3\u03c0x) + 3) + 4 from x = -1.1 to x = 0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "61.4", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (1(1(-2x^2 - 2x)^2 + 4(-2x^2 - 2x) - 2) - 2)/(1(1(-2x^2 - 2x)^2 + 4(-2x^2 - 2x) - 2) - 3) and g(x) = (-3(-5x^2 + 2x + 3))/(1(-5x^2 + 2x + 3)) between the vertical lines x = -2.2 and x = 1.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13.8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3(-3(2x + 2) + 1) and g(x) = (2((3x + 2)/(-3x)) - 1)/(1((3x + 2)/(-3x)) - 3) from x = -0.8 to x = -0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.8", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1|((1(5x - 4) - 1)/(2(5x - 4) - 3)) - 2| - 1 and g(x) = (-1(-1sin(2\u03c0x + 1) - 3) - 1)/(-2(-1sin(2\u03c0x + 1) - 3) + 3) 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}", "role": "user"}], "ground_truth": "1.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2|(5((1x)/(1x)) - 4)| - 3 and g(x) = -3cos(1\u03c0(-1x - 4) - 1) - 3 from x = -2.6 to x = -2.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (2(1(5x + 5) + 4) + 2)/(1(1(5x + 5) + 4) + 3), g(x) = -1|((-1x + 1)/(-2x + 3)) + 2| + 3, x = 1.3, and x = 1.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-3((2(2x^2 - 5x - 3) + 1)/(-3(2x^2 - 5x - 3) - 1)))/(1((2(2x^2 - 5x - 3) + 1)/(-3(2x^2 - 5x - 3) - 1)) + 3) and g(x) = (2(-3cos(2\u03c0x - 3) + 1) - 2)/(1(-3cos(2\u03c0x - 3) + 1) + 1) from x = -1.2 to x = -0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2|(-2|(3|x - 1| - 3) - 2|)| + 3, g(x) = 1(-3x + 1)^2 - 3(-3x + 1) + 4, x = -0.6, and x = 1.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14.7", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 4(3cos(2\u03c0(-5x - 4)) - 3), g(x) = (-2((3x - 1)/(2x + 2)) - 1)/(1((3x - 1)/(2x + 2)) + 2), x = 2.8, and x = 3.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-1(-3((-2x - 1)/(-1x - 1))^2 - 5((-2x - 1)/(-1x - 1)) - 1))/(2(-3((-2x - 1)/(-1x - 1))^2 - 5((-2x - 1)/(-1x - 1)) - 1) - 1), g(x) = -2(1cos(3\u03c0x - 3) + 1) + 5, x = -0.7, and x = -0.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (1((2(3e^(1x) + 2) + 2)/(-1(3e^(1x) + 2) - 3)) + 1)/(-1((2(3e^(1x) + 2) + 2)/(-1(3e^(1x) + 2) - 3)) + 3), g(x) = 3sin(2\u03c0(3x^2 - 1x)) - 1, x = -3.4, and x = -3.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3(1sin(3\u03c0((3x - 2)/(3x + 1)) + 3) + 1)^2 + 3(1sin(3\u03c0((3x - 2)/(3x + 1)) + 3) + 1) - 4, g(x) = (-3(-4x^2 - 4x - 3))/(-1(-4x^2 - 4x - 3) - 1), x = -0.2, and x = -0.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3sin(3\u03c0(-4((3x)/(-3x - 2)) - 5) + 1) + 1, g(x) = -3cos(2\u03c0(-1x - 5) + 2) - 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}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 3(2sin(1\u03c0(3x - 2) - 1) - 2)^2 - 5(2sin(1\u03c0(3x - 2) - 1) - 2) - 4 and g(x) = (-2(-1e^(2x) - 2) - 2)/(3(-1e^(2x) - 2) - 1) from x = -1.0 to x = -0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16.6", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 4((-1((3x)/(2x)) + 3)/(2((3x)/(2x)) + 3))^2 + 4((-1((3x)/(2x)) + 3)/(2((3x)/(2x)) + 3)) - 1, g(x) = 1|(2x + 5)|, x = -2.6, and x = -2.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1|((2(3sin(2\u03c0x - 2) - 1))/(1(3sin(2\u03c0x - 2) - 1) + 1)) - 3| + 3, g(x) = 3|(-3sin(2\u03c0x) - 1)|, x = 2.6, and x = 2.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2((-2(2sin(1\u03c0x)) - 1)/(2(2sin(1\u03c0x)))) - 4 and g(x) = (3(2x + 3) - 2)/(1(2x + 3) - 3) from x = 1.0 to x = 2.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-1(1|(2|x - 3|) - 1|) - 3)/(2(1|(2|x - 3|) - 1|)) and g(x) = -3|(1cos(2\u03c0x - 1) + 1) - 3| between the vertical lines x = 2.2 and x = 2.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33.7", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (2((-1(4x^2 + 3x + 2) - 1)/(3(4x^2 + 3x + 2) - 2)) + 3)/(-1((-1(4x^2 + 3x + 2) - 1)/(3(4x^2 + 3x + 2) - 2)) + 2) and g(x) = -2(2|x - 1| - 1)^2 + 1(2|x - 1| - 1) + 1 between the vertical lines x = 0.6 and x = 1.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2(-3(-5x^2 + 5x + 3) + 4) - 2 and g(x) = 4(5x + 3)^2 + 1(5x + 3) + 4 between the vertical lines x = -1.8 and x = -0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "27.4", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1(2cos(2\u03c0(-2|x + 2| + 2) + 3)) and g(x) = 3e^(-1(1x - 1)) - 1 between the vertical lines x = 3.6 and x = 3.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2|(2cos(3\u03c0(-2x^2 - 4x + 4) - 3) + 1) - 3| + 1 and g(x) = 4(-4x - 2)^2 - 4(-4x - 2) between the vertical lines x = -1.0 and x = -0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3(3cos(1\u03c0((1x - 1)/(-3x + 4)) - 1) - 2)^2 + 2(3cos(1\u03c0((1x - 1)/(-3x + 4)) - 1) - 2) + 5 and g(x) = -4(3|x + 3| - 1)^2 + 2(3|x + 3| - 1) + 2 from x = -4.4 to x = -1.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "68.8", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2|(-1|((2x - 1)/(1x - 3))| + 1) - 3| + 1 and g(x) = 2|(-5x^2 - 5x + 5) + 2| + 2 between the vertical lines x = 0.9 and x = 2.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60.4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2(1sin(1\u03c0(5x^2 - 1x) - 3) - 2)^2 + 3(1sin(1\u03c0(5x^2 - 1x) - 3) - 2) + 5 and g(x) = -3(3e^(1x))^2 - 1(3e^(1x)) - 3 from x = -3.0 to x = -2.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3|(-3(-2|x + 3| - 1) + 4) + 3| + 2 and g(x) = -2((3x + 2)/(-2x - 2))^2 - 2((3x + 2)/(-2x - 2)) - 1 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}", "role": "user"}], "ground_truth": "46.6", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1|((-3((1x + 2)/(2x)) - 3)/(-1((1x + 2)/(2x)) + 3)) - 2|, g(x) = (1(2e^(1x) + 2) - 1)/(-3(2e^(1x) + 2) - 3), x = -0.1, and x = 0.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-3(-4(2|x|) + 2))/(-1(-4(2|x|) + 2) + 2) and g(x) = -4(2x^2 - 4x - 3)^2 - 4 from x = -0.0 to x = 0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 5(-3cos(1\u03c0(3|x + 1| - 2)) + 3) + 2 and g(x) = -5(4x + 5) between the vertical lines x = -2.7 and x = -2.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2|(2(5x^2 + 5x - 3) + 3) - 2| + 1, g(x) = -3(-2cos(2\u03c0x - 1) - 2) + 5, x = -0.7, and x = -0.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1((1(3x^2 - 4x - 5) - 3)/(1(3x^2 - 4x - 5))) - 4 and g(x) = 3|((-1x - 1)/(1x - 3)) - 1| - 3 between the vertical lines x = -0.6 and x = 0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3|(-1|(4x^2 - 2x - 2) - 1| + 3)| - 3, g(x) = 1(-4x + 5)^2 + 1(-4x + 5) + 2, x = 1.3, and x = 1.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 3|(-4(-5x^2 + 2x + 2) - 4) - 1| + 1 and g(x) = 2e^(-2(1|x + 3| - 2)) + 3 from x = -0.7 to x = -0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1|(-4(-2e^(1x) + 1)^2 - 5(-2e^(1x) + 1)) - 2| + 1 and g(x) = (1(-5x^2 + 5x - 4) + 1)/(2(-5x^2 + 5x - 4) - 3) from x = -0.4 to x = -0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3(2e^(2(-1|x + 1| - 1)) + 2) + 1 and g(x) = 1(1sin(3\u03c0x - 2) + 3)^2 - 4(1sin(3\u03c0x - 2) + 3) - 3 from x = 2.5 to x = 2.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2|(-1e^(-2(-4x^2 + 4)) + 1) + 3| - 1 and g(x) = -5(-1|x + 1|) - 3 between the vertical lines x = -1.1 and x = -1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -4(3sin(2\u03c0(1|x - 1| - 2) + 1) - 3)^2 + 5(3sin(2\u03c0(1|x - 1| - 2) + 1) - 3) + 3 and g(x) = 4(3sin(1\u03c0x - 2) + 3) + 2 between the vertical lines x = 2.0 and x = 2.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (1((-1(2x^2 - 5x))/(-3(2x^2 - 5x) + 4)) - 1)/(1((-1(2x^2 - 5x))/(-3(2x^2 - 5x) + 4)) - 3) and g(x) = -1sin(1\u03c0(-1x^2 - 3x - 3) - 2) - 1 between the vertical lines x = -0.3 and x = 2.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2|(-3sin(2\u03c0(2|x + 3| - 1)) + 1)| - 3 and g(x) = (1(-3|x + 1| + 1) + 2)/(-3(-3|x + 1| + 1) - 2) from x = -1.5 to x = -0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1(-2|(3|x - 2| + 1) - 3| - 2) - 2, g(x) = 2(-5x - 5)^2 + 4(-5x - 5) - 1, x = -1.4, and x = -0.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1(1(-1e^(2x) + 1) + 5) + 2 and g(x) = (1((2x - 1)/(-1x - 2)) - 3)/(2((2x - 1)/(-1x - 2)) - 1) between the vertical lines x = -0.2 and x = 0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "49.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-1(-3|((3x + 3)/(3x + 2)) + 3|) - 2)/(-2(-3|((3x + 3)/(3x + 2)) + 3|) - 2), g(x) = 5(-2cos(1\u03c0x + 3) + 1) - 1, x = -1.3, and x = -0.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.5", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1|(-1|(-2x - 5)| + 1) + 3|, g(x) = 2cos(1\u03c0(1|x - 3| - 3) + 2), x = -1.5, and x = -1.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 5((-3(-3sin(3\u03c0x + 2) - 3))/(-2(-3sin(3\u03c0x + 2) - 3) + 1))^2 - 1 and g(x) = -1(-2sin(2\u03c0x + 3) - 3)^2 - 4(-2sin(2\u03c0x + 3) - 3) + 4 from x = 1.4 to x = 1.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.7", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 3sin(2\u03c0((1(-5x^2 - 3x - 1))/(1(-5x^2 - 3x - 1) + 2)) - 1) + 1 and g(x) = (-1(-1sin(3\u03c0x - 1) - 1) - 3)/(1(-1sin(3\u03c0x - 1) - 1) + 1) 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}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1sin(1\u03c0(5(1|x + 2| - 2)^2 - 2(1|x + 2| - 2) - 4) + 2), g(x) = (-1(3|x - 1| + 1) + 1)/(-1(3|x - 1| + 1)), x = 2.8, and x = 2.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1cos(1\u03c0(-2(-2|x + 3| + 2) - 2)) + 2, g(x) = -3(-2x + 1)^2 - 5(-2x + 1), x = 0.9, and x = 1.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 3|(-2|(-3x^2 - 1x + 2) - 2| + 1) + 1| - 3 and g(x) = -2sin(2\u03c0(-1x - 3) + 2) - 2 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}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3(3(3|x + 1| - 1) - 4) - 4 and g(x) = -5((1x - 1)/(-2x + 1))^2 + 2((1x - 1)/(-2x + 1)) + 3 from x = 0.3 to x = 0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (1((2(-1x^2 - 2) - 2)/(2(-1x^2 - 2) + 3)) - 3)/(-1((2(-1x^2 - 2) - 2)/(2(-1x^2 - 2) + 3)) - 2) and g(x) = 3cos(2\u03c0(2x + 5) - 1) - 2 from x = 1.5 to x = 1.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (2((1(-4x^2 + 4) - 3)/(-2(-4x^2 + 4) - 3)) + 1)/(-2((1(-4x^2 + 4) - 3)/(-2(-4x^2 + 4) - 3)) - 3) and g(x) = (1(-3x^2 - 2x - 4) - 2)/(-2(-3x^2 - 2x - 4) - 1) from x = -1.1 to x = 1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1(-1cos(1\u03c0((-2x - 1)/(3x)) - 2) + 1)^2 + 2(-1cos(1\u03c0((-2x - 1)/(3x)) - 2) + 1) - 4, g(x) = 1((-2x + 3)/(-2x - 1)) + 5, x = 0.1, and x = 0.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 5((-1(-2x - 3) + 2)/(1(-2x - 3))) - 4 and g(x) = -4(3cos(3\u03c0x - 3) - 1) - 4 from x = 2.3 to x = 2.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2|(5(2cos(1\u03c0x - 3) + 1) - 2)| - 2 and g(x) = (3(3|x + 2| - 2) - 3)/(1(3|x + 2| - 2) - 3) from x = -1.7 to x = -1.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1cos(3\u03c0(-4(5x + 2)^2 - 5)), g(x) = -3e^(-1((-2x - 3)/(1x + 3))) + 2, x = -1.7, and x = -1.5999999999999999. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3sin(1\u03c0(-2((1x - 2)/(-2x)) + 5) + 2) + 1 and g(x) = -1(-3x - 1) + 3 between the vertical lines x = -0.1 and x = 0.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1|(-1(1x - 4) + 4) + 2| + 1, g(x) = 3(1cos(2\u03c0x - 1)) + 4, x = 4.1, and x = 4.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3cos(3\u03c0((-2(1x^2 + 4x - 3) + 3)/(1(1x^2 + 4x - 3) + 3)) - 1) + 1, g(x) = 1(2|x + 3| + 2) + 1, x = -3.1, and x = -2.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2cos(2\u03c0((-3(5x + 5) + 2)/(2(5x + 5) + 2)) + 1), g(x) = 3cos(1\u03c0(1|x - 1| + 2) - 3) - 3, x = 3.9, and x = 4.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1((-2(1|x + 2|) + 3)/(1(1|x + 2|) + 2))^2 + 3((-2(1|x + 2|) + 3)/(1(1|x + 2|) + 2)) + 3 and g(x) = 2|(2|x| + 3) - 3| - 3 between the vertical lines x = -2.1 and x = 1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1cos(1\u03c0(3(-2x^2 + 2x - 3) - 4) - 2) - 3, g(x) = (1(3sin(2\u03c0x) + 2) - 3)/(3(3sin(2\u03c0x) + 2) + 2), x = -2.4, and x = -2.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-2(-1(-4x^2 - 1x - 4) + 4))/(-2(-1(-4x^2 - 1x - 4) + 4) - 3), g(x) = 3cos(1\u03c0(5x + 4) - 3) - 2, x = 1.8, and x = 2.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 5(5(2|x + 2| - 3)^2 - 5)^2 - 5 and g(x) = 1(-2|x - 1|) + 4 from x = -3.0 to x = -2.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.7", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-2(5(-4x + 2)^2 + 3(-4x + 2) - 2) - 2)/(-2(5(-4x + 2)^2 + 3(-4x + 2) - 2) + 3) and g(x) = (1(2sin(1\u03c0x - 2) - 1) - 2)/(2(2sin(1\u03c0x - 2) - 1) - 1) between the vertical lines x = 2.6 and x = 3.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3(2(-1x - 1) + 5) + 4 and g(x) = -2(-1cos(1\u03c0x - 2) - 2)^2 + 5(-1cos(1\u03c0x - 2) - 2) - 5 between the vertical lines x = -2.8 and x = -2.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3sin(3\u03c0(-3(1|x - 2| + 1)^2 + 5(1|x - 2| + 1) + 1) + 3) + 2, g(x) = (-1(-1cos(3\u03c0x + 2)) - 3)/(-3(-1cos(3\u03c0x + 2)) - 3), x = -4.4, and x = -4.300000000000001. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 4(2((-3x + 1)/(1x + 1))^2 - 1((-3x + 1)/(1x + 1)) - 4) - 3, g(x) = -1(2|x - 2|) + 4, x = -0.2, and x = 1.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (1(2sin(1\u03c0(-2|x - 3| + 1) - 3) + 1) - 3)/(-3(2sin(1\u03c0(-2|x - 3| + 1) - 3) + 1) - 2) and g(x) = 3e^(-2((-3x + 1)/(-1x + 3))) - 3 between the vertical lines x = 0.3 and x = 0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2e^(2((-1((-2x - 3)/(-2x - 2)) + 3)/(3((-2x - 3)/(-2x - 2)) - 2))) + 1 and g(x) = 1|(-1e^(-1x) + 2)| - 3 from x = -1.8 to x = -0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (1(1(-1|x + 1| + 3)^2 + 1(-1|x + 1| + 3) - 5) - 2)/(-3(1(-1|x + 1| + 3)^2 + 1(-1|x + 1| + 3) - 5) - 1) and g(x) = -2e^(-1(5x + 3)) - 1 from x = 0.6 to x = 4.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (2(-2sin(1\u03c0(-4x^2 + 1x - 2) - 2) + 1) - 1)/(1(-2sin(1\u03c0(-4x^2 + 1x - 2) - 2) + 1) + 3) and g(x) = (2(3x) + 1)/(3(3x) - 1) from x = 3.4 to x = 3.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2sin(2\u03c0(1(3|x| - 2)^2 + 2(3|x| - 2) + 4) - 3) + 2 and g(x) = 2e^(-1(-3x^2 + 1x + 4)) + 2 from x = 1.1 to x = 1.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-1((1(2e^(1x) - 2) + 3)/(1(2e^(1x) - 2))) - 1)/(2((1(2e^(1x) - 2) + 3)/(1(2e^(1x) - 2))) + 3), g(x) = 2|(3cos(2\u03c0x + 3) - 3) + 3| - 3, x = -1.1, and x = -1.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3|(-5(5x + 3)^2 + 2(5x + 3) + 4)| - 3, g(x) = 1(4x + 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}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -4((-3(1x) - 3)/(2(1x) - 1))^2 + 3((-3(1x) - 3)/(2(1x) - 1)) + 3 and g(x) = 2cos(2\u03c0(-2|x + 2| + 3) - 2) from x = -1.8 to x = -1.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-2(-5(1x^2 + 1x)^2 - 3(1x^2 + 1x) + 5))/(2(-5(1x^2 + 1x)^2 - 3(1x^2 + 1x) + 5) - 1), g(x) = -3(1cos(2\u03c0x + 3) + 2)^2 + 1, x = -1.5, and x = 0.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "23.6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2sin(1\u03c0(3(-3x)^2 - 5(-3x) + 5) + 2) + 3 and g(x) = 2((1x + 2)/(-3x)) - 1 from x = -0.4 to x = -0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3cos(1\u03c0(-2(2|x - 1| - 2) - 1) + 3) - 1, g(x) = -4(-2e^(1x) + 2) + 3, x = -0.8, and x = -0.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (1(-2|((-2x + 1)/(-2x - 3)) - 2| + 2) - 3)/(-3(-2|((-2x + 1)/(-2x - 3)) - 2| + 2) + 1) and g(x) = 1(-3sin(1\u03c0x + 1) + 1)^2 + 2(-3sin(1\u03c0x + 1) + 1) - 2 between the vertical lines x = 2.6 and x = 3.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14.4", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1sin(2\u03c0(3((1x + 3)/(3x + 3))) + 2) + 2 and g(x) = 3cos(1\u03c0(2|x - 1| + 1) - 2) + 1 between the vertical lines x = -1.0 and x = -0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 3cos(3\u03c0(5(-2x^2 + 1x + 2) + 3) - 3) - 2 and g(x) = (1(3x + 1) - 2)/(-2(3x + 1) - 3) between the vertical lines x = -3.4 and x = -3.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2cos(3\u03c0(2|(3|x - 3| - 3) + 2| + 3) - 3) - 3 and g(x) = (1(-1|x + 3| + 2) - 1)/(2(-1|x + 3| + 2) - 1) between the vertical lines x = -1.6 and x = -1.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1|(-1(5x - 5)^2 - 1(5x - 5) - 3) + 3| + 1 and g(x) = -1|(2e^(-1x) + 3) + 1| - 1 between the vertical lines x = 0.4 and x = 1.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.9", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-2(5(-3|x - 3| - 3) - 5) - 2)/(3(5(-3|x - 3| - 3) - 5) - 2) and g(x) = (3(5x^2 + 4x - 5) - 3)/(3(5x^2 + 4x - 5) - 2) between the vertical lines x = -1.6 and x = 0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.9", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1(-1|(1|x + 2| + 2) - 2| + 2)^2 + 4(-1|(1|x + 2| + 2) - 2| + 2) - 1, g(x) = (-1(-1|x| + 2) - 1)/(3(-1|x| + 2) + 2), x = -3.8, and x = -2.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 3e^(-2(2(-3x + 1) + 2)) - 3 and g(x) = -3(-2|x + 3| - 1)^2 - 3(-2|x + 3| - 1) + 1 from x = -3.4 to x = -2.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1cos(1\u03c0(-2((1x + 1)/(3x + 2))^2 - 4((1x + 1)/(3x + 2)) - 2) - 2) + 3 and g(x) = (-1(-2cos(1\u03c0x - 3) - 1) + 3)/(3(-2cos(1\u03c0x - 3) - 1) + 3) from x = -2.5 to x = -1.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 4(-3cos(1\u03c0((-3x - 2)/(-1x - 2)) - 3) - 3)^2 + 1(-3cos(1\u03c0((-3x - 2)/(-1x - 2)) - 3) - 3) - 3 and g(x) = -1cos(2\u03c0(2|x - 1| + 2)) + 2 from x = -1.9 to x = -1.7999999999999998. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.9", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2cos(1\u03c0(-3((-3x + 2)/(-3x + 1)) + 3)) + 3, g(x) = 1|(3x - 1) - 1| - 1, x = -0.1, and x = 2.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -4((2(-3|x - 3| - 1))/(-2(-3|x - 3| - 1) - 1)) - 4 and g(x) = (1(-3cos(1\u03c0x - 1) - 2) - 3)/(-3(-3cos(1\u03c0x - 1) - 2) - 2) from x = 3.0 to x = 3.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1(5(1x^2 - 3) - 4) + 3, g(x) = -2e^(-1(-5x^2 + 4x + 1)) - 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}", "role": "user"}], "ground_truth": "17.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1e^(2(-3(3|x - 2| + 2) - 3)) + 2, g(x) = -1(-3x)^2 + 4, x = -0.5, and x = 0.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-2((-3(4x + 4) - 2)/(1(4x + 4) + 2)) + 3)/(-3((-3(4x + 4) - 2)/(1(4x + 4) + 2)) - 2) and g(x) = 2(2x - 4) from x = -1.1 to x = 2.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "27.6", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 5(3(-1cos(1\u03c0x + 2))^2 + 2(-1cos(1\u03c0x + 2)) - 1) - 5, g(x) = -2e^(-2(3x - 5)) - 1, x = 4.0, and x = 4.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6.6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2|(1|(-1x^2)| - 2) - 2| and g(x) = -3(-3cos(3\u03c0x - 2)) + 5 from x = -1.3 to x = -1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1|(4(2|x| - 1)^2 + 1(2|x| - 1) - 5) - 3| + 1, g(x) = 2sin(3\u03c0(-1|x - 2| + 3) + 3) + 2, x = -1.2, and x = -1.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-1(1((3x + 2)/(2x + 2)) + 5) + 2)/(1(1((3x + 2)/(2x + 2)) + 5) + 3) and g(x) = 1sin(2\u03c0(-4x^2 + 5x - 5) - 3) 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}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1(1((3x - 3)/(3x + 1))^2 - 3((3x - 3)/(3x + 1)) + 5)^2 - 3(1((3x - 3)/(3x + 1))^2 - 3((3x - 3)/(3x + 1)) + 5) + 1 and g(x) = -3|(1x - 2) - 2| + 3 between the vertical lines x = 3.8 and x = 4.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-2((-2(3e^(-1x) - 1) - 3)/(-3(3e^(-1x) - 1) - 3)) + 2)/(3((-2(3e^(-1x) - 1) - 3)/(-3(3e^(-1x) - 1) - 3)) + 1) and g(x) = 2sin(3\u03c0(1|x| - 3) - 2) between the vertical lines x = 1.9 and x = 2.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2((-1(5x - 2) - 2)/(1(5x - 2) + 3))^2 + 1((-1(5x - 2) - 2)/(1(5x - 2) + 3)) - 1 and g(x) = 2cos(3\u03c0(-3x^2 + 5x - 5) + 3) - 3 from x = -4.4 to x = -4.300000000000001. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2sin(2\u03c0((-3(-1x - 3) - 3)/(1(-1x - 3) + 3)) - 3) and g(x) = -3cos(1\u03c0(2x + 5) + 2) from x = -0.1 to x = 0.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 5((-2(2cos(2\u03c0x + 1)) - 1)/(-2(2cos(2\u03c0x + 1)) - 2))^2 - 1((-2(2cos(2\u03c0x + 1)) - 1)/(-2(2cos(2\u03c0x + 1)) - 2)) + 1 and g(x) = 2(-2e^(-1x) + 2) + 1 from x = 2.2 to x = 2.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.6", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3|(1((1x)/(-1x + 2)) + 5) + 3|, g(x) = 5(1sin(2\u03c0x - 1) + 1)^2 + 3(1sin(2\u03c0x - 1) + 1), x = 2.2, and x = 2.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-1(-3|(3sin(1\u03c0x - 1) - 2) + 2| + 2) - 1)/(-2(-3|(3sin(1\u03c0x - 1) - 2) + 2| + 2) + 3) and g(x) = -1(-5x^2 - 5) + 2 from x = 2.3 to x = 3.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "47.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3|(3(1x - 5) + 3) + 1| + 2 and g(x) = -1|(-3sin(2\u03c0x + 2) - 1) + 1| + 3 from x = 3.4 to x = 3.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2(-1(1e^(-2x)) + 2)^2 + 5(-1(1e^(-2x)) + 2) - 4 and g(x) = -5((-3x - 2)/(-3x + 4))^2 - 3((-3x - 2)/(-3x + 4)) - 4 between the vertical lines x = -0.8 and x = -0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1((-2(-1x^2 + 2) - 3)/(-1(-1x^2 + 2) + 3)) - 4, g(x) = 2|(5x^2 + 5x - 2) + 3| - 3, x = -1.0, and x = 0.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2(-1((-3x - 2)/(2x + 3)) + 2)^2 - 3(-1((-3x - 2)/(2x + 3)) + 2) - 2 and g(x) = -4(4x^2 - 1x - 5) - 3 between the vertical lines x = -1.0 and x = 1.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "84.6", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 4(-3(1cos(1\u03c0x - 2) + 2)^2 + 5) and g(x) = 2|(-1|x - 3| + 3) + 1| between the vertical lines x = -4.2 and x = -2.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "78.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-1(-3sin(2\u03c0(-2x^2 - 4x + 5) + 2)) + 3)/(-2(-3sin(2\u03c0(-2x^2 - 4x + 5) + 2)) + 3) and g(x) = -3sin(3\u03c0(1x^2 + 1x - 4) - 1) - 3 between the vertical lines x = -4.8 and x = -4.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (1(2cos(1\u03c0((-2x - 1)/(-3x + 2)) + 2) + 1) - 2)/(-2(2cos(1\u03c0((-2x - 1)/(-3x + 2)) + 2) + 1) - 1) and g(x) = (-2(2|x + 1| - 2) + 2)/(-2(2|x + 1| - 2)) 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}", "role": "user"}], "ground_truth": "1.4", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (2(-3((-1x + 1)/(1x + 3)) - 4) + 2)/(-2(-3((-1x + 1)/(1x + 3)) - 4) + 1), g(x) = -5(-3sin(1\u03c0x) - 2)^2 + 4(-3sin(1\u03c0x) - 2) + 3, x = -0.2, and x = 1.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "96.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2(-5(-1sin(1\u03c0x - 1) + 3) - 3) + 3 and g(x) = 3|(-2x^2 + 2x - 4) - 1| + 1 from x = -1.1 to x = 2.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "67.7", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1(2(2e^(-2x) + 1) - 5) + 1, g(x) = -4(1cos(1\u03c0x - 3))^2 + 4(1cos(1\u03c0x - 3)), x = 2.3, and x = 3.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 3(-3|((-2x - 2)/(-3x + 1)) + 2|)^2 + 4(-3|((-2x - 2)/(-3x + 1)) + 2|) - 5 and g(x) = -3e^(-1(3|x + 3| - 3)) from x = -0.1 to x = 0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1(-2cos(3\u03c0((-1x - 2)/(1x)) - 3) - 3)^2 + 3(-2cos(3\u03c0((-1x - 2)/(1x)) - 3) - 3) - 2 and g(x) = 1(-2x^2 + 2x - 1) + 5 between the vertical lines x = -3.7 and x = -2.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18.9", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (1(-5(3sin(2\u03c0x + 3) + 2) - 4))/(2(-5(3sin(2\u03c0x + 3) + 2) - 4) + 2), g(x) = 2(1|x + 2|)^2 - 2(1|x + 2|) - 3, x = 1.2, and x = 3.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "56.9", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-1(-2(-3|x - 1| + 2)^2 - 5(-3|x - 1| + 2) - 1) - 3)/(2(-2(-3|x - 1| + 2)^2 - 5(-3|x - 1| + 2) - 1) + 3), g(x) = (-1(4x - 2) - 3)/(-3(4x - 2) + 1), x = 1.6, and x = 2.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1sin(1\u03c0((3(1|x + 1| + 3) + 2)/(-2(1|x + 1| + 3) + 3)) - 3) - 1 and g(x) = -3|((1x)/(-1x + 2)) + 2| - 1 from x = 3.9 to x = 4.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -4(3cos(2\u03c0(4x - 1) - 1) - 1)^2 - 4(3cos(2\u03c0(4x - 1) - 1) - 1) + 1 and g(x) = 5(4x + 2) - 2 from x = -2.1 to x = -1.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 3sin(1\u03c0(-4(-1x^2 + 3x + 2) - 3) + 3) and g(x) = 1e^(2(-4x - 3)) from x = 4.3 to x = 4.3999999999999995. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 4(3cos(2\u03c0(-1x^2 - 4x) + 1) + 1)^2 - 4(3cos(2\u03c0(-1x^2 - 4x) + 1) + 1) - 5 and g(x) = (3(2e^(1x) + 2))/(-1(2e^(1x) + 2) + 3) between the vertical lines x = 3.4 and x = 3.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2(-3|(3|x + 2| - 2) - 3| + 2) + 1 and g(x) = -3(-3|x + 1| - 1) - 4 from x = -0.6 to x = 0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2e^(2((-1(-5x^2 + 2x - 5) - 2)/(-1(-5x^2 + 2x - 5) + 2))) - 2 and g(x) = 2|(-4x^2 - 4x + 2) + 1| - 3 from x = -2.1 to x = -0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7.7", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1cos(2\u03c0(-3(2|x + 3| - 1)^2 + 3(2|x + 3| - 1)) + 2) + 2 and g(x) = (2(-3e^(1x) - 3) + 3)/(1(-3e^(1x) - 3)) between the vertical lines x = 0.5 and x = 0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1|(-3e^(1(-5x + 1)) + 1) + 2| + 2 and g(x) = 5(2sin(2\u03c0x + 1)) + 4 between the vertical lines x = 1.3 and x = 1.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 5(2((-2x + 2)/(-2x - 2))) - 4 and g(x) = (1(-3x^2 + 2x + 2))/(2(-3x^2 + 2x + 2) - 1) from x = -0.4 to x = 1.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-1(1|(1x - 5) - 3| - 1) + 2)/(-1(1|(1x - 5) - 3| - 1)) and g(x) = -1(2|x + 1| - 3) + 2 from x = -3.1 to x = 1.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3|(-2|(-2cos(3\u03c0x - 2) + 1) - 3| + 2) - 1| + 1 and g(x) = -5(1|x - 1| - 3) + 1 between the vertical lines x = -4.3 and x = -4.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2e^(-1(-1((3x)/(-3x - 2))^2 - 1((3x)/(-3x - 2)) - 5)) - 3 and g(x) = -1((3x + 3)/(2x - 1))^2 - 4((3x + 3)/(2x - 1)) - 4 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}", "role": "user"}], "ground_truth": "-131.7", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2((-3(2x^2 - 2x + 4))/(3(2x^2 - 2x + 4) - 2))^2 + 2, g(x) = 5(-1e^(-1x) + 3)^2 - 4(-1e^(-1x) + 3) - 4, x = -1.4, and x = -0.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6.9", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 5(-4(1x^2 - 5x - 1)^2 + 1(1x^2 - 5x - 1) - 1) - 1 and g(x) = -3(4x + 5)^2 - 3(4x + 5) - 1 between the vertical lines x = -0.4 and x = 0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1((2((-3x + 1)/(-2x - 3)) - 2)/(-1((-3x + 1)/(-2x - 3)) - 2))^2 + 4((2((-3x + 1)/(-2x - 3)) - 2)/(-1((-3x + 1)/(-2x - 3)) - 2)) - 4, g(x) = 4(-1e^(2x) + 3)^2 + 4(-1e^(2x) + 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}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3e^(2(3(2x) - 2)) - 1 and g(x) = -5(-1|x + 1| + 1)^2 + 4(-1|x + 1| + 1) - 1 between the vertical lines x = -2.0 and x = -1.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 5(3(4x - 2)^2 + 1(4x - 2) - 3) - 5, g(x) = -2|((1x - 1)/(-3x - 1)) - 1|, x = 0.2, and x = 0.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-2(1e^(-1(-1x - 5)) - 1) + 1)/(-1(1e^(-1(-1x - 5)) - 1)) and g(x) = 2|(-2sin(1\u03c0x - 1) - 1)| - 1 from x = -3.6 to x = -2.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.8", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -4((3(2|x - 1| + 1) + 2)/(3(2|x - 1| + 1) - 1)) + 3, g(x) = 1cos(3\u03c0(1|x + 3| - 3) + 2) - 2, x = 0.0, and x = 0.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1(2|(-1|x - 1|) - 1| - 3) + 5, g(x) = 1(-3x^2 + 1x + 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}", "role": "user"}], "ground_truth": "4.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1(3|(-1x^2 - 5x - 2) - 1| - 3) + 1 and g(x) = (-2((1x - 3)/(-2x + 1)) - 1)/(1((1x - 3)/(-2x + 1)) + 2) 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}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-1(-3(3sin(1\u03c0x - 3) - 1)^2 + 2))/(-3(-3(3sin(1\u03c0x - 3) - 1)^2 + 2) + 2), g(x) = -2sin(1\u03c0(-1x^2 - 1x - 4) + 3) - 2, x = 1.9, and x = 3.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.5", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 5(-3|(-3sin(2\u03c0x - 2) - 1)| + 1) + 1, g(x) = -4(3cos(2\u03c0x + 2) - 2)^2 + 1(3cos(2\u03c0x + 2) - 2) - 3, x = 0.4, and x = 0.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13.9", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (1((-2(5x^2 + 1x + 4) - 1)/(-2(5x^2 + 1x + 4) - 2)) - 2)/(3((-2(5x^2 + 1x + 4) - 1)/(-2(5x^2 + 1x + 4) - 2)) - 2), g(x) = 3|(-1x^2 + 4x + 4)| - 3, x = 4.7, and x = 4.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2cos(1\u03c0(-4(-2|x + 1|)^2 + 1)) - 2, g(x) = -1|(2|x + 3| - 1) + 2|, x = -2.6, and x = -2.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1|(3(3|x - 3| - 3)^2 - 1(3|x - 3| - 3) - 3) + 1| and g(x) = -3|(-1cos(3\u03c0x - 3) + 1) + 1| + 2 between the vertical lines x = 1.4 and x = 2.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (2(-3(-4x^2 + 3x - 4)^2 - 3(-4x^2 + 3x - 4) + 5) - 1)/(-1(-3(-4x^2 + 3x - 4)^2 - 3(-4x^2 + 3x - 4) + 5)) and g(x) = -1|(-3e^(-2x) - 1) + 3| - 2 from x = 0.2 to x = 0.30000000000000004. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (3(-1(2cos(1\u03c0x - 2) + 2)^2 + 5(2cos(1\u03c0x - 2) + 2) - 4))/(-3(-1(2cos(1\u03c0x - 2) + 2)^2 + 5(2cos(1\u03c0x - 2) + 2) - 4) + 4), g(x) = 3(-1e^(2x) + 1) - 2, x = 0.4, and x = 0.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7.7", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2|((-1(-1x^2 + 1x + 4) - 1)/(3(-1x^2 + 1x + 4) - 1)) + 3| + 2, g(x) = 2(-2|x - 3|)^2 + 2(-2|x - 3|) - 1, x = 1.7, and x = 4.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20.5", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1(2e^(1(4x + 4)) - 3)^2 - 3(2e^(1(4x + 4)) - 3) + 4, g(x) = 1(-1x^2 + 4x + 5)^2 + 3(-1x^2 + 4x + 5) + 3, x = -1.5, and x = -0.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3|(-1|(-3x^2 + 2x - 2) + 2| - 1) + 3| - 2 and g(x) = (-1(-2x^2 + 5x + 4) + 3)/(-2(-2x^2 + 5x + 4)) between the vertical lines x = -0.6 and x = 3.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "63.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (2(-1cos(2\u03c0(-1x^2 + 1x - 5) + 2) + 1) + 2)/(2(-1cos(2\u03c0(-1x^2 + 1x - 5) + 2) + 1) + 3) and g(x) = 3sin(3\u03c0(3|x + 1| + 3) + 3) + 3 between the vertical lines x = -3.4 and x = -3.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-1(-2|(-2cos(1\u03c0x + 3)) + 1| - 3) + 2)/(2(-2|(-2cos(1\u03c0x + 3)) + 1| - 3) - 3) and g(x) = 1((3x - 2)/(3x - 1))^2 + 2((3x - 2)/(3x - 1)) between the vertical lines x = 0.5 and x = 0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 4(-3(5x^2 - 1x - 3) - 3) - 1, g(x) = -2((2x - 2)/(-3x + 4)) + 4, x = 0.7, and x = 1.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -5(2cos(3\u03c0((-1x + 1)/(1x + 3)) + 3) - 3)^2 + 2(2cos(3\u03c0((-1x + 1)/(1x + 3)) + 3) - 3) + 4 and g(x) = 5(3sin(3\u03c0x - 2) + 2) - 2 between the vertical lines x = -3.3 and x = -3.1999999999999997. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (2(-1(1|x + 1| + 1) - 4) - 2)/(2(-1(1|x + 1| + 1) - 4) + 3), g(x) = 4(-3sin(1\u03c0x - 2) - 2)^2 + 4(-3sin(1\u03c0x - 2) - 2) + 2, x = 2.4, and x = 2.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-2(-3cos(2\u03c0(-2x + 2) - 3)) - 3)/(1(-3cos(2\u03c0(-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}", "role": "user"}], "ground_truth": "22.3", "dataset": "MATH"}
{"messages": [{"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}", "role": "user"}], "ground_truth": "21.5", "dataset": "MATH"}
{"messages": [{"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}", "role": "user"}], "ground_truth": "3.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2(-1(2cos(3\u03c0x + 3))^2 - 2(2cos(3\u03c0x + 3)) - 1)^2 - 1(-1(2cos(3\u03c0x + 3))^2 - 2(2cos(3\u03c0x + 3)) - 1) and g(x) = (-1(2cos(2\u03c0x + 3) + 2))/(-1(2cos(2\u03c0x + 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}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"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(2\u03c0x - 3) - 1) - 1)/(1(-1sin(2\u03c0x - 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}", "role": "user"}], "ground_truth": "40.9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-2(-1|(-1sin(3\u03c0x - 1)) + 3|) + 2)/(-3(-1|(-1sin(3\u03c0x - 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}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3|(2|(1cos(3\u03c0x + 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}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"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}", "role": "user"}], "ground_truth": "7.3", "dataset": "MATH"}
{"messages": [{"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(2\u03c0(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}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3|(-2|(-2x - 3) + 1| - 2) + 3| + 1 and g(x) = -2(-3sin(2\u03c0x + 3) - 1)^2 + 5(-3sin(2\u03c0x + 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}", "role": "user"}], "ground_truth": "17.7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1sin(2\u03c0(-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}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3|(3|(-2sin(2\u03c0x - 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}", "role": "user"}], "ground_truth": "1.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3|(2sin(1\u03c0(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}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"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(3\u03c0x - 2) - 2) + 1)/(-2(2cos(3\u03c0x - 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}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"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(1\u03c0x + 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}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"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}", "role": "user"}], "ground_truth": "9.6", "dataset": "MATH"}
{"messages": [{"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(3\u03c0(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}", "role": "user"}], "ground_truth": "1.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (1(-1sin(1\u03c0(2|x + 1| + 3) + 2) - 3) - 1)/(1(-1sin(1\u03c0(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}", "role": "user"}], "ground_truth": "5.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1|(-2|(2cos(1\u03c0x - 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}", "role": "user"}], "ground_truth": "3.8", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -3(1cos(3\u03c0(2|x + 3| + 2)) + 2)^2 + 1(1cos(3\u03c0(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}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"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(2\u03c0x - 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}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"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(2\u03c0(-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}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1cos(3\u03c0((-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}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"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}", "role": "user"}], "ground_truth": "26.4", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (1(2cos(1\u03c0(2x^2 + 4x + 2) - 2) - 3))/(1(2cos(1\u03c0(2x^2 + 4x + 2) - 2) - 3) + 2) and g(x) = 5(3cos(3\u03c0x - 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}", "role": "user"}], "ground_truth": "43.0", "dataset": "MATH"}
{"messages": [{"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(2\u03c0x + 2) - 2)^2 + 3(-3cos(2\u03c0x + 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}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"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}", "role": "user"}], "ground_truth": "2.4", "dataset": "MATH"}
{"messages": [{"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(1\u03c0((-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}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"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}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2|(3cos(2\u03c0((2x + 2)/(-2x + 3)) - 2) + 2) + 2| - 3 and g(x) = 1sin(2\u03c0(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}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"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}", "role": "user"}], "ground_truth": "5.9", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1sin(2\u03c0(-4((-2x - 3)/(3x + 2))^2 - 2((-2x - 3)/(3x + 2)) + 1)) + 2 and g(x) = 3cos(1\u03c0(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}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -3|(3(1e^(-1x) - 2)) + 3| + 2, g(x) = 2cos(2\u03c0(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}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"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(1\u03c0(-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}", "role": "user"}], "ground_truth": "1.4", "dataset": "MATH"}
{"messages": [{"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}", "role": "user"}], "ground_truth": "8.4", "dataset": "MATH"}
{"messages": [{"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}", "role": "user"}], "ground_truth": "29.2", "dataset": "MATH"}
{"messages": [{"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}", "role": "user"}], "ground_truth": "11.7", "dataset": "MATH"}
{"messages": [{"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}", "role": "user"}], "ground_truth": "-2.1", "dataset": "MATH"}
{"messages": [{"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(3\u03c0(-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}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1|(1cos(3\u03c0(2x^2 - 2x + 2) - 2)) - 2| + 2 and g(x) = -3cos(1\u03c0(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}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"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}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1((-3(2cos(3\u03c0x + 1) + 2) + 1)/(-1(2cos(3\u03c0x + 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}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"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}", "role": "user"}], "ground_truth": "6.4", "dataset": "MATH"}
{"messages": [{"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}", "role": "user"}], "ground_truth": "1.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1|(-3|(2cos(3\u03c0x) + 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}", "role": "user"}], "ground_truth": "1.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (1(3cos(2\u03c0((3x - 1)/(2x)) + 1) - 1) + 3)/(-1(3cos(2\u03c0((3x - 1)/(2x)) + 1) - 1) + 2), g(x) = 2|(3sin(3\u03c0x + 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}", "role": "user"}], "ground_truth": "16.0", "dataset": "MATH"}
{"messages": [{"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}", "role": "user"}], "ground_truth": "10.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -4(5((-1x - 3)/(-3x + 2)) + 1)^2 + 2 and g(x) = (3(1cos(1\u03c0x + 1)) - 1)/(-3(1cos(1\u03c0x + 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}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"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}", "role": "user"}], "ground_truth": "7.3", "dataset": "MATH"}
{"messages": [{"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(3\u03c0(-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}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"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}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"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}", "role": "user"}], "ground_truth": "18.9", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2sin(2\u03c0(-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}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"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}", "role": "user"}], "ground_truth": "14.5", "dataset": "MATH"}
{"messages": [{"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}", "role": "user"}], "ground_truth": "-15.3", "dataset": "MATH"}
{"messages": [{"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(1\u03c0(-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}", "role": "user"}], "ground_truth": "1.8", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1(-2cos(3\u03c0(1x^2 + 5) + 1) - 1), g(x) = (1(1cos(3\u03c0x) + 2) + 1)/(-3(1cos(3\u03c0x) + 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}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2|(2cos(3\u03c0(-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}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"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(2\u03c0(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}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"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(2\u03c0(-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}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"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}", "role": "user"}], "ground_truth": "4.1", "dataset": "MATH"}
{"messages": [{"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(3\u03c0(-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}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"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(1\u03c0((-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}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -4(3sin(1\u03c0(3|x - 1| - 2)) + 1) + 4 and g(x) = 3|(3sin(3\u03c0x - 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}", "role": "user"}], "ground_truth": "4.9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2|(2cos(3\u03c0((-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}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1|(-2(-1cos(2\u03c0x + 1) + 1)) + 2| + 1 and g(x) = 1(-2cos(2\u03c0x + 1) + 2)^2 - 1(-2cos(2\u03c0x + 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}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"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}", "role": "user"}], "ground_truth": "32.3", "dataset": "MATH"}
{"messages": [{"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(2\u03c0(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}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"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(2\u03c0x - 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}", "role": "user"}], "ground_truth": "5.0", "dataset": "MATH"}
{"messages": [{"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(1\u03c0x + 3) - 2) + 2)/(-2(-1sin(1\u03c0x + 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}", "role": "user"}], "ground_truth": "66.9", "dataset": "MATH"}
{"messages": [{"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(1\u03c0x - 1)) + 3)/(2(-2sin(1\u03c0x - 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}", "role": "user"}], "ground_truth": "6.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2(-1(1x^2 + 1x - 1)) - 2 and g(x) = 2(3sin(3\u03c0x + 3) - 2)^2 + 4(3sin(3\u03c0x + 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}", "role": "user"}], "ground_truth": "4.5", "dataset": "MATH"}
{"messages": [{"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}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1(5(-3sin(1\u03c0x + 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}", "role": "user"}], "ground_truth": "20.0", "dataset": "MATH"}
{"messages": [{"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(2\u03c0(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}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"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(2\u03c0(-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}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"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}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"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}", "role": "user"}], "ground_truth": "42.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -5(-2sin(3\u03c0(-2|x - 1|) + 2) - 2)^2 - 5(-2sin(3\u03c0(-2|x - 1|) + 2) - 2) + 2 and g(x) = 2sin(3\u03c0(-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}", "role": "user"}], "ground_truth": "13.4", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1sin(1\u03c0(-4(-1x^2 - 5x + 4) - 5) + 3) - 2, g(x) = 4(-3cos(2\u03c0x + 1) - 1)^2 + 3(-3cos(2\u03c0x + 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}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 4(3(-2cos(3\u03c0x + 3) + 2)^2 - 4(-2cos(3\u03c0x + 3) + 2) + 2)^2 - 2(3(-2cos(3\u03c0x + 3) + 2)^2 - 4(-2cos(3\u03c0x + 3) + 2) + 2) - 1 and g(x) = 3|(2cos(1\u03c0x + 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}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"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(1\u03c0(-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}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -3|(1(1cos(1\u03c0x + 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}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2(-2cos(1\u03c0(1|x + 2| - 3) + 1) + 1)^2 - 1(-2cos(1\u03c0(1|x + 2| - 3) + 1) + 1) - 2 and g(x) = -1cos(3\u03c0(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}", "role": "user"}], "ground_truth": "4.4", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 3(-1sin(3\u03c0(-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}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"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(1\u03c0((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}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1(3cos(1\u03c0((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}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3sin(3\u03c0(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}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1(1(-3sin(3\u03c0x - 1) + 2) - 5)^2 - 4(1(-3sin(3\u03c0x - 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}", "role": "user"}], "ground_truth": "14.7", "dataset": "MATH"}
{"messages": [{"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}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"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}", "role": "user"}], "ground_truth": "9.1", "dataset": "MATH"}
{"messages": [{"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}", "role": "user"}], "ground_truth": "27.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-2(-2cos(3\u03c0(-5x + 1) + 2)) + 3)/(1(-2cos(3\u03c0(-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}", "role": "user"}], "ground_truth": "2.0", "dataset": "MATH"}
{"messages": [{"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}", "role": "user"}], "ground_truth": "29.9", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2|(-1cos(3\u03c0(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}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 4(2|(1x^2 + 3x - 5) + 3| - 3) - 3 and g(x) = 1cos(3\u03c0(-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}", "role": "user"}], "ground_truth": "4.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (2(-3(-1cos(2\u03c0x + 1) + 2) - 5) - 3)/(2(-3(-1cos(2\u03c0x + 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}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1sin(1\u03c0(2((-2x - 1)/(-2x + 3)) - 2) - 3) - 3, g(x) = -4(3cos(3\u03c0x) - 2)^2 - 3(3cos(3\u03c0x) - 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}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2cos(1\u03c0(-3|(5x^2 + 1x - 4) - 3| - 2) - 2) and g(x) = 2cos(3\u03c0(-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}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -5(-4(2sin(1\u03c0x + 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}", "role": "user"}], "ground_truth": "71.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-3(-1e^(2((-2x + 1)/(1x - 3))) + 1) - 1)/(-1(-1e^(2((-2x + 1)/(1x - 3))) + 1) - 1) and g(x) = -2sin(1\u03c0(2|x - 3| + 3) + 3) + 3 between the vertical lines x = -1.1 and x = -0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (1(4(1|x - 3| - 2)^2 + 5(1|x - 3| - 2) + 4))/(-1(4(1|x - 3| - 2)^2 + 5(1|x - 3| - 2) + 4)), g(x) = 3sin(1\u03c0(-1x^2 + 3x + 4) - 1), x = -2.0, and x = -1.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 4(-3cos(1\u03c0(-3x + 5) + 2)) + 5 and g(x) = 2|(3x + 4) - 2| + 2 from x = 0.4 to x = 0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1((2((-3x - 2)/(-1x - 1)) + 2)/(3((-3x - 2)/(-1x - 1)) + 1)) - 2, g(x) = 1(-3cos(2\u03c0x + 3) - 3) - 1, x = 1.0, and x = 1.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -5(3|(3x + 4) - 1| + 1)^2 - 2(3|(3x + 4) - 1| + 1) - 4 and g(x) = -3((1x + 2)/(1x + 1))^2 - 1((1x + 2)/(1x + 1)) from x = -1.2 to x = -0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-36.8", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2(-1(-3e^(-1x) + 3)^2 - 2(-3e^(-1x) + 3) - 2) - 2, g(x) = -1((3x + 1)/(-1x + 2)) + 1, x = -0.5, and x = -0.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1sin(1\u03c0(2|(3x + 2) - 3| - 3) + 1) - 2, g(x) = -1e^(-1(5x^2 + 5x - 2)), x = -1.2, and x = 0.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -3cos(2\u03c0((3(-3|x - 3| + 1) + 1)/(1(-3|x - 3| + 1))) + 1) + 3, g(x) = (3(-3|x + 2| - 2) - 3)/(3(-3|x + 2| - 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}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2|(-3((-1x + 3)/(-3x + 1)) + 1) + 2| + 3, g(x) = -1sin(2\u03c0((-3x - 2)/(1x)) - 3) - 3, x = -0.2, and x = -0.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-1((2((2x - 3)/(3x - 1)) - 3)/(3((2x - 3)/(3x - 1)) + 3)) - 2)/(2((2((2x - 3)/(3x - 1)) - 3)/(3((2x - 3)/(3x - 1)) + 3))), g(x) = (-3(3x - 4) + 2)/(-2(3x - 4)), x = 1.8, and x = 2.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 5(-3sin(1\u03c0(1x^2 + 1x + 4)) - 2)^2 + 2(-3sin(1\u03c0(1x^2 + 1x + 4)) - 2) - 4, g(x) = -2(-4x - 3)^2 - 1(-4x - 3), x = -0.9, and x = -0.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.6", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2|((2(1x^2 + 4x - 4))/(3(1x^2 + 4x - 4) + 1)) + 2| + 1 and g(x) = -2(-1e^(-2x) - 3) - 1 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}", "role": "user"}], "ground_truth": "1.4", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-2(-1|(-1x - 2)| - 3) - 2)/(2(-1|(-1x - 2)| - 3) - 1), g(x) = 2sin(3\u03c0(2|x + 1|) - 3) + 1, x = 3.7, and x = 3.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2|(4(3|x + 1| - 1)^2 - 3(3|x + 1| - 1) - 5)| - 1 and g(x) = (1(3cos(3\u03c0x + 1) + 3) + 3)/(1(3cos(3\u03c0x + 1) + 3) + 2) between the vertical lines x = -1.0 and x = -0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2sin(3\u03c0(4(-3x^2 + 1x + 1)^2 + 3(-3x^2 + 1x + 1) - 5)) - 2 and g(x) = -1|(2|x + 3| + 2) - 2| - 2 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}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-2(-1e^(-1((-1x + 2)/(2x + 1))) + 1) + 2)/(1(-1e^(-1((-1x + 2)/(2x + 1))) + 1) + 3) and g(x) = -3cos(1\u03c0(-1|x| + 2) + 2) + 1 from x = 1.1 to x = 2.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2((-1((-3x - 3)/(3x + 3)) - 3)/(-3((-3x - 3)/(3x + 3)) + 2)) + 4 and g(x) = 1|(-5x^2 - 4x + 1) + 3| + 1 from x = 0.0 to x = 0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.6", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3(3cos(1\u03c0(-1x^2 + 2x + 1) + 3) + 2) - 2, g(x) = -1(2|x + 2| - 3)^2 + 5(2|x + 2| - 3) - 1, x = -4.2, and x = -4.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1(4(-2|x + 2| + 1) - 4)^2 - 5(4(-2|x + 2| + 1) - 4) + 1, g(x) = -2|(-2x - 2)| - 2, x = -2.8, and x = -1.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2(1(-2x) - 4) + 3, g(x) = 2cos(1\u03c0(-2|x - 3| - 2) - 3) + 1, x = -1.7, and x = -1.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.7", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2|(1e^(-2(1x + 2)) - 2) - 2| + 1, g(x) = 2sin(1\u03c0(-3|x - 3| - 2)) + 3, x = -2.9, and x = -2.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (3((2(-2cos(3\u03c0x + 1) - 1) + 3)/(2(-2cos(3\u03c0x + 1) - 1) - 1)))/(3((2(-2cos(3\u03c0x + 1) - 1) + 3)/(2(-2cos(3\u03c0x + 1) - 1) - 1)) + 3) and g(x) = -2e^(2(-4x + 3)) + 2 from x = 2.1 to x = 2.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2cos(3\u03c0((3(2|x + 3|) + 2)/(1(2|x + 3|) + 1))) and g(x) = 2(2cos(1\u03c0x) + 3) - 2 between the vertical lines x = -1.2 and x = -0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1(-2sin(1\u03c0((-1x - 3)/(2x + 3)) - 2) + 2)^2 + 5(-2sin(1\u03c0((-1x - 3)/(2x + 3)) - 2) + 2) - 3 and g(x) = -4(-3cos(2\u03c0x + 1))^2 + 5(-3cos(2\u03c0x + 1)) - 1 between the vertical lines x = 1.1 and x = 1.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2sin(3\u03c0(5(-1x^2 + 4x - 2)^2 + 3(-1x^2 + 4x - 2) + 1) + 2) + 2 and g(x) = 4(5x^2 - 3x - 1) 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}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-1(-1sin(3\u03c0((-2x + 3)/(2x + 1)) + 1) - 3) + 2)/(2(-1sin(3\u03c0((-2x + 3)/(2x + 1)) + 1) - 3) + 3) and g(x) = 3cos(2\u03c0(-1x^2 - 5x + 5) + 3) between the vertical lines x = 3.8 and x = 3.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1|(-4((1x - 3)/(-3x + 2))^2 - 3((1x - 3)/(-3x + 2)) - 1) + 2| + 3, g(x) = 3(-1|x + 1| - 2)^2 + 1(-1|x + 1| - 2) + 2, x = 0.4, and x = 0.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-34.8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 3(-3(-2cos(3\u03c0x - 2) + 2) + 5) + 4 and g(x) = -2(3|x - 3| - 2)^2 + 3(3|x - 3| - 2) + 4 from x = 1.3 to x = 1.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.4", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2((-2((-3x + 2)/(2x - 1)) + 1)/(3((-3x + 2)/(2x - 1)) - 1))^2 - 3((-2((-3x + 2)/(2x - 1)) + 1)/(3((-3x + 2)/(2x - 1)) - 1)) and g(x) = 2|((1x - 2)/(-1x + 3)) + 2| - 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}", "role": "user"}], "ground_truth": "89.8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2(-3cos(1\u03c0(1x^2 + 2x + 3) + 3))^2 - 5 and g(x) = 3|(3e^(-1x) + 2) - 2| + 3 from x = 1.7 to x = 1.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1|(1(-2|x + 1| + 1)^2 + 1(-2|x + 1| + 1) - 5) - 3| + 3 and g(x) = -1(1|x| - 1)^2 - 3(1|x| - 1) - 3 between the vertical lines x = 0.6 and x = 1.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1|(3(-3x - 2) + 2) + 3| + 1 and g(x) = 2(1cos(3\u03c0x - 3) + 2)^2 - 3(1cos(3\u03c0x - 3) + 2) - 3 from x = -0.6 to x = -0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1|(1sin(3\u03c0(-2|x + 2| + 1) - 2) + 2) + 3| + 2 and g(x) = -3|(5x + 4) - 2| - 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}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 5(-2sin(1\u03c0(2x - 4) - 1) - 2)^2 + 4(-2sin(1\u03c0(2x - 4) - 1) - 2) + 2 and g(x) = 3|(-2|x| + 2) + 1| - 2 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}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1|(2sin(1\u03c0(-5x + 4) - 2) + 2)| - 3, g(x) = -3(-3sin(3\u03c0x - 2) + 2) - 4, x = -1.6, and x = 0.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 5(-4(2e^(-1x) - 3) + 4)^2 - 4(-4(2e^(-1x) - 3) + 4) - 4, g(x) = (-3(-3cos(1\u03c0x - 2) - 3) + 1)/(2(-3cos(1\u03c0x - 2) - 3) - 3), x = -0.7, and x = -0.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1|(2|((-2x - 2)/(1x + 2)) + 2| - 3) - 1| - 2 and g(x) = 5(-1x^2 + 3x - 5) - 3 between the vertical lines x = -2.0 and x = -1.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "81.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3|(-3((-2x + 3)/(3x - 1)) - 4) + 1| - 3 and g(x) = -1|(-1x^2 + 4x + 5) + 2| - 2 from x = 1.4 to x = 4.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -5(3sin(3\u03c0(1x^2 + 1x - 4) + 2) + 2)^2 - 2(3sin(3\u03c0(1x^2 + 1x - 4) + 2) + 2) + 5, g(x) = (-2(3|x - 2| + 1) + 3)/(-3(3|x - 2| + 1) - 2), x = 3.9, and x = 4.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 3cos(1\u03c0(1(1x^2 + 3x) - 1) - 2) + 3 and g(x) = -2cos(2\u03c0((2x + 3)/(-2x - 3)) - 3) from x = -3.6 to x = -3.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-3(-5(-2sin(1\u03c0x - 3) + 1)^2 - 4(-2sin(1\u03c0x - 3) + 1) + 3) - 3)/(-2(-5(-2sin(1\u03c0x - 3) + 1)^2 - 4(-2sin(1\u03c0x - 3) + 1) + 3) - 3) and g(x) = -3|((-3x)/(1x + 3))| - 2 between the vertical lines x = 1.9 and x = 3.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8.4", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 4(1((1x + 3)/(1x + 2))^2 + 1((1x + 3)/(1x + 2)) + 1)^2 - 1(1((1x + 3)/(1x + 2))^2 + 1((1x + 3)/(1x + 2)) + 1) + 2 and g(x) = -2sin(3\u03c0(1|x + 3| - 1) + 3) + 3 between the vertical lines x = -2.6 and x = -2.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -5((3((-1x + 2)/(1x - 3)) - 3)/(3((-1x + 2)/(1x - 3)) - 2)) + 2 and g(x) = (2((-3x - 1)/(-3x - 3)) + 2)/(-1((-3x - 1)/(-3x - 3)) + 2) between the vertical lines x = -1.2 and x = 2.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28.6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-1(-2(1e^(-2x) - 1)^2 + 5(1e^(-2x) - 1) - 4) + 3)/(-2(-2(1e^(-2x) - 1)^2 + 5(1e^(-2x) - 1) - 4) - 3) and g(x) = 5(4x - 1) + 4 from x = -0.3 to x = 0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15.4", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1(-2|((2x + 1)/(-1x - 2)) - 3| - 2) - 3, g(x) = 4(1e^(2x) - 3) + 2, x = -1.6, and x = -0.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -5(-3|((1x - 2)/(-3x + 4)) + 1| + 1) + 1 and g(x) = -3(-2|x - 3| + 3)^2 - 2(-2|x - 3| + 3) + 1 from x = 0.9 to x = 1.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 4(1|(-3x + 3) - 3| - 2) + 5 and g(x) = 2((2x + 1)/(2x + 3)) + 5 from x = -1.7 to x = -0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "81.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2|(1|(3|x - 1|) - 1| - 3) - 1| + 3, g(x) = 4(-3sin(1\u03c0x + 3) - 3)^2 - 2(-3sin(1\u03c0x + 3) - 3), x = 2.4, and x = 2.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1|(-2|((2x - 3)/(3x + 1)) - 2| - 1) - 1| + 1 and g(x) = 3e^(2(1x + 2)) - 2 from x = -1.7 to x = -0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "23.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3(3|(1cos(1\u03c0x + 3) - 2) + 1| + 1) + 1 and g(x) = 4(3x + 1) + 5 between the vertical lines x = -2.2 and x = -1.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.6", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3((2(-1|x + 2|) + 2)/(-2(-1|x + 2|) - 3)) + 4, g(x) = -2|(-1x + 1) + 3| - 3, x = -3.6, and x = -0.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "81.9", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1sin(3\u03c0((3((2x - 3)/(-3x - 1)) + 1)/(3((2x - 3)/(-3x - 1)) - 1)) + 2) and g(x) = 1sin(3\u03c0(-4x + 2)) between the vertical lines x = 3.3 and x = 3.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 3sin(2\u03c0(1(4x + 4) - 5)) - 2 and g(x) = 1(-3x + 5) - 4 between the vertical lines x = 0.5 and x = 0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1sin(3\u03c0((3((1x - 1)/(-2x + 3)))/(-1((1x - 1)/(-2x + 3)) - 2)) + 1) + 2 and g(x) = 5(2x^2 + 3x)^2 - 3(2x^2 + 3x) 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}", "role": "user"}], "ground_truth": "4.7", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (2((2(3|x + 2| - 2) - 1)/(2(3|x + 2| - 2) + 2)) + 2)/(-2((2(3|x + 2| - 2) - 1)/(2(3|x + 2| - 2) + 2))) and g(x) = -1sin(1\u03c0((3x + 3)/(1x + 1))) - 1 between the vertical lines x = -2.3 and x = -1.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1((2(-2sin(1\u03c0x - 1) - 1) + 2)/(-2(-2sin(1\u03c0x - 1) - 1) - 3))^2 + 4((2(-2sin(1\u03c0x - 1) - 1) + 2)/(-2(-2sin(1\u03c0x - 1) - 1) - 3)) - 2, g(x) = -2(-1x + 4)^2 - 2, x = 3.3, and x = 4.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (2(3(3|x - 1| - 2)) - 3)/(-1(3(3|x - 1| - 2))) and g(x) = -3(-2sin(3\u03c0x + 1) - 3)^2 + 3(-2sin(3\u03c0x + 1) - 3) + 2 between the vertical lines x = 0.4 and x = 1.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "48.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (2((1(4x + 3) + 3)/(-2(4x + 3) + 3)) + 1)/(-3((1(4x + 3) + 3)/(-2(4x + 3) + 3)) - 1) and g(x) = 2((1x + 2)/(-2x + 3)) - 4 from x = -3.2 to x = 0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8.6", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (2(3cos(3\u03c0(-5x - 4) + 1) + 1))/(2(3cos(3\u03c0(-5x - 4) + 1) + 1) - 1), g(x) = -2cos(3\u03c0((-2x + 3)/(1x + 2))) - 2, x = 1.4, and x = 1.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1e^(2(1|(-4x^2 + 5x + 5)| - 3)) - 2, g(x) = -2e^(-1(4x + 3)) - 2, x = -1.0, and x = -0.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1e^(2((-1((3x + 3)/(-1x - 3)) + 3)/(3((3x + 3)/(-1x - 3)) - 1))), g(x) = 2|(-1x^2 - 5x + 1)| - 1, x = 0.1, and x = 0.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-1(-4(-1e^(-2x) + 2) - 2) - 3)/(3(-4(-1e^(-2x) + 2) - 2)) and g(x) = -1(1x^2 + 4x + 4)^2 + 4(1x^2 + 4x + 4) + 2 between the vertical lines x = -4.1 and x = -0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1(-2cos(2\u03c0(1x^2 + 1x + 3) + 1) - 2) + 3 and g(x) = (1(2|x - 3| - 3) - 2)/(1(2|x - 3| - 3)) between the vertical lines x = 3.9 and x = 4.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (3(-5(3cos(3\u03c0x - 3) - 1)) + 1)/(-1(-5(3cos(3\u03c0x - 3) - 1)) - 1), g(x) = 1|((1x)/(-2x + 3)) + 2| - 2, x = -4.9, and x = -4.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.4", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -4(-1cos(1\u03c0((-2x + 2)/(-1x + 2)) - 2)) + 1 and g(x) = -1(2x^2 - 4x - 5) - 4 between the vertical lines x = 1.8 and x = 1.9000000000000001. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-2(-3|(2sin(2\u03c0x + 2)) - 2| + 2) - 2)/(2(-3|(2sin(2\u03c0x + 2)) - 2| + 2) - 3), g(x) = 2|(-2x^2 - 1) + 3| + 2, x = -2.0, and x = -1.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6.9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 4(2(-3sin(1\u03c0x - 3)) + 4) - 5 and g(x) = 3(3cos(3\u03c0x - 3) - 3) + 1 from x = 1.8 to x = 3.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (2(-1(2x + 3)^2 + 5(2x + 3) - 3) - 2)/(2(-1(2x + 3)^2 + 5(2x + 3) - 3) - 1) and g(x) = (-2((1x + 2)/(-1x + 3)) - 3)/(-3((1x + 2)/(-1x + 3))) from x = 0.7 to x = 1.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -4((2((-1x - 3)/(-2x - 2)) - 1)/(3((-1x - 3)/(-2x - 2)) - 2)) + 2 and g(x) = (-1(-1cos(1\u03c0x) - 2) - 3)/(1(-1cos(1\u03c0x) - 2) - 2) between the vertical lines x = -4.6 and x = -3.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -4(-3(1sin(2\u03c0x - 2) - 3) - 4)^2 + 1(-3(1sin(2\u03c0x - 2) - 3) - 4) + 1 and g(x) = -5(3|x + 2| + 1)^2 - 1(3|x + 2| + 1) + 5 from x = -3.2 to x = -2.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 3|(-2(-5x)^2 + 2(-5x) + 3) - 3| + 2 and g(x) = 2(1sin(1\u03c0x + 1) + 1)^2 - 3(1sin(1\u03c0x + 1) + 1) + 3 from x = -0.2 to x = -0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -5(-2sin(1\u03c0((1x - 3)/(1x)) + 2) + 3)^2 + 4, g(x) = 4(1cos(2\u03c0x + 1) - 3) + 3, x = -0.0, and x = 0.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3e^(-1(-1((1x - 3)/(-2x))^2 + 1((1x - 3)/(-2x)) + 4)) + 1 and g(x) = 3sin(2\u03c0(-1x^2 - 2x + 3) - 3) + 1 from x = 2.4 to x = 2.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1(2sin(1\u03c0((3x + 3)/(-2x - 3)) + 1) - 3) + 3 and g(x) = -5(1x + 2) + 1 between the vertical lines x = -1.6 and x = -1.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1e^(-1(1|(-1x^2 - 1x + 5)| - 2)) + 3, g(x) = -1cos(1\u03c0((-2x - 3)/(-1x - 2)) + 3), x = 1.5, and x = 2.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (3(-1(-1x^2 - 2x - 2) - 2) - 3)/(3(-1(-1x^2 - 2x - 2) - 2) + 2), g(x) = 3sin(3\u03c0(2|x - 3| - 1) + 1), x = 0.9, and x = 1.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-2(4((3x - 1)/(2x + 2)) + 3))/(-2(4((3x - 1)/(2x + 2)) + 3) - 1) and g(x) = 1sin(3\u03c0(1x^2 - 5) - 3) + 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}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1(5(-1sin(3\u03c0x)))^2 - 2(5(-1sin(3\u03c0x))) - 2, g(x) = 3|((-3x - 1)/(-3x + 2)) + 3| + 3, x = 0.9, and x = 1.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8.4", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (2(-1|(-5x) - 2| + 1) - 3)/(-3(-1|(-5x) - 2| + 1) - 3), g(x) = -2cos(2\u03c0(-3x^2 - 4x - 1)) + 2, x = -0.7, and x = -0.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-2((2(3x^2 + 1x - 3) - 3)/(1(3x^2 + 1x - 3) + 2)) + 1)/(2((2(3x^2 + 1x - 3) - 3)/(1(3x^2 + 1x - 3) + 2)) + 2), g(x) = -1|(-1|x + 2| + 2) - 1| - 1, x = -0.9, and x = 0.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.6", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1sin(1\u03c0(3(-2x^2 + 4x - 2) + 4) - 3) - 1, g(x) = (-2(-2x) - 2)/(-2(-2x)), x = 0.3, and x = 0.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2cos(2\u03c0(1((1x - 2)/(3x + 2))^2 + 4((1x - 2)/(3x + 2)) + 1) - 3) + 1, g(x) = 1(-4x - 3) + 2, x = -0.6, and x = -0.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -5(1|((1x - 3)/(2x + 3)) + 1| - 2)^2 + 3(1|((1x - 3)/(2x + 3)) + 1| - 2) + 5 and g(x) = -5(-2x^2 - 4x - 3) - 3 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}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 3cos(2\u03c0(1|(2|x + 1| - 1) - 2|)) - 3 and g(x) = 2sin(2\u03c0(1x + 3) - 1) + 1 from x = 1.9 to x = 2.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1|((-3(1|x| - 1))/(3(1|x| - 1) - 2))| + 2, g(x) = 1(-3cos(1\u03c0x) - 2)^2 - 2(-3cos(1\u03c0x) - 2) + 2, x = -1.7, and x = -1.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "27.8", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-2(1(2|x + 3| - 2) - 4) + 1)/(-2(1(2|x + 3| - 2) - 4)) and g(x) = (-3(1x^2 - 1x - 2) + 3)/(-1(1x^2 - 1x - 2) + 2) between the vertical lines x = -0.2 and x = 2.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14.6", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1((-1(1x^2 + 1x + 5) - 1)/(-1(1x^2 + 1x + 5) + 3)) - 1 and g(x) = 4(3cos(1\u03c0x + 3) - 1) - 4 between the vertical lines x = 1.4 and x = 2.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (1((3(-2x^2 + 4x + 5) + 1)/(2(-2x^2 + 4x + 5) + 3)) + 1)/(3((3(-2x^2 + 4x + 5) + 1)/(2(-2x^2 + 4x + 5) + 3)) - 1), g(x) = 1sin(2\u03c0(-3|x + 3| + 3) - 2) - 3, x = -0.9, and x = 2.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15.7", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2(3(-1|x + 1| + 3)) - 1, g(x) = 4(-1|x| + 3)^2 - 3(-1|x| + 3) - 3, x = 1.9, and x = 4.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16.7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1(1(3e^(1x) + 3) - 2) + 5 and g(x) = 4(3x^2 + 1x - 4)^2 + 4(3x^2 + 1x - 4) - 2 from x = -1.5 to x = -1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-2(1(-2|x + 1| + 2) + 1) - 3)/(-3(1(-2|x + 1| + 2) + 1) - 2) and g(x) = (-2(-2x - 1) - 2)/(3(-2x - 1)) between the vertical lines x = -3.0 and x = -0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2|(5(-5x + 3)) - 2| - 2 and g(x) = (3((3x + 1)/(-3x - 2)) + 2)/(-3((3x + 1)/(-3x - 2)) + 2) from x = 0.5 to x = 0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1(-1|(-1|x + 2| - 3) + 2| + 3)^2 - 3(-1|(-1|x + 2| - 3) + 2| + 3) - 2 and g(x) = 4((-2x - 2)/(3x + 1)) - 1 from x = -3.7 to x = 3.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "63.9", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -3(-2|(-3|x| + 2) + 2| + 2) - 1, g(x) = 2cos(3\u03c0(2x^2 + 1x - 1)) + 2, x = 1.9, and x = 2.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3(4(1x^2 + 1x - 4) + 4) - 1 and g(x) = 3|(2cos(3\u03c0x - 2) + 1)| - 2 between the vertical lines x = -2.3 and x = 1.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "82.5", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -5(-3|(1cos(3\u03c0x + 1) - 1) + 1|)^2 - 3(-3|(1cos(3\u03c0x + 1) - 1) + 1|) - 5, g(x) = -4(3x^2 + 5x) + 4, x = 0.4, and x = 0.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2|(1((1x + 2)/(-2x))^2 + 5((1x + 2)/(-2x)) + 5) + 2| + 1 and g(x) = -3(-2x - 1)^2 + 2(-2x - 1) + 2 from x = -1.8 to x = 0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 4(1sin(3\u03c0(-3|x| - 3) - 3) - 2)^2 - 3(1sin(3\u03c0(-3|x| - 3) - 3) - 2) - 5, g(x) = (-1(-3x + 4) - 3)/(-3(-3x + 4) - 1), x = 1.3, and x = 1.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3(3sin(3\u03c0(-3x - 4) - 3) - 2)^2 - 4(3sin(3\u03c0(-3x - 4) - 3) - 2) - 3 and g(x) = -1(1cos(3\u03c0x - 3) + 2) + 1 from x = 1.6 to x = 1.7000000000000002. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1(-1|(2|x + 2| + 3) - 1| - 1) + 5, g(x) = 4(1x^2 - 1x - 4) + 1, x = -1.6, and x = 2.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2|(1(-4x^2 + 4x - 3) - 3) + 3| - 2, g(x) = -3(2sin(1\u03c0x - 3) - 1)^2 + 4(2sin(1\u03c0x - 3) - 1) - 1, x = 2.2, and x = 2.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2((2(1cos(3\u03c0x + 3) + 3) + 3)/(-3(1cos(3\u03c0x + 3) + 3) - 3)) + 4 and g(x) = 4(1x^2 + 4x + 4)^2 + 4(1x^2 + 4x + 4) - 1 between the vertical lines x = -2.8 and x = -1.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-1(-4(-2cos(2\u03c0x + 1) + 2)^2 + 4) + 1)/(2(-4(-2cos(2\u03c0x + 1) + 2)^2 + 4) - 1) and g(x) = -5(-2|x - 2| + 2) - 3 from x = 3.0 to x = 3.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1|(4(3x^2 + 1x - 3)) - 3| - 3 and g(x) = 1|(-2cos(2\u03c0x + 1) + 1) - 1| - 2 from x = -1.2 to x = 0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 4((1(2e^(-2x) + 3) - 2)/(1(2e^(-2x) + 3) + 3))^2 - 5((1(2e^(-2x) + 3) - 2)/(1(2e^(-2x) + 3) + 3)) + 2 and g(x) = (2(-2|x - 3| + 1) + 1)/(-1(-2|x - 3| + 1) - 3) between the vertical lines x = 1.8 and x = 4.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1|(2(2x^2 - 2x - 1)^2 + 3(2x^2 - 2x - 1) + 5) + 2| and g(x) = -1(3cos(3\u03c0x + 1) - 3)^2 - 1(3cos(3\u03c0x + 1) - 3) between the vertical lines x = -0.6 and x = -0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 5(4(5x^2 + 1x - 4)^2 + 4(5x^2 + 1x - 4))^2 - 2(4(5x^2 + 1x - 4)^2 + 4(5x^2 + 1x - 4)) - 5 and g(x) = (3((-1x - 3)/(1x)) + 1)/(-2((-1x - 3)/(1x)) + 3) between the vertical lines x = 0.7 and x = 0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-1((-3(-1cos(1\u03c0x + 1) + 1))/(1(-1cos(1\u03c0x + 1) + 1) + 2)))/(1((-3(-1cos(1\u03c0x + 1) + 1))/(1(-1cos(1\u03c0x + 1) + 1) + 2))) and g(x) = -3(-1|x + 3|) - 3 from x = -3.7 to x = -2.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3((-1(3|x| - 2))/(3(3|x| - 2) - 2)) - 3 and g(x) = 2e^(1(-1x - 2)) + 3 from x = -0.9 to x = 0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20.8", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1e^(-1(1|(2x - 3) - 1| + 2)) + 1 and g(x) = 1|(5x) + 1| - 2 between the vertical lines x = -0.8 and x = 0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.8", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-2(-1|(-1x^2 + 2x + 2) + 1|) + 3)/(-1(-1|(-1x^2 + 2x + 2) + 1|) + 2), g(x) = 2cos(3\u03c0((-1x)/(3x + 1)) + 3) + 2, x = -0.4, and x = -0.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1|(2|(4x - 1) - 3| + 1) + 1| - 1 and g(x) = -3|(-2sin(2\u03c0x + 1) + 1) + 2| - 2 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}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1cos(1\u03c0(3|(-2x - 2) - 2| + 1)) - 3 and g(x) = -1(3|x - 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}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1((-3(-1x^2 + 1x + 2) + 2)/(2(-1x^2 + 1x + 2) + 2)) - 3 and g(x) = -1|((-1x - 2)/(-2x + 3)) - 1| + 1 from x = 2.0 to x = 2.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1(-1(-2|x - 3| + 3)^2 + 5(-2|x - 3| + 3) + 5)^2 + 2(-1(-2|x - 3| + 3)^2 + 5(-2|x - 3| + 3) + 5) - 5, g(x) = -3|(-2|x - 2|) - 2| + 2, x = 1.0, and x = 1.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1e^(-1(-3(-2|x - 3| + 1) + 4)) + 2 and g(x) = 2|(-4x - 2)| - 3 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}", "role": "user"}], "ground_truth": "3.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1(-4(1x^2 - 3x + 2) - 2) + 4 and g(x) = -5(-2sin(3\u03c0x - 3) + 2)^2 + 5(-2sin(3\u03c0x - 3) + 2) from x = 2.6 to x = 3.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11.9", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 4(1(-1cos(1\u03c0x + 2) - 1)^2 + 1(-1cos(1\u03c0x + 2) - 1) - 2) + 2 and g(x) = (-1(3cos(1\u03c0x - 3)) - 2)/(-2(3cos(1\u03c0x - 3)) + 3) between the vertical lines x = -2.4 and x = -1.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.4", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (2(1cos(3\u03c0(-2|x - 3| - 2)) + 3))/(-2(1cos(3\u03c0(-2|x - 3| - 2)) + 3) - 1), g(x) = 3cos(2\u03c0(3x^2 - 4x + 1) - 1) - 3, x = 2.7, and x = 2.8000000000000003. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (2(1|(-1sin(3\u03c0x - 2) - 1) - 3| + 3) - 1)/(1(1|(-1sin(3\u03c0x - 2) - 1) - 3| + 3) - 3) and g(x) = 1|(-3|x + 2| + 2) - 1| - 3 from x = -4.3 to x = 0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1(-2sin(3\u03c0(2|x + 2|) + 3) - 3) + 5 and g(x) = 3|(2x^2 - 4x + 3) - 1| - 2 from x = -0.2 to x = 2.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2|((1(1sin(1\u03c0x)) + 2)/(3(1sin(1\u03c0x)) + 3)) - 3| + 1 and g(x) = 3e^(1(-3x^2 + 3x + 3)) + 3 from x = -0.8 to x = -0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3|((-3(1x^2 - 3x + 2))/(-1(1x^2 - 3x + 2) - 2)) - 2| and g(x) = -5(3sin(2\u03c0x + 3) + 2)^2 - 2(3sin(2\u03c0x + 3) + 2) - 1 between the vertical lines x = -3.7 and x = -3.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1e^(-1((2(-2|x - 1| + 3) + 3)/(-2(-2|x - 1| + 3) - 2))), g(x) = -4(3cos(1\u03c0x - 3) - 1) + 5, x = -2.7, and x = -1.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15.9", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3e^(1(-1((2x - 2)/(-3x - 1))^2 - 4((2x - 2)/(-3x - 1)) - 5)) + 2 and g(x) = -1|(1|x + 2| - 2) + 1| + 3 between the vertical lines x = -4.3 and x = 0.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-1((2(2sin(3\u03c0x - 1) - 3) - 2)/(-2(2sin(3\u03c0x - 1) - 3) + 3)) + 1)/(-2((2(2sin(3\u03c0x - 1) - 3) - 2)/(-2(2sin(3\u03c0x - 1) - 3) + 3)) + 1), g(x) = 4(2|x| - 1)^2 + 1(2|x| - 1) - 2, x = -0.8, and x = -0.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1|((-3(-3cos(3\u03c0x) - 2))/(-3(-3cos(3\u03c0x) - 2) - 2))| and g(x) = 1sin(2\u03c0(-5x - 5) + 3) + 3 from x = -2.4 to x = -2.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -3e^(-1((-1(2x^2 - 5x + 2) - 1)/(-2(2x^2 - 5x + 2)))) + 3, g(x) = -3(3cos(1\u03c0x - 2) - 1)^2 - 4(3cos(1\u03c0x - 2) - 1) + 5, x = 0.9, and x = 1.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.4", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1cos(2\u03c0(-3(4x^2 - 1x - 4)^2 + 5(4x^2 - 1x - 4) - 5) - 1) + 2, g(x) = -5(-2|x| + 1) - 2, x = 0.9, and x = 1.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 4(-3cos(2\u03c0(4x^2 - 4x + 4) - 1) + 1)^2 - 3(-3cos(2\u03c0(4x^2 - 4x + 4) - 1) + 1) - 4 and g(x) = 4(-3|x + 3|)^2 + 3(-3|x + 3|) - 2 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}", "role": "user"}], "ground_truth": "1.8", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1sin(1\u03c0((-1(-2|x - 2| + 2) + 3)/(-3(-2|x - 2| + 2) - 1)) - 2) + 3 and g(x) = 1sin(2\u03c0(-3|x + 3| + 1) - 2) + 3 between the vertical lines x = 0.7 and x = 0.7999999999999999. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 4(2cos(2\u03c0(-2x - 3) - 2))^2 + 5(2cos(2\u03c0(-2x - 3) - 2)) + 3 and g(x) = 1((-2x + 1)/(3x + 2)) + 3 between the vertical lines x = -3.8 and x = -3.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.8", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1|(-5(1x^2 - 2x - 5) - 5) - 3| + 3, g(x) = -4(-2x^2 + 1x - 4) - 2, x = -0.3, and x = 1.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 4(-2sin(2\u03c0(-1x^2 - 1x + 1) - 1))^2 + 4(-2sin(2\u03c0(-1x^2 - 1x + 1) - 1)) + 4, g(x) = 3|(4x - 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}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1sin(1\u03c0((3(-1x^2 + 5x - 5) - 2)/(2(-1x^2 + 5x - 5) + 3)) + 2) + 1, g(x) = -1sin(1\u03c0((1x)/(1x + 3)) - 2), x = 0.8, and x = 0.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1((1(-3cos(1\u03c0x - 3)) - 2)/(-2(-3cos(1\u03c0x - 3)) - 3)) + 1 and g(x) = 1|(-5x^2 - 4x - 3) + 2| + 1 from x = -2.7 to x = -1.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22.8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1cos(1\u03c0((-3(3x + 1))/(-1(3x + 1) - 2)) + 2) + 2 and g(x) = 3cos(2\u03c0((2x - 3)/(1x)) + 2) + 3 from x = -0.0 to x = 0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1cos(1\u03c0(3((-2x + 3)/(1x))^2 + 4((-2x + 3)/(1x)) + 2) - 2) - 2, g(x) = (-1((3x - 2)/(-1x - 3)) + 2)/(2((3x - 2)/(-1x - 3)) + 1), x = 2.5, and x = 3.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1|(-1(3sin(2\u03c0x + 1) + 2)) - 1| + 3, g(x) = -1(2sin(3\u03c0x - 1) + 3)^2 + 5(2sin(3\u03c0x - 1) + 3) - 4, x = -3.0, and x = -2.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1|((-2((-2x - 2)/(-3x + 2)) - 3)/(1((-2x - 2)/(-3x + 2)))) - 3| + 1, g(x) = -2sin(2\u03c0((3x - 1)/(-3x - 3))) + 3, x = -0.3, and x = -0.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-3(-1((3x + 1)/(-1x + 3))^2 + 5((3x + 1)/(-1x + 3)) - 4) - 2)/(1(-1((3x + 1)/(-1x + 3))^2 + 5((3x + 1)/(-1x + 3)) - 4) - 2) and g(x) = -2|(-4x^2 - 5x + 2) - 1| + 1 from x = -0.0 to x = 0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2cos(2\u03c0(2(4x^2 - 5x - 2) - 4) - 3) + 1 and g(x) = -2(3e^(-1x) - 2) + 5 between the vertical lines x = -0.2 and x = -0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (2((-3(5x + 2))/(3(5x + 2))) + 2)/(-1((-3(5x + 2))/(3(5x + 2))) - 3) and g(x) = -3(-2x^2 + 4x)^2 - 4(-2x^2 + 4x) between the vertical lines x = -0.3 and x = 0.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (2(-3(1x^2 + 1x - 1)^2 - 5(1x^2 + 1x - 1) + 2))/(2(-3(1x^2 + 1x - 1)^2 - 5(1x^2 + 1x - 1) + 2) - 1) and g(x) = -1cos(1\u03c0((3x + 3)/(2x - 1)) + 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}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-1((-2(3|x + 3| - 1) + 2)/(2(3|x + 3| - 1) + 2)))/(-2((-2(3|x + 3| - 1) + 2)/(2(3|x + 3| - 1) + 2)) + 3), g(x) = 1(2x) - 3, x = -2.7, and x = 1.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1(-3(-2cos(2\u03c0x - 3)) - 5)^2 - 3(-3(-2cos(2\u03c0x - 3)) - 5) + 4, g(x) = -1|((-1x - 1)/(3x + 1)) + 3| - 1, x = -2.3, and x = -1.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "23.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2|(-3(-2x^2 + 4x - 3)^2 - 5(-2x^2 + 4x - 3) - 3)| + 1 and g(x) = 2(-2sin(3\u03c0x) - 1)^2 - 4(-2sin(3\u03c0x) - 1) - 5 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}", "role": "user"}], "ground_truth": "3.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2(-2cos(1\u03c0(4x - 2) - 1) - 2) - 2 and g(x) = -3sin(1\u03c0(-2x) - 2) + 3 between the vertical lines x = 0.7 and x = 1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.6", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-1(-2(-4x + 4)) - 1)/(3(-2(-4x + 4)) + 2), g(x) = 3|(1sin(3\u03c0x + 3) + 1) - 1| - 1, x = 2.3, and x = 2.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1sin(2\u03c0(1(-1|x - 3| - 2) - 3) - 2) - 3, g(x) = 3cos(2\u03c0(-4x - 3) + 3) - 1, x = -3.6, and x = -3.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3(-2|(-1x^2 + 2x) - 2| + 3)^2 + 5(-2|(-1x^2 + 2x) - 2| + 3) + 1, g(x) = (-3(-3|x + 2| + 2) + 1)/(-2(-3|x + 2| + 2)), x = -0.2, and x = 0.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3(5(1cos(1\u03c0x + 1) - 1)^2 + 3(1cos(1\u03c0x + 1) - 1)) + 3, g(x) = -2e^(1(1x + 2)) + 3, x = -4.4, and x = -4.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-2((3(-3x^2 + 5x + 4) - 2)/(-1(-3x^2 + 5x + 4) - 1)) + 3)/(3((3(-3x^2 + 5x + 4) - 2)/(-1(-3x^2 + 5x + 4) - 1)) + 2), g(x) = -1|(-4x + 4) - 1| - 2, x = -0.4, and x = 2.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6.6", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3sin(1\u03c0(-3((-3x - 1)/(1x + 1))^2 + 4((-3x - 1)/(1x + 1)) - 5) + 1) + 2, g(x) = (-2(-3x^2 + 2x - 5))/(-2(-3x^2 + 2x - 5) - 1), x = -1.5, and x = -1.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -5(-1(-3x^2 - 4x + 2)^2 + 5(-3x^2 - 4x + 2) - 5) - 2, g(x) = -1sin(1\u03c0(1|x + 2| - 2) + 1) + 1, x = -1.5, and x = 0.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (3(5(2x + 1) - 3) - 2)/(2(5(2x + 1) - 3) - 3) and g(x) = 1|(-3sin(1\u03c0x + 2) + 3) + 1| - 1 from x = -3.8 to x = -2.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.7", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-3(-1|(-4x^2 + 1x) - 3| - 1) + 2)/(-2(-1|(-4x^2 + 1x) - 3| - 1)) and g(x) = 2|(2cos(2\u03c0x + 1) - 1) - 3| - 3 between the vertical lines x = 1.9 and x = 2.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (1(2|(2sin(3\u03c0x - 1) - 3) + 3| - 3) - 1)/(-2(2|(2sin(3\u03c0x - 1) - 3) + 3| - 3) + 1) and g(x) = 1(1|x + 2| - 3)^2 - 1(1|x + 2| - 3) - 2 between the vertical lines x = -1.3 and x = -1.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1|(-2((2x - 3)/(-1x - 3))^2 - 2((2x - 3)/(-1x - 3)) + 2)| + 1 and g(x) = 2sin(2\u03c0(1x + 2) + 2) - 2 from x = 0.1 to x = 0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1(4(2|x - 1| + 2)^2 + 3(2|x - 1| + 2) + 2) - 5, g(x) = 5(-5x + 5)^2 - 1(-5x + 5) + 4, x = 0.4, and x = 1.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2|(-2e^(2((-1x + 2)/(3x + 1))) + 3) + 3| and g(x) = -3|((-2x + 3)/(-3x + 4))| + 3 between the vertical lines x = 0.5 and x = 0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 3cos(3\u03c0((1((3x + 3)/(1x + 3)) - 3)/(2((3x + 3)/(1x + 3)) + 1)) - 2) and g(x) = 3e^(-1(1|x - 3| - 2)) from x = -1.7 to x = -1.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2|(-4(-5x^2 - 3x + 5) + 2) - 1| - 3 and g(x) = (2(1|x - 3| - 3) + 2)/(-1(1|x - 3| - 3) + 2) between the vertical lines x = -1.5 and x = -1.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 5(-5(-3cos(2\u03c0x - 3) - 2) + 3) + 3, g(x) = -2e^(2((-1x)/(-2x + 1))), x = -1.0, and x = -0.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "71.5", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (3(-3cos(3\u03c0(1x^2 + 4x + 5) + 1)) - 3)/(-2(-3cos(3\u03c0(1x^2 + 4x + 5) + 1)) + 3), g(x) = -3|(1x - 3) - 1| - 3, x = 3.3, and x = 3.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1|(-2sin(2\u03c0((-2x + 2)/(3x + 3)) - 2) + 2) + 1| - 1 and g(x) = -1|(2cos(3\u03c0x - 2) + 2) + 1| + 1 from x = 3.4 to x = 3.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1sin(1\u03c0(2|((2x + 2)/(-1x + 3)) - 2| - 2) + 2) - 1 and g(x) = 1cos(1\u03c0((1x - 3)/(-2x - 2)) - 3) - 2 from x = -0.9 to x = -0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (1(-1(-3x - 5)^2 - 3(-3x - 5) + 4))/(-2(-1(-3x - 5)^2 - 3(-3x - 5) + 4) - 2), g(x) = 2|(-5x + 1) + 3|, x = -2.1, and x = -0.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36.4", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2(3cos(3\u03c0(4x + 4) + 1) - 2)^2 + 3, g(x) = 2|(3x^2 + 3x + 2)|, x = -0.4, and x = -0.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3|(-1|(-1|x + 3| - 2) - 1| - 2) - 1| + 3 and g(x) = -2|(-4x) - 1| + 1 between the vertical lines x = -2.4 and x = 4.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "85.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2sin(3\u03c0(-1((-3x - 3)/(-3x - 3))^2 - 1((-3x - 3)/(-3x - 3)) - 5) + 2) and g(x) = 5(4x^2 - 4x - 1)^2 + 5(4x^2 - 4x - 1) - 2 from x = -0.2 to x = 0.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3(1sin(3\u03c0(-5x - 2)) - 1)^2 + 5(1sin(3\u03c0(-5x - 2)) - 1) + 3 and g(x) = (1(-5x + 4) + 1)/(1(-5x + 4) + 3) from x = 1.7 to x = 1.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -3|((1(5x - 2) + 3)/(-2(5x - 2) - 3))|, g(x) = -1((2x - 2)/(-3x)) - 2, x = 0.4, and x = 1.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1sin(1\u03c0(1|(4x + 4) - 2| - 3) + 1) and g(x) = -3(-3sin(1\u03c0x - 1) + 2) - 1 from x = -1.0 to x = 0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14.6", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-1((-3(-1x^2 + 2x + 1))/(2(-1x^2 + 2x + 1) + 1)) + 3)/(-2((-3(-1x^2 + 2x + 1))/(2(-1x^2 + 2x + 1) + 1)) - 1) and g(x) = (1(1sin(1\u03c0x + 3) + 3) - 3)/(3(1sin(1\u03c0x + 3) + 3)) between the vertical lines x = -0.5 and x = 2.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -4((-3((-1x - 1)/(1x + 2)) + 2)/(2((-1x - 1)/(1x + 2)) + 3))^2 + 2 and g(x) = -1|(4x^2 + 1x + 5) + 2| + 1 from x = -2.3 to x = -0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (3(-5(-3e^(-2x) - 1)^2 + 4(-3e^(-2x) - 1) - 2) + 3)/(-3(-5(-3e^(-2x) - 1)^2 + 4(-3e^(-2x) - 1) - 2) + 2), g(x) = -1(-1|x + 3| + 1)^2 - 5(-1|x + 3| + 1) - 2, x = -4.2, and x = -1.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7.9", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -5(3(-1sin(2\u03c0x + 3) - 3) + 3) + 1 and g(x) = 3(1|x - 2| + 1) + 2 between the vertical lines x = -4.9 and x = -4.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -3e^(2(-1|(2x - 4)| + 2)) + 1, g(x) = 1(4x - 1)^2 + 2(4x - 1) + 1, x = -0.2, and x = 0.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-1(4(-1|x - 2| + 3)^2 + 1(-1|x - 2| + 3) - 5) - 2)/(-3(4(-1|x - 2| + 3)^2 + 1(-1|x - 2| + 3) - 5) - 2) and g(x) = -3((2x + 1)/(-1x - 3)) between the vertical lines x = -0.4 and x = 0.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 4(-3e^(2((2x + 2)/(1x + 3))) + 1) - 4, g(x) = 3sin(3\u03c0((1x - 3)/(-2x - 3)) - 2) + 2, x = -3.0, and x = -2.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1|(1(2sin(2\u03c0x + 1) - 3) - 4) - 2| - 3 and g(x) = (2(2|x + 1| + 3))/(1(2|x + 1| + 3) - 2) from x = -1.1 to x = -0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2|((1(-2x^2 + 4) + 2)/(2(-2x^2 + 4) + 1)) - 1| - 3 and g(x) = -2(-3|x - 3| - 2) + 2 between the vertical lines x = -1.5 and x = 1.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "85.6", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1(1(-2|x - 1| + 3) - 1)^2 - 5(1(-2|x - 1| + 3) - 1) - 3 and g(x) = 3cos(2\u03c0((3x - 2)/(3x))) + 1 between the vertical lines x = -0.1 and x = 2.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1cos(3\u03c0((-2((-1x + 1)/(2x - 1)) + 2)/(1((-1x + 1)/(2x - 1)) + 3)) - 2) - 3 and g(x) = -1sin(3\u03c0(-3|x - 1| - 3) - 3) - 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}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3sin(3\u03c0(-1|(-1x^2 - 3x - 2)| + 2) + 1) + 1 and g(x) = -1e^(-1(3|x - 2|)) - 1 between the vertical lines x = 1.7 and x = 1.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (3(-1|((-2x - 2)/(2x - 3)) - 2| + 1) - 1)/(-3(-1|((-2x - 2)/(2x - 3)) - 2| + 1)) and g(x) = 1cos(3\u03c0(-2x - 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}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-2(1|(-2|x + 3| + 3) + 3| + 1))/(-3(1|(-2|x + 3| + 3) + 3| + 1)) and g(x) = 1|(-5x - 4) + 1| - 1 between the vertical lines x = -0.9 and x = -0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1|(3|(2|x + 1| - 1) - 3| - 1) + 3| - 2 and g(x) = (-3(1x^2 - 1x - 5) - 3)/(2(1x^2 - 1x - 5) - 1) between the vertical lines x = -1.8 and x = 2.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38.7", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1(-3|((-2x + 1)/(2x)) + 2| - 3)^2 + 3(-3|((-2x + 1)/(2x)) + 2| - 3) + 4 and g(x) = (2(2sin(1\u03c0x - 2) - 1) + 1)/(-3(2sin(1\u03c0x - 2) - 1) + 1) between the vertical lines x = 1.4 and x = 2.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "92.4", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -3((-2(3e^(2x)) + 3)/(-1(3e^(2x)) - 1)) + 3, g(x) = (-3((-2x - 1)/(1x + 1)) - 1)/(-1((-2x - 1)/(1x + 1)) - 3), x = 1.0, and x = 1.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 5(-1|((-1x + 1)/(-3x + 1))| + 2)^2 - 2(-1|((-1x + 1)/(-3x + 1))| + 2) + 4, g(x) = 3((-1x + 1)/(3x + 2))^2 - 5((-1x + 1)/(3x + 2)) - 3, x = -1.1, and x = -0.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-11.6", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2((-2(-3x - 5) - 3)/(1(-3x - 5) + 2)) + 5 and g(x) = 4((-1x + 1)/(2x - 1)) between the vertical lines x = -0.8 and x = 0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21.8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1(-2|((2x + 3)/(-2x - 2)) - 2| + 2) + 4 and g(x) = -1(2x^2 + 1x + 2)^2 + 3(2x^2 + 1x + 2) - 2 from x = -1.1 to x = 0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "54.8", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1|((-2(-3x - 3))/(2(-3x - 3) + 3)) + 3| - 3, g(x) = 3((3x - 1)/(3x + 3))^2 + 5((3x - 1)/(3x + 3)) + 5, x = -0.6, and x = -0.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2|((3(-1e^(2x) - 3) - 2)/(-3(-1e^(2x) - 3) + 2)) + 3| - 2 and g(x) = -4(2e^(-2x) - 2)^2 + 5(2e^(-2x) - 2) + 5 between the vertical lines x = -0.3 and x = 0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -5(-5(1x + 4) - 4) + 2, g(x) = (-2(3sin(1\u03c0x + 1) + 1))/(1(3sin(1\u03c0x + 1) + 1) + 1), x = -3.1, and x = -2.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 5(-4(-3cos(2\u03c0x) - 2) - 3)^2 - 2(-4(-3cos(2\u03c0x) - 2) - 3) - 4 and g(x) = -2|(-1x^2 + 5x) + 1| - 2 between the vertical lines x = -0.3 and x = -0.19999999999999998. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13.7", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-3(3(3sin(1\u03c0x - 2)) + 2) - 1)/(2(3(3sin(1\u03c0x - 2)) + 2) + 3), g(x) = 2|((2x - 3)/(1x + 2)) - 1|, x = -4.2, and x = -3.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2(-1(-1e^(1x) + 1)^2 - 1(-1e^(1x) + 1) + 1) + 4, g(x) = 2|((3x - 2)/(3x + 3)) + 1| + 3, x = -0.4, and x = 0.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (3((-2(-1e^(-2x) + 2) + 1)/(3(-1e^(-2x) + 2) + 2)) - 2)/(1((-2(-1e^(-2x) + 2) + 1)/(3(-1e^(-2x) + 2) + 2))) and g(x) = 3|(-2x - 5) + 2| between the vertical lines x = -0.7 and x = 0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "54.4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (2((1(-4x^2 + 2x + 2) - 3)/(-1(-4x^2 + 2x + 2) - 2)) - 1)/(-1((1(-4x^2 + 2x + 2) - 3)/(-1(-4x^2 + 2x + 2) - 2)) + 3) and g(x) = 1|(-1x^2 - 1x - 5) + 2| - 2 from x = -0.4 to x = 1.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.4", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (2((-1(1|x - 2| - 1) + 1)/(3(1|x - 2| - 1) - 2)) - 2)/(2((-1(1|x - 2| - 1) + 1)/(3(1|x - 2| - 1) - 2))), g(x) = (-2((-1x + 1)/(-3x - 3)) + 3)/(3((-1x + 1)/(-3x - 3)) + 3), x = 0.4, and x = 3.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6.8", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1(1(-2|x + 3| - 1)^2 + 1(-2|x + 3| - 1) - 4)^2 - 1(1(-2|x + 3| - 1)^2 + 1(-2|x + 3| - 1) - 4) + 4 and g(x) = 3|(-3sin(1\u03c0x - 1) + 2) - 1| between the vertical lines x = -2.5 and x = -1.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2|((3(-2|x - 2| - 3) - 3)/(-2(-2|x - 2| - 3) + 1)) + 3| + 1 and g(x) = -1|(1x^2 - 1x - 3) - 3| from x = -2.4 to x = -1.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.7", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (2(-1sin(2\u03c0(-2x - 4) - 2) + 2) - 2)/(-3(-1sin(2\u03c0(-2x - 4) - 2) + 2)) and g(x) = 1sin(3\u03c0((-2x - 3)/(-2x + 1)) + 2) - 1 between the vertical lines x = -4.2 and x = -3.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -5((-3(-1x - 4) - 1)/(3(-1x - 4) - 2))^2 + 1((-3(-1x - 4) - 1)/(3(-1x - 4) - 2)) + 1, g(x) = (-1((-3x - 1)/(-3x - 1)) + 2)/(1((-3x - 1)/(-3x - 1)) + 1), x = -4.0, and x = -3.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (1(-2|(-4x - 2) + 2| + 2) - 1)/(-1(-2|(-4x - 2) + 2| + 2) + 3) and g(x) = -1(-1x - 2)^2 - 3(-1x - 2) + 3 from x = -3.0 to x = 2.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (3(-4(3cos(2\u03c0x + 1) + 3)^2 - 1(3cos(2\u03c0x + 1) + 3) + 2))/(-2(-4(3cos(2\u03c0x + 1) + 3)^2 - 1(3cos(2\u03c0x + 1) + 3) + 2) - 1), g(x) = -1e^(1((1x)/(1x - 3))) + 3, x = 0.4, and x = 1.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1cos(2\u03c0(-1(2x^2 + 4x - 3) - 4) - 3) - 2 and g(x) = 3(-2x + 5) - 2 from x = 2.6 to x = 2.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1(5(1e^(1x) - 2)^2 + 4(1e^(1x) - 2) - 5)^2 - 4(5(1e^(1x) - 2)^2 + 4(1e^(1x) - 2) - 5) + 1 and g(x) = 1|(1cos(3\u03c0x - 2) + 1) - 3| + 3 between the vertical lines x = 1.0 and x = 1.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.7", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3cos(3\u03c0((1(3|x + 2| + 2) - 3)/(-3(3|x + 2| + 2))) + 2) - 2, g(x) = -2((-3x - 2)/(-3x))^2 + 2((-3x - 2)/(-3x)) - 3, x = -2.4, and x = -1.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (2(-1(-5x - 4)^2 + 3(-5x - 4) + 4) + 1)/(2(-1(-5x - 4)^2 + 3(-5x - 4) + 4) - 3), g(x) = -4(1cos(1\u03c0x - 3) - 2) - 1, x = -1.5, and x = -0.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (3(4(-3e^(-1x))^2 - 1(-3e^(-1x)) + 3) + 2)/(-3(4(-3e^(-1x))^2 - 1(-3e^(-1x)) + 3) + 2) and g(x) = 4(2sin(2\u03c0x + 2) - 1)^2 + 2(2sin(2\u03c0x + 2) - 1) - 4 from x = 1.7 to x = 1.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1(1cos(1\u03c0(-2x^2 - 2) - 3) - 3)^2 - 4(1cos(1\u03c0(-2x^2 - 2) - 3) - 3) - 3 and g(x) = -2(-3|x| + 3) + 4 from x = 4.5 to x = 4.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -5(4(-4x^2 + 1x + 2) - 2) - 4, g(x) = 1|((-3x)/(-3x - 1)) - 2| + 2, x = -0.6, and x = 0.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39.9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1(-1(-3x^2 - 5x - 2) - 4) - 5 and g(x) = 1(-2|x + 2| + 1)^2 - 5(-2|x + 2| + 1) - 4 from x = -4.3 to x = -1.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (1(4(3|x| - 2)^2 - 4(3|x| - 2) - 2) + 3)/(-3(4(3|x| - 2)^2 - 4(3|x| - 2) - 2) - 3) and g(x) = 1(4x^2 - 4x + 5) - 4 from x = 0.7 to x = 1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3|(-3sin(1\u03c0(-3|x + 1| - 1) + 2) - 2) + 1| - 2 and g(x) = -3|((2x + 2)/(-2x))| + 1 from x = 1.6 to x = 1.7000000000000002. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -5(2(-2|x - 3| + 2)^2 - 1(-2|x - 3| + 2) - 4) - 3 and g(x) = (1(-2|x - 2|) + 1)/(1(-2|x - 2|) + 2) from x = 3.3 to x = 4.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13.4", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -5(1|(4x^2 - 1x + 3) - 1| - 2) - 5 and g(x) = -1|((1x + 2)/(2x + 2))| between the vertical lines x = -1.0 and x = -0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2((-1(-1|x - 3| + 1) - 2)/(3(-1|x - 3| + 1) - 2)) + 5, g(x) = 3cos(3\u03c0(1x^2 + 1x - 3) - 1), x = 2.9, and x = 3.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1(5(2x - 5)^2 - 5(2x - 5) - 4)^2 + 5(5(2x - 5)^2 - 5(2x - 5) - 4) - 1 and g(x) = -1sin(2\u03c0((3x)/(1x + 2)) - 3) + 3 between the vertical lines x = 3.3 and x = 3.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2cos(1\u03c0((3(2x^2 - 3x - 3) + 2)/(1(2x^2 - 3x - 3) + 1)) + 3) and g(x) = 2((2x + 2)/(2x - 1)) + 3 between the vertical lines x = -0.5 and x = -0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-1(3(-1x + 4)^2 - 5(-1x + 4) - 3) - 2)/(2(3(-1x + 4)^2 - 5(-1x + 4) - 3) - 3) and g(x) = 1|(2x^2 + 1x + 4) + 2| + 2 from x = 1.7 to x = 4.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "93.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3(-3(4x^2 + 1x - 5) - 1)^2 + 2 and g(x) = 1sin(2\u03c0(-2|x - 2| - 2) + 2) + 1 from x = -1.2 to x = -1.0999999999999999. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3sin(2\u03c0(1|(5x^2 + 3x - 3)| - 2) - 3) + 3 and g(x) = (-3(-1e^(2x) + 1))/(-2(-1e^(2x) + 1) - 3) from x = 2.4 to x = 2.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (1(-1sin(3\u03c0(5x^2 - 2x - 2) - 2)))/(-3(-1sin(3\u03c0(5x^2 - 2x - 2) - 2)) + 1), g(x) = 2sin(3\u03c0(2|x + 3| - 2) + 2) - 1, x = 0.7, and x = 0.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (2(-4(-2e^(2x) + 2)^2 - 4(-2e^(2x) + 2) + 5))/(2(-4(-2e^(2x) + 2)^2 - 4(-2e^(2x) + 2) + 5) - 1) and g(x) = -2cos(1\u03c0((2x)/(2x + 3)) - 3) + 3 between the vertical lines x = -0.2 and x = 0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.8", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2|(-2|(-2x^2 - 2) + 2| - 2)| - 3 and g(x) = (3(-4x^2 - 3x + 1) + 2)/(1(-4x^2 - 3x + 1) + 2) between the vertical lines x = -0.3 and x = 0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (1(-1sin(3\u03c0((-2x - 2)/(-1x)) + 2) + 2) + 3)/(2(-1sin(3\u03c0((-2x - 2)/(-1x)) + 2) + 2) + 1) and g(x) = (-3(3sin(3\u03c0x + 2) - 1))/(2(3sin(3\u03c0x + 2) - 1) + 1) between the vertical lines x = -2.8 and x = -2.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-2(-1cos(2\u03c0(-1x - 3) - 1) - 1) + 3)/(-2(-1cos(2\u03c0(-1x - 3) - 1) - 1)) and g(x) = 2|(1x + 4) + 1| + 1 between the vertical lines x = 2.4 and x = 3.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11.7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1|((3(3|x + 3| - 2) + 2)/(-3(3|x + 3| - 2) + 4)) - 3| and g(x) = -1((-2x + 1)/(-2x + 3))^2 + 4((-2x + 1)/(-2x + 3)) + 2 from x = 1.0 to x = 1.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-12.6", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2|(1|((-2x + 1)/(-3x - 1)) + 3| - 2) - 3| - 2 and g(x) = -5(2x^2 + 3x + 5)^2 - 1(2x^2 + 3x + 5) between the vertical lines x = -0.4 and x = -0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "47.9", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2|(5((-3x + 3)/(1x)) - 5) + 2| - 2 and g(x) = 5(-1sin(1\u03c0x - 2)) - 3 between the vertical lines x = 0.8 and x = 1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2|(2|(1x + 2) + 3|)| + 2, g(x) = -3e^(-2(3x^2 + 1x - 2)) - 3, x = -3.8, and x = -0.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15.7", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-3(-1(3cos(1\u03c0x + 1) - 2)^2 + 5(3cos(1\u03c0x + 1) - 2) - 5) - 3)/(-1(-1(3cos(1\u03c0x + 1) - 2)^2 + 5(3cos(1\u03c0x + 1) - 2) - 5) - 1) and g(x) = 2|((1x + 3)/(1x + 2)) - 2| + 2 between the vertical lines x = -1.3 and x = -0.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -4(-3(-3cos(1\u03c0x + 1) - 3)^2 + 2(-3cos(1\u03c0x + 1) - 3) + 5)^2 + 1(-3(-3cos(1\u03c0x + 1) - 3)^2 + 2(-3cos(1\u03c0x + 1) - 3) + 5) + 4 and g(x) = 2cos(3\u03c0((-2x - 3)/(-1x + 2))) - 3 between the vertical lines x = -3.1 and x = -3.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3(-1|(1|x + 1|)| + 2)^2 + 3(-1|(1|x + 1|)| + 2) and g(x) = 1cos(3\u03c0(-2x^2 + 4x + 5) - 2) - 1 from x = -3.2 to x = -3.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-1(-1(-4x^2 + 2x + 2)^2 - 4(-4x^2 + 2x + 2) + 5) + 1)/(3(-1(-4x^2 + 2x + 2)^2 - 4(-4x^2 + 2x + 2) + 5) - 1), g(x) = 4(3x + 2) - 2, x = -1.1, and x = -0.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 3(-2|(-1|x| - 3) + 3| + 3) + 2 and g(x) = 5(-2sin(3\u03c0x + 3) - 3)^2 + 2(-2sin(3\u03c0x + 3) - 3) - 2 between the vertical lines x = 1.5 and x = 1.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-1(-1(-2cos(1\u03c0x + 3) + 1) - 3) - 2)/(2(-1(-2cos(1\u03c0x + 3) + 1) - 3) + 2), g(x) = 1|(-2|x + 3| + 3) + 3| - 3, x = -1.4, and x = 1.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.8", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 4(-1(-2x - 1)^2 - 5(-2x - 1) - 5) and g(x) = -1(-2sin(3\u03c0x) + 2)^2 + 2(-2sin(3\u03c0x) + 2) + 4 between the vertical lines x = 0.7 and x = 0.7999999999999999. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2sin(2\u03c0(1|(3|x + 1| - 2) - 2| - 3) + 2) - 1, g(x) = -1|(-2|x - 3| - 3)| + 3, x = 2.0, and x = 2.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2cos(2\u03c0(-5(2|x + 2| + 2)^2 + 5(2|x + 2| + 2) - 2)) + 3 and g(x) = -3cos(3\u03c0(-5x^2 - 4x - 5) - 3) + 1 between the vertical lines x = -4.4 and x = -4.300000000000001. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (2(2e^(-1(-5x - 1)) + 2))/(-3(2e^(-1(-5x - 1)) + 2) - 2) and g(x) = 3((-2x + 1)/(2x - 3))^2 - 4((-2x + 1)/(2x - 3)) - 3 between the vertical lines x = -0.3 and x = 1.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-3(3(-1sin(3\u03c0x) + 1)^2 - 1(-1sin(3\u03c0x) + 1) - 3) + 1)/(1(3(-1sin(3\u03c0x) + 1)^2 - 1(-1sin(3\u03c0x) + 1) - 3) - 3) and g(x) = 2((2x)/(1x - 2)) + 1 from x = 3.3 to x = 3.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.7", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2|((2(-3|x + 3| + 2))/(3(-3|x + 3| + 2) + 3)) + 2| and g(x) = 2|(1|x + 2| - 2)| between the vertical lines x = -3.9 and x = -3.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (1(-3(-3cos(2\u03c0x + 3) - 1) - 3) + 2)/(1(-3(-3cos(2\u03c0x + 3) - 1) - 3) + 2) and g(x) = (-1(1cos(3\u03c0x - 2) + 3) + 1)/(1(1cos(3\u03c0x - 2) + 3) - 3) from x = -3.4 to x = -2.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13.4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (3(2|(-1|x + 3| - 3) + 1| - 3))/(-3(2|(-1|x + 3| - 3) + 1| - 3) + 4) and g(x) = -3((-1x + 1)/(-3x + 4))^2 + 4((-1x + 1)/(-3x + 4)) from x = 1.1 to x = 1.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-3(-1(-3e^(-2x) + 3)^2 + 3(-3e^(-2x) + 3) + 1) - 3)/(3(-1(-3e^(-2x) + 3)^2 + 3(-3e^(-2x) + 3) + 1) + 2) and g(x) = -3(-5x + 4)^2 - 1(-5x + 4) - 1 between the vertical lines x = 0.8 and x = 0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (1((-3((1x - 2)/(1x + 3)))/(2((1x - 2)/(1x + 3)) + 2)) - 1)/(-2((-3((1x - 2)/(1x + 3)))/(2((1x - 2)/(1x + 3)) + 2)) - 2) and g(x) = 3sin(1\u03c0(1x^2 + 4x - 2) + 2) + 1 from x = -0.9 to x = -0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.4", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3sin(2\u03c0(-5(5x - 2) - 3) + 3) - 2, g(x) = 4(-2|x + 1| + 2) + 2, x = 0.4, and x = 0.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (2(2(2|x| + 1)^2 - 2(2|x| + 1)) - 1)/(-1(2(2|x| + 1)^2 - 2(2|x| + 1)) - 1) and g(x) = (2(2cos(1\u03c0x - 1)))/(1(2cos(1\u03c0x - 1)) + 1) from x = 1.7 to x = 2.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3(-5(-2x + 3)^2 - 4(-2x + 3) + 1)^2 + 3 and g(x) = 5((-1x - 3)/(2x - 1)) - 5 from x = 1.2 to x = 2.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12.4", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (3(1e^(-1(-1|x - 3| - 2))) - 1)/(-2(1e^(-1(-1|x - 3| - 2))) + 1) and g(x) = -1|(-3x + 5) + 3| + 2 between the vertical lines x = 1.5 and x = 3.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1cos(3\u03c0(-1|(2x^2 + 5x - 1) - 3| - 1) - 2) + 2 and g(x) = -1|(3|x| - 2) - 1| + 3 from x = -0.3 to x = -0.19999999999999998. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1|(-3(1|x| - 3)^2 - 4(1|x| - 3) + 5) - 3| and g(x) = (-3(-3x^2 + 1x - 1) - 2)/(3(-3x^2 + 1x - 1)) between the vertical lines x = -3.5 and x = -3.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -5(-1(2|x| - 3))^2 + 4 and g(x) = (-2(-1sin(3\u03c0x + 3) - 3) + 3)/(-2(-1sin(3\u03c0x + 3) - 3) - 1) between the vertical lines x = -1.8 and x = -1.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1((2(3cos(1\u03c0x + 2) - 1) - 2)/(-3(3cos(1\u03c0x + 2) - 1) - 2)) + 1, g(x) = 1|(-5x^2 + 5x - 3) + 2| + 3, x = -1.1, and x = -0.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9.4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1cos(1\u03c0(1(1|x + 3| + 3)^2 - 3(1|x + 3| + 3) + 5) + 2) - 3 and g(x) = -3(4x - 3) - 4 from x = 0.6 to x = 0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (1(3cos(1\u03c0((2x)/(2x - 3)) - 1) - 2) + 1)/(2(3cos(1\u03c0((2x)/(2x - 3)) - 1) - 2)), g(x) = 4((1x - 1)/(3x + 1))^2 - 4((1x - 1)/(3x + 1)), x = 2.4, and x = 3.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1(-5(-3cos(1\u03c0x + 3) - 2)^2 - 3(-3cos(1\u03c0x + 3) - 2) + 5)^2 + 3(-5(-3cos(1\u03c0x + 3) - 2)^2 - 3(-3cos(1\u03c0x + 3) - 2) + 5) - 2 and g(x) = (2(-2|x - 2| - 1) - 1)/(-3(-2|x - 2| - 1) - 2) from x = 1.6 to x = 1.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7.4", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1|((3(-5x^2 - 2x + 5) - 3)/(-1(-5x^2 - 2x + 5) - 3)) - 3| + 2 and g(x) = (-1(2cos(3\u03c0x) + 2) - 1)/(2(2cos(3\u03c0x) + 2) - 3) between the vertical lines x = 0.9 and x = 1.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "43.9", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 3(-2|(-2sin(1\u03c0x - 3) - 3) - 1| + 2) - 3 and g(x) = (2(-3x^2 - 5x + 3) - 2)/(2(-3x^2 - 5x + 3) + 2) between the vertical lines x = -2.2 and x = 0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "61.7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1(-5(2|x + 2| - 3) - 5)^2 - 4(-5(2|x + 2| - 3) - 5) - 1 and g(x) = -2(-3sin(2\u03c0x - 3)) - 1 from x = -1.0 to x = -0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.9", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-2(3sin(1\u03c0(-4x^2 + 2x + 1) + 2) - 1) + 2)/(2(3sin(1\u03c0(-4x^2 + 2x + 1) + 2) - 1) - 3) and g(x) = 4((-1x + 1)/(-2x - 3)) + 1 between the vertical lines x = 3.9 and x = 4.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-1(-1((-1x)/(-3x + 4)) + 1))/(1(-1((-1x)/(-3x + 4)) + 1) + 1) and g(x) = (-1(-5x - 2) - 3)/(-3(-5x - 2) - 1) from x = -0.1 to x = 1.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8.8", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (2(3cos(2\u03c0(2|x - 3| - 3) + 1) - 2) - 2)/(3(3cos(2\u03c0(2|x - 3| - 3) + 1) - 2) + 2), g(x) = 1e^(2(2x - 5)) - 2, x = -0.8, and x = -0.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.9", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (1(-4(-4x^2 + 1x - 2) - 3))/(-1(-4(-4x^2 + 1x - 2) - 3) + 3) and g(x) = 3|((3x - 2)/(2x + 3))| - 3 between the vertical lines x = 0.3 and x = 2.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (3(-4((-2x)/(1x + 1))^2 - 4((-2x)/(1x + 1)) + 4) - 2)/(1(-4((-2x)/(1x + 1))^2 - 4((-2x)/(1x + 1)) + 4) + 3), g(x) = -2cos(3\u03c0((2x - 3)/(-3x + 4)) + 3) - 3, x = -0.3, and x = 4.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13.4", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1(2cos(1\u03c0(-2x + 2) + 1) - 1)^2 + 3, g(x) = (1((-1x + 2)/(-1x + 2)) + 1)/(1((-1x + 2)/(-1x + 2)) + 3), x = -3.1, and x = -2.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1(-3(4x + 5) - 3)^2 - 4(-3(4x + 5) - 3) + 2 and g(x) = 1|(4x^2 - 3x) + 3| + 2 from x = -2.1 to x = -1.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12.9", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (2(1|(-3|x + 2| - 2)| - 2) - 3)/(-1(1|(-3|x + 2| - 2)| - 2) - 3) and g(x) = (-2((2x - 1)/(-3x + 2)) - 1)/(-2((2x - 1)/(-3x + 2)) + 3) between the vertical lines x = -2.5 and x = -1.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (3(3e^(-1(4x + 3)) + 3) - 3)/(-1(3e^(-1(4x + 3)) + 3) - 2) and g(x) = -4(-1cos(1\u03c0x - 3) + 1) + 5 from x = 3.6 to x = 4.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3(3|(-1x + 3) - 3| - 1) + 5 and g(x) = 4(-2sin(2\u03c0x - 3) + 2) - 1 from x = -0.0 to x = 0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-3(-1|((-1x + 3)/(2x - 1)) - 3| - 1) + 2)/(2(-1|((-1x + 3)/(2x - 1)) - 3| - 1) + 1) and g(x) = 3e^(-2(-2|x - 2| + 3)) - 3 from x = 1.0 to x = 3.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -4(-4(-2sin(1\u03c0x + 1))^2 + 4(-2sin(1\u03c0x + 1)) - 1) - 4 and g(x) = -2e^(-1(3|x - 1| + 3)) - 1 from x = -2.5 to x = -2.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1(-1cos(2\u03c0(1|x - 2| - 2) - 2) - 2)^2 + 5(-1cos(2\u03c0(1|x - 2| - 2) - 2) - 2) + 3 and g(x) = 3(-2sin(2\u03c0x - 1) - 3) + 1 between the vertical lines x = 1.5 and x = 2.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8.8", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (3((-2(1x - 4) + 3)/(3(1x - 4) + 3)))/(1((-2(1x - 4) + 3)/(3(1x - 4) + 3)) - 3) and g(x) = -2|(-3cos(1\u03c0x - 3) + 3) - 3| + 1 between the vertical lines x = -2.6 and x = -2.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-1(1sin(3\u03c0((-1x + 1)/(2x)) - 1) - 3) - 1)/(3(1sin(3\u03c0((-1x + 1)/(2x)) - 1) - 3) - 2), g(x) = -1(-1|x| - 1)^2 - 5(-1|x| - 1) - 3, x = -3.4, and x = 3.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-3((-1(3x^2 + 4x - 3) + 3)/(-2(3x^2 + 4x - 3) - 1)) + 3)/(-2((-1(3x^2 + 4x - 3) + 3)/(-2(3x^2 + 4x - 3) - 1)) - 1) and g(x) = 3e^(1(3x)) from x = -1.2 to x = 0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "26.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 3|(1|((-2x + 3)/(2x)) - 1|)| - 3 and g(x) = 1(-1cos(1\u03c0x - 2) + 2) - 2 from x = 0.6 to x = 1.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2cos(3\u03c0((3(2x^2 - 1x - 1) - 1)/(2(2x^2 - 1x - 1)))) - 2 and g(x) = (-3((2x + 1)/(-1x + 2)) + 1)/(1((2x + 1)/(-1x + 2)) + 1) from x = 1.1 to x = 1.2000000000000002. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2|(-3|(2sin(3\u03c0x) - 1) + 1| + 3) + 3| + 3 and g(x) = (1((1x - 3)/(-1x + 2)) - 2)/(-1((1x - 3)/(-1x + 2)) - 3) from x = -4.2 to x = -4.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1|(5(-1x^2 + 3x) + 5) + 2| - 1, g(x) = -3sin(3\u03c0(1x + 1) + 2) + 2, x = 3.2, and x = 3.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 3|(-3cos(1\u03c0(4x - 4) + 2) - 2) + 1| + 1 and g(x) = 2|(-3|x + 3| + 1) - 3| + 1 between the vertical lines x = -2.8 and x = -2.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1(-1e^(2(-1x^2 + 1)) + 1)^2 + 3(-1e^(2(-1x^2 + 1)) + 1) + 5, g(x) = -3cos(3\u03c0(-2x - 2) - 2) + 1, x = -0.7, and x = 0.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "46.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-2(-1(-5x)^2 + 2(-5x) + 5) + 1)/(1(-1(-5x)^2 + 2(-5x) + 5)) and g(x) = -3sin(1\u03c0(-1x^2 - 5x) - 3) + 1 from x = 0.1 to x = 0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1cos(2\u03c0(-3|(2|x + 2| + 2)| + 1) - 1) + 1 and g(x) = 3(2e^(-2x) - 2) + 1 from x = 0.0 to x = 0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (2(-2|(-4x - 2) + 3| - 1) - 1)/(-1(-2|(-4x - 2) + 3| - 1) - 2) and g(x) = -1(-2sin(1\u03c0x - 2) - 3)^2 - 1(-2sin(1\u03c0x - 2) - 3) - 5 from x = -0.0 to x = 0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1|(1e^(2(-3|x - 1| + 2)) + 1) - 2| + 3 and g(x) = 1(2x + 1) - 2 from x = 1.6 to x = 1.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (3(1sin(1\u03c0((2x + 2)/(2x + 2)) - 3) - 3) + 3)/(3(1sin(1\u03c0((2x + 2)/(2x + 2)) - 3) - 3) + 2) and g(x) = 3(-2sin(3\u03c0x - 3)) - 3 between the vertical lines x = -0.4 and x = 0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3(2sin(3\u03c0(-3x^2 + 5x + 5) - 1))^2 - 3(2sin(3\u03c0(-3x^2 + 5x + 5) - 1)) + 3 and g(x) = -5(-2x^2 - 3x - 3)^2 - 5(-2x^2 - 3x - 3) + 5 from x = -0.7 to x = -0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-1(-2|(2|x + 2| + 1) - 2| + 1) - 1)/(-3(-2|(2|x + 2| + 1) - 2| + 1) + 1) and g(x) = (-1(3cos(3\u03c0x + 2) - 3) - 2)/(-1(3cos(3\u03c0x + 2) - 3)) between the vertical lines x = -3.4 and x = -3.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 4(5((3x + 3)/(-1x)) - 3)^2 - 3(5((3x + 3)/(-1x)) - 3), g(x) = 3sin(1\u03c0((2x + 1)/(-3x + 4)) + 1) - 2, x = -0.8, and x = -0.7000000000000001. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1|((2(3|x - 1| - 1) - 3)/(-2(3|x - 1| - 1) - 3)) + 1| + 2 and g(x) = 1e^(-1((3x - 3)/(2x))) - 3 from x = 0.6 to x = 0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1(1cos(2\u03c0((1x - 1)/(2x + 2)) - 1) + 2)^2 - 5(1cos(2\u03c0((1x - 1)/(2x + 2)) - 1) + 2) + 2 and g(x) = 4(-3cos(3\u03c0x + 3) + 1) - 4 between the vertical lines x = 1.6 and x = 1.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3|(5(-1cos(1\u03c0x - 2) + 1)^2 - 1(-1cos(1\u03c0x - 2) + 1) - 1) - 3| - 1 and g(x) = -1cos(3\u03c0(2|x + 3|) + 1) - 2 between the vertical lines x = 1.1 and x = 2.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "23.7", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (1(-1(2e^(2x))^2 + 2(2e^(2x)) + 2))/(3(-1(2e^(2x))^2 + 2(2e^(2x)) + 2) - 1) and g(x) = 2cos(3\u03c0(-1|x + 1| - 1) - 1) + 2 between the vertical lines x = 3.5 and x = 3.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"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(1\u03c0((-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}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"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}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"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}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3sin(1\u03c0(-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}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"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(3\u03c0(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}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"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(1\u03c0x + 3) - 2)^2 - 3(-2sin(1\u03c0x + 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}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"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(2\u03c0x - 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}", "role": "user"}], "ground_truth": "84.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3|(-1cos(2\u03c0(-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}", "role": "user"}], "ground_truth": "0.7", "dataset": "MATH"}
{"messages": [{"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(3\u03c0x + 1) - 1))/(2(-2cos(3\u03c0x + 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}", "role": "user"}], "ground_truth": "3.9", "dataset": "MATH"}
{"messages": [{"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}", "role": "user"}], "ground_truth": "2.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1|(2|(3cos(2\u03c0x - 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}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"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}", "role": "user"}], "ground_truth": "8.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -5(3sin(2\u03c0(1x^2 - 5x) - 2))^2 + 2(3sin(2\u03c0(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}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"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}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-1(2sin(2\u03c0(4x^2 + 3x - 1) + 1) + 3) + 2)/(-2(2sin(2\u03c0(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}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2|(-3sin(3\u03c0(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}", "role": "user"}], "ground_truth": "1.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2(3cos(1\u03c0(2x^2 - 4x + 5) - 3)), g(x) = -5(-2sin(1\u03c0x + 2) + 3)^2 + 1(-2sin(1\u03c0x + 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}", "role": "user"}], "ground_truth": "0.7", "dataset": "MATH"}
{"messages": [{"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}", "role": "user"}], "ground_truth": "6.5", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1cos(1\u03c0(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}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1sin(3\u03c0((-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}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"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}", "role": "user"}], "ground_truth": "9.4", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2cos(1\u03c0(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}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"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}", "role": "user"}], "ground_truth": "8.9", "dataset": "MATH"}
{"messages": [{"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}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"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}", "role": "user"}], "ground_truth": "12.6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3|(4((-1x - 2)/(-1x - 1)) - 3) + 2| and g(x) = -3sin(1\u03c0(-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}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 3|(1sin(1\u03c0(2x^2 - 3x - 3) - 1)) + 1| and g(x) = 3sin(1\u03c0((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}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"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}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2cos(1\u03c0(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}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"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}", "role": "user"}], "ground_truth": "16.7", "dataset": "MATH"}
{"messages": [{"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(2\u03c0(-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}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3sin(2\u03c0(-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}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"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(3\u03c0x + 3)) + 3)/(1(-1cos(3\u03c0x + 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}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1cos(1\u03c0(2|(2|x - 3| + 2) + 1| - 1) - 3) + 1 and g(x) = -2(3cos(1\u03c0x - 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}", "role": "user"}], "ground_truth": "0.7", "dataset": "MATH"}
{"messages": [{"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(2\u03c0(-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}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1(1sin(1\u03c0((1x - 2)/(-2x + 1)) - 3) - 1) + 5, g(x) = 2cos(3\u03c0(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}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"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}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"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(2\u03c0x - 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}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"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(2\u03c0x) + 3)^2 - 5(2sin(2\u03c0x) + 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}", "role": "user"}], "ground_truth": "3.1", "dataset": "MATH"}
{"messages": [{"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}", "role": "user"}], "ground_truth": "2.8", "dataset": "MATH"}
{"messages": [{"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(1\u03c0(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}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"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}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 4(4(3cos(2\u03c0x) + 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}", "role": "user"}], "ground_truth": "17.6", "dataset": "MATH"}
{"messages": [{"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}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"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}", "role": "user"}], "ground_truth": "2.4", "dataset": "MATH"}
{"messages": [{"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}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"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}", "role": "user"}], "ground_truth": "17.8", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 4(3sin(1\u03c0(-1|x + 2| - 3) - 1) + 1)^2 + 4(3sin(1\u03c0(-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}", "role": "user"}], "ground_truth": "5.4", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2cos(3\u03c0(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}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"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}", "role": "user"}], "ground_truth": "0.7", "dataset": "MATH"}
{"messages": [{"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}", "role": "user"}], "ground_truth": "-7.7", "dataset": "MATH"}
{"messages": [{"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}", "role": "user"}], "ground_truth": "74.0", "dataset": "MATH"}
{"messages": [{"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(3\u03c0(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}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"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}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2(4(-1sin(3\u03c0x + 1) + 1) + 2)^2 - 2(4(-1sin(3\u03c0x + 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}", "role": "user"}], "ground_truth": "37.2", "dataset": "MATH"}
{"messages": [{"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}", "role": "user"}], "ground_truth": "21.7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1sin(1\u03c0((-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}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"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(2\u03c0(-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}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"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}", "role": "user"}], "ground_truth": "6.6", "dataset": "MATH"}
{"messages": [{"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(2\u03c0x + 3) - 3)^2 + 4(-3sin(2\u03c0x + 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}", "role": "user"}], "ground_truth": "8.6", "dataset": "MATH"}
{"messages": [{"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(2\u03c0(-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}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"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}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"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(2\u03c0(-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}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"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(2\u03c0((-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}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"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}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"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}", "role": "user"}], "ground_truth": "9.4", "dataset": "MATH"}
{"messages": [{"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}", "role": "user"}], "ground_truth": "7.1", "dataset": "MATH"}
{"messages": [{"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(3\u03c0x - 1) + 2)^2 - 3(-2cos(3\u03c0x - 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}", "role": "user"}], "ground_truth": "14.1", "dataset": "MATH"}
{"messages": [{"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}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"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}", "role": "user"}], "ground_truth": "9.5", "dataset": "MATH"}
{"messages": [{"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}", "role": "user"}], "ground_truth": "34.3", "dataset": "MATH"}
{"messages": [{"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(1\u03c0x + 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}", "role": "user"}], "ground_truth": "0.7", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (1(-2cos(1\u03c0(-3x + 5) - 3) + 1) - 1)/(2(-2cos(1\u03c0(-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}", "role": "user"}], "ground_truth": "4.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2sin(3\u03c0((-1(-2x^2 + 4x - 2) - 1)/(1(-2x^2 + 4x - 2) - 3))) - 2 and g(x) = 2cos(1\u03c0(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}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2|(-3(-5x^2 + 1x - 2) - 3) - 2| + 1 and g(x) = 2sin(2\u03c0((-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}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2(-2sin(3\u03c0(-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}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (2(1cos(3\u03c0(-1|x + 2| - 2)) + 1) + 2)/(-2(1cos(3\u03c0(-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}", "role": "user"}], "ground_truth": "19.7", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1(-1(-3sin(1\u03c0x) + 1)^2 - 3(-3sin(1\u03c0x) + 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}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 5(1sin(3\u03c0(1|x| - 1)) - 1)^2 + 2(1sin(3\u03c0(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}", "role": "user"}], "ground_truth": "15.4", "dataset": "MATH"}
{"messages": [{"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}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"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}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"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}", "role": "user"}], "ground_truth": "2.5", "dataset": "MATH"}
{"messages": [{"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}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"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}", "role": "user"}], "ground_truth": "4.1", "dataset": "MATH"}
{"messages": [{"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(2\u03c0((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}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2cos(1\u03c0((-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}", "role": "user"}], "ground_truth": "9.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (2(3cos(2\u03c0(-2x^2 + 5x - 3)) + 2) + 3)/(-3(3cos(2\u03c0(-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}", "role": "user"}], "ground_truth": "3.6", "dataset": "MATH"}
{"messages": [{"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(2\u03c0x) - 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}", "role": "user"}], "ground_truth": "37.9", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3sin(1\u03c0((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}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1(-3(-3sin(1\u03c0x + 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}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"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(3\u03c0(-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}", "role": "user"}], "ground_truth": "4.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2(3sin(2\u03c0(3|x + 3| - 2) + 2) + 2)^2 - 1(3sin(2\u03c0(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}", "role": "user"}], "ground_truth": "2.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 3|((-1(-3cos(1\u03c0x) - 2) + 3)/(-2(-3cos(1\u03c0x) - 2) - 3)) + 3| - 2 and g(x) = -3sin(1\u03c0(-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}", "role": "user"}], "ground_truth": "34.8", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -3sin(2\u03c0((-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}", "role": "user"}], "ground_truth": "5.6", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 5(3sin(1\u03c0(-4x^2 + 1x - 5) + 2))^2 + 3(3sin(1\u03c0(-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}", "role": "user"}], "ground_truth": "2.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1(4(-3cos(1\u03c0x - 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}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3(2cos(3\u03c0(3|x - 3| - 2) + 1) - 2) + 2, g(x) = 1cos(1\u03c0(-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}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1|(1(-2cos(3\u03c0x))^2 - 5(-2cos(3\u03c0x)) - 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}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"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(1\u03c0x) - 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}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"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}", "role": "user"}], "ground_truth": "2.8", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2((2(-2x) - 3)/(3(-2x)))^2 + 3((2(-2x) - 3)/(3(-2x))) - 2, g(x) = -4(2cos(3\u03c0x + 1))^2 + 5(2cos(3\u03c0x + 1)) + 5, x = -4.8, and x = -4.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1cos(2\u03c0(-2|(3x - 4) - 2| + 2) + 2) + 2 and g(x) = -5((-2x + 2)/(2x - 1))^2 - 1((-2x + 2)/(2x - 1)) + 4 between the vertical lines x = 3.2 and x = 3.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 4(-2|(-4x^2 + 4x + 3) + 3| + 3) + 2 and g(x) = 2(-3x - 1) - 2 between the vertical lines x = 1.5 and x = 2.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 3(2((-2x)/(2x + 2)) - 1)^2 + 5(2((-2x)/(2x + 2)) - 1) + 2 and g(x) = 3(-5x^2 + 2x + 3) - 4 from x = -0.3 to x = 0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (3(2sin(3\u03c0(-2|x + 3| + 3) + 3) + 1) - 3)/(1(2sin(3\u03c0(-2|x + 3| + 3) + 3) + 1) - 2) and g(x) = 1(1cos(3\u03c0x - 3) + 1)^2 + 5(1cos(3\u03c0x - 3) + 1) + 1 between the vertical lines x = -0.5 and x = -0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 4(1|(-1sin(3\u03c0x + 3) - 2) + 2| + 3) + 5, g(x) = -1(-4x + 1) + 1, x = 4.4, and x = 4.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3cos(1\u03c0(1|((-1x - 2)/(-1x + 3)) + 2| - 3) + 3) - 2 and g(x) = 1|(-3|x - 1| + 2) + 1| - 2 from x = 2.6 to x = 2.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (2(-2(-3sin(2\u03c0x - 2) - 2) - 2) - 3)/(2(-2(-3sin(2\u03c0x - 2) - 2) - 2) + 2) and g(x) = 3|(-1e^(1x) + 2) + 3| - 2 between the vertical lines x = 0.9 and x = 1.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1e^(1(-3((2x - 1)/(-3x - 2))^2 - 4((2x - 1)/(-3x - 2)) + 4)) - 1 and g(x) = (-2(5x^2 + 5x - 5) - 1)/(-3(5x^2 + 5x - 5)) from x = -1.3 to x = -0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.8", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2(2(2|x + 2| - 1) + 1) - 4 and g(x) = 4(-2x^2 - 3x + 3)^2 + 4 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}", "role": "user"}], "ground_truth": "4.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-3(1|(2x - 5)| - 2) - 3)/(-2(1|(2x - 5)| - 2) + 3) and g(x) = 2sin(1\u03c0(2x - 2) + 2) + 2 from x = -3.8 to x = -3.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 4(2|(2|x + 1| - 3) - 3| - 3)^2 + 5(2|(2|x + 1| - 3) - 3| - 3) - 5 and g(x) = 3cos(3\u03c0(1x - 1) + 2) + 2 between the vertical lines x = -3.8 and x = -3.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (1(2|(3sin(2\u03c0x + 3) - 2) + 1|) - 1)/(-1(2|(3sin(2\u03c0x + 3) - 2) + 1|) + 2), g(x) = -1(3e^(2x) - 3) + 3, x = -0.4, and x = -0.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (1(-2(-1|x + 3| + 1) + 2) + 3)/(-1(-2(-1|x + 3| + 1) + 2) + 2) and g(x) = (3(-4x^2 + 4x + 3) + 1)/(1(-4x^2 + 4x + 3) - 2) from x = -2.7 to x = -0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19.7", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (3((-1(4x^2 + 5x - 3) - 2)/(-1(4x^2 + 5x - 3) + 3)) - 2)/(-1((-1(4x^2 + 5x - 3) - 2)/(-1(4x^2 + 5x - 3) + 3)) - 1), g(x) = (3(-3x^2 - 4x - 3) - 3)/(2(-3x^2 - 4x - 3) - 1), x = -1.4, and x = 0.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (1((-3(-3e^(1x) + 2) + 1)/(-2(-3e^(1x) + 2) - 2)) - 2)/(-2((-3(-3e^(1x) + 2) + 1)/(-2(-3e^(1x) + 2) - 2)) + 3), g(x) = -2sin(1\u03c0(-1|x - 1| - 1) - 3) + 1, x = -2.7, and x = -2.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-2(1sin(3\u03c0(2x^2 + 2x) - 1)) + 2)/(1(1sin(3\u03c0(2x^2 + 2x) - 1)) + 1), g(x) = 1(-3cos(1\u03c0x + 2) - 2)^2 - 3(-3cos(1\u03c0x + 2) - 2) - 5, x = -2.6, and x = -2.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40.9", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-2(3sin(3\u03c0((-2x - 3)/(3x - 1)) - 1) + 1) + 3)/(-3(3sin(3\u03c0((-2x - 3)/(3x - 1)) - 1) + 1) + 1), g(x) = (3(1|x - 3|) + 1)/(-3(1|x - 3|) - 1), x = 0.5, and x = 0.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-2((-3(-3|x + 2| + 3) + 3)/(-2(-3|x + 2| + 3) + 3)) + 1)/(-3((-3(-3|x + 2| + 3) + 3)/(-2(-3|x + 2| + 3) + 3))), g(x) = -1|(3x - 5) + 1| + 2, x = -1.3, and x = 0.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6.6", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 3(-3(-1|x - 1| + 1)^2 - 1(-1|x - 1| + 1) + 1)^2 + 4(-3(-1|x - 1| + 1)^2 - 1(-1|x - 1| + 1) + 1) + 5 and g(x) = 1((2x - 3)/(-3x))^2 - 3((2x - 3)/(-3x)) + 2 between the vertical lines x = -1.2 and x = 0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-6.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -3((-1(-3|x + 1| + 3) - 2)/(-3(-3|x + 1| + 3) + 2)), g(x) = -1cos(3\u03c0(-2x^2 - 3)) + 3, x = -2.0, and x = -1.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1((-3(4x + 1))/(-2(4x + 1) - 3))^2 - 3 and g(x) = -2(2e^(-1x) - 1)^2 - 4(2e^(-1x) - 1) - 2 between the vertical lines x = -0.8 and x = -0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2|((3(-5x^2 + 4) + 1)/(-2(-5x^2 + 4) - 1)) + 2| - 2 and g(x) = -2sin(3\u03c0(-5x^2 + 4x - 4) - 1) - 1 between the vertical lines x = -2.7 and x = -2.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1(3cos(2\u03c0(-1x^2 - 5x + 3) + 1) - 2) - 2, g(x) = 2|(4x^2 + 3x - 3) - 3| - 1, x = -1.7, and x = -1.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 3(1sin(3\u03c0((-2x - 3)/(-2x)) + 3) + 2) - 4 and g(x) = -1e^(-1(-5x^2 + 5x + 4)) from x = -0.1 to x = 0.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -5(-5((-1x + 3)/(-1x - 2))^2 + 5((-1x + 3)/(-1x - 2)) - 4) + 1 and g(x) = 4(-1cos(1\u03c0x + 1) + 3)^2 + 1(-1cos(1\u03c0x + 1) + 3) - 1 between the vertical lines x = 2.0 and x = 3.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -4(4((-2x - 2)/(-3x + 1))^2 + 2((-2x - 2)/(-3x + 1)) - 4) + 5, g(x) = -1(-2|x - 3| - 2) + 4, x = -2.3, and x = -0.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (3((1(2|x + 3| + 2) + 1)/(1(2|x + 3| + 2) - 3)))/(1((1(2|x + 3| + 2) + 1)/(1(2|x + 3| + 2) - 3))), g(x) = 1e^(-1(-3|x + 1| + 1)), x = -1.7, and x = -0.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.4", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -5(-1(1|x + 2|) + 4)^2 - 2(-1(1|x + 2|) + 4) - 2, g(x) = 3sin(3\u03c0(-3x - 2) - 1) - 1, x = 2.4, and x = 2.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3cos(1\u03c0((3(1x^2 + 1x + 1) + 3)/(-1(1x^2 + 1x + 1))) + 2) and g(x) = 3|(-2|x - 3| + 1) + 2| - 3 between the vertical lines x = 0.9 and x = 2.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (1(3sin(3\u03c0((3x + 3)/(1x)) - 2)) + 3)/(-1(3sin(3\u03c0((3x + 3)/(1x)) - 2)) + 3) and g(x) = 1|(1x^2 - 1x - 2) + 2| - 2 from x = -4.5 to x = -2.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "23.5", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (2(2|(4x - 3) - 3| - 3) + 2)/(-2(2|(4x - 3) - 3| - 3) - 1), g(x) = -2(-4x - 3) - 1, x = 1.2, and x = 1.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10.4", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1(2|(-2|x + 1| + 1) - 2| - 2) - 1, g(x) = 1(2sin(2\u03c0x + 1) - 1)^2 + 4(2sin(2\u03c0x + 1) - 1) - 1, x = -1.8, and x = -1.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3sin(2\u03c0(-1(4x^2 - 4x) + 3) - 1) - 2 and g(x) = 4(-1cos(1\u03c0x - 1) + 1)^2 - 5(-1cos(1\u03c0x - 1) + 1) - 4 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}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3(-2|(2x^2 + 5x + 2) - 2| + 3) + 1 and g(x) = (1(1e^(1x) + 1) + 2)/(1(1e^(1x) + 1) + 3) between the vertical lines x = -0.3 and x = 0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2(5(3x)^2 + 4(3x) + 2)^2 + 3 and g(x) = -2(4x^2 - 1x - 2)^2 + 1(4x^2 - 1x - 2) - 1 from x = -0.3 to x = 0.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1(3sin(2\u03c0(-3x^2 + 2x + 1) + 2))^2 - 1(3sin(2\u03c0(-3x^2 + 2x + 1) + 2)) and g(x) = (-1((1x + 3)/(1x + 2)))/(2((1x + 3)/(1x + 2)) - 3) from x = 1.4 to x = 1.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3((-3((2x + 1)/(-1x - 1)) - 2)/(1((2x + 1)/(-1x - 1))))^2 - 5((-3((2x + 1)/(-1x - 1)) - 2)/(1((2x + 1)/(-1x - 1)))) + 2, g(x) = 1cos(2\u03c0((1x - 2)/(-2x + 3))) + 1, x = -0.3, and x = -0.19999999999999998. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 3cos(3\u03c0(3(-3x^2 + 1x) - 2)) + 2 and g(x) = 2(-2x^2 - 1x + 1) - 1 from x = -0.4 to x = -0.30000000000000004. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2cos(1\u03c0(5(2|x - 3| + 3)^2 + 5(2|x - 3| + 3) - 3) + 3), g(x) = 1(3e^(2x))^2 + 2(3e^(2x)) - 5, x = -0.4, and x = -0.30000000000000004. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3(-3sin(1\u03c0(-2|x - 2|) + 1) - 3)^2 - 2(-3sin(1\u03c0(-2|x - 2|) + 1) - 3) + 2 and g(x) = -2(1x^2 + 5x - 4)^2 - 2(1x^2 + 5x - 4) + 2 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}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1cos(3\u03c0(-3|(1|x + 3| - 2) - 3|) - 2) + 3 and g(x) = (2(-2x - 4) + 2)/(1(-2x - 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}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (2(5(-5x^2 + 3x + 3)^2 + 4(-5x^2 + 3x + 3)) + 1)/(-2(5(-5x^2 + 3x + 3)^2 + 4(-5x^2 + 3x + 3)) - 3) and g(x) = -2sin(3\u03c0(2x^2 + 5x) + 3) - 1 from x = -2.1 to x = -2.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (2(3|(-5x^2 - 1x + 3) + 3| + 3) - 3)/(1(3|(-5x^2 - 1x + 3) + 3| + 3) - 2) and g(x) = -2(1cos(2\u03c0x + 2)) + 3 from x = 0.9 to x = 1.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1((1(-2|x - 1| + 3) + 2)/(-2(-2|x - 1| + 3) - 1)) - 2, g(x) = -2cos(3\u03c0(3x^2 - 3x + 2) - 2) + 3, x = 2.8, and x = 2.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1|((1((1x - 1)/(3x - 2)) - 1)/(-2((1x - 1)/(3x - 2)) + 3)) + 1| + 2 and g(x) = (2(3x + 3) + 2)/(-3(3x + 3) - 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}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3(-5(4x^2 - 4x)^2 + 3(4x^2 - 4x) + 4) + 5 and g(x) = -5((1x - 3)/(-2x - 1)) + 2 between the vertical lines x = 0.9 and x = 1.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3(-1|(2x - 1) - 1| + 3) and g(x) = 2(-3x^2 - 2x + 3) - 3 between the vertical lines x = -0.8 and x = 1.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-1((-3(1cos(1\u03c0x - 3)) + 2)/(-1(1cos(1\u03c0x - 3)) + 3)) - 1)/(1((-3(1cos(1\u03c0x - 3)) + 2)/(-1(1cos(1\u03c0x - 3)) + 3))) and g(x) = 1(2x^2 - 1x - 4)^2 + 1(2x^2 - 1x - 4) - 3 between the vertical lines x = 0.7 and x = 1.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1(1(-1x^2 - 1x))^2 - 3(1(-1x^2 - 1x)) - 4 and g(x) = 5(-2|x + 1| + 3)^2 + 2(-2|x + 1| + 3) + 1 between the vertical lines x = -2.0 and x = 0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "61.7", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2((-1(-4x^2 - 5x) + 3)/(3(-4x^2 - 5x) + 1)) + 4 and g(x) = -2sin(2\u03c0(-1x^2 - 3x - 5) - 1) - 3 between the vertical lines x = -1.3 and x = -0.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (2(2|(-2e^(1x) + 3)| - 2) - 1)/(3(2|(-2e^(1x) + 3)| - 2) + 3), g(x) = 2e^(-2((1x - 2)/(-1x + 2))) - 2, x = 0.2, and x = 0.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1((-2(4x^2 + 4x) - 3)/(3(4x^2 + 4x) - 1)) + 1 and g(x) = -5(-2|x - 1| - 1)^2 - 3(-2|x - 1| - 1) + 5 between the vertical lines x = 0.1 and x = 0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 5(1(-1e^(2x)) + 1)^2 + 3(1(-1e^(2x)) + 1) - 4 and g(x) = 3e^(-1(-3x + 4)) - 2 from x = -0.3 to x = 0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-2((1(-3x^2 + 1x + 1))/(3(-3x^2 + 1x + 1) - 2)) - 2)/(-2((1(-3x^2 + 1x + 1))/(3(-3x^2 + 1x + 1) - 2))) and g(x) = -3(-1cos(3\u03c0x - 3))^2 - 1(-1cos(3\u03c0x - 3)) + 2 from x = 0.4 to x = 0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (1((2((-1x - 3)/(2x - 1)) + 2)/(-3((-1x - 3)/(2x - 1)) - 2)) - 3)/(-3((2((-1x - 3)/(2x - 1)) + 2)/(-3((-1x - 3)/(2x - 1)) - 2)) - 3) and g(x) = 1(3x^2 + 2x - 5)^2 + 4(3x^2 + 2x - 5) - 5 from x = -2.0 to x = 1.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1|(2(-4x^2 + 1x) - 5) + 2| - 2 and g(x) = -2e^(1(-3|x + 2| - 1)) + 2 from x = -0.2 to x = 0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2(-2(3sin(2\u03c0x + 2) - 2) + 1)^2 - 2(-2(3sin(2\u03c0x + 2) - 2) + 1) - 5 and g(x) = -1((2x + 3)/(-1x + 2)) - 2 between the vertical lines x = 1.0 and x = 1.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "89.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2|((-2(-3sin(2\u03c0x + 3) - 1))/(-2(-3sin(2\u03c0x + 3) - 1) + 3)) + 2| - 3 and g(x) = -5(-1x + 2) - 4 from x = 2.4 to x = 3.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 5((3(4x^2 - 2x - 5) + 2)/(-3(4x^2 - 2x - 5) - 3)) and g(x) = 3(1x + 4) - 2 between the vertical lines x = -5.0 and x = -0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "25.6", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2sin(3\u03c0((-1(-4x - 2))/(-2(-4x - 2) + 3)) + 2) + 2, g(x) = 1|(3x + 5) + 2| - 1, x = -1.5, and x = -1.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2|(-1(1x + 2) + 3) + 2| - 1 and g(x) = 2e^(1(2|x + 3|)) - 1 from x = -4.0 to x = -2.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11.6", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1|((2(-5x^2 - 3x + 4) - 1)/(3(-5x^2 - 3x + 4) + 1))| + 1 and g(x) = 2sin(2\u03c0((1x - 2)/(-1x - 1)) - 3) between the vertical lines x = -1.0 and x = -0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1sin(1\u03c0(2(-4x^2 + 2x + 5)^2 + 3(-4x^2 + 2x + 5) + 1) + 3) - 2 and g(x) = 2(-1x^2)^2 + 5(-1x^2) + 2 between the vertical lines x = 1.2 and x = 1.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2(-2cos(2\u03c0((-3x - 2)/(2x - 1)) + 2) - 1)^2 - 2 and g(x) = -2|(1sin(1\u03c0x + 3) + 1)| - 2 between the vertical lines x = -1.5 and x = -0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (3(3|(-1x^2 + 1x + 4) + 1| - 2) + 1)/(2(3|(-1x^2 + 1x + 4) + 1| - 2) - 1) and g(x) = -5(-5x - 4) - 1 from x = -2.0 to x = -1.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-3(3(-2cos(3\u03c0x - 1) + 3) + 5) - 3)/(-3(3(-2cos(3\u03c0x - 1) + 3) + 5) - 1) and g(x) = 2(-2x - 1)^2 + 1 between the vertical lines x = -0.6 and x = -0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -3(-1cos(2\u03c0(-1|x + 1| + 3) - 1)) - 5, g(x) = -1sin(1\u03c0((-1x + 2)/(-1x + 3)) + 2) - 2, x = 2.9, and x = 3.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1(-2sin(3\u03c0(1|x| - 3) - 1))^2 + 5(-2sin(3\u03c0(1|x| - 3) - 1)) - 4, g(x) = (2(-4x^2 - 2x - 2) - 2)/(2(-4x^2 - 2x - 2) - 1), x = 2.8, and x = 3.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-1(3(-3x^2 - 5x + 4) + 5) + 2)/(-1(3(-3x^2 - 5x + 4) + 5)), g(x) = 3(1x^2 + 3x - 4) - 3, x = -2.4, and x = 0.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60.8", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (2(-1|(1sin(3\u03c0x - 3)) + 1| + 2) + 1)/(-3(-1|(1sin(3\u03c0x - 3)) + 1| + 2) - 1), g(x) = -3sin(1\u03c0((1x + 2)/(-3x - 3)) - 3) + 1, x = -1.0, and x = -0.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2|(-2(3sin(3\u03c0x + 3) - 2) - 1) - 1| - 1 and g(x) = -1e^(1(-3x - 1)) between the vertical lines x = -1.2 and x = -1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2|((1(5x + 3) + 2)/(-2(5x + 3) + 1))| + 3 and g(x) = -3(1|x - 1| - 1)^2 - 2(1|x - 1| - 1) + 3 between the vertical lines x = -0.6 and x = 2.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-2(1(3x + 1)^2 - 3(3x + 1) - 4) + 1)/(-3(1(3x + 1)^2 - 3(3x + 1) - 4) + 4) and g(x) = 3|(-4x + 4) - 3| - 1 from x = 0.4 to x = 1.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2(1(-2|x + 1| + 1)^2 - 4(-2|x + 1| + 1) - 2)^2 - 5(1(-2|x + 1| + 1)^2 - 4(-2|x + 1| + 1) - 2) and g(x) = 5(-3cos(3\u03c0x) - 2)^2 - 4 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}", "role": "user"}], "ground_truth": "1.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2(2(3cos(3\u03c0x + 3) + 3) - 5) + 5 and g(x) = -3sin(3\u03c0((-2x + 1)/(-3x)) + 3) + 1 from x = -0.2 to x = -0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2|(1cos(3\u03c0(-2|x + 3| - 3)) - 2) + 3| + 3 and g(x) = (3(4x^2 - 1x + 5) - 3)/(-3(4x^2 - 1x + 5) - 2) between the vertical lines x = 3.8 and x = 3.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2|(-1(-3sin(1\u03c0x - 3) + 2) - 4) + 3| - 2 and g(x) = -3(1x^2 + 4x - 1)^2 - 5(1x^2 + 4x - 1) + 2 between the vertical lines x = -4.4 and x = -3.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9.6", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1|(4(-2sin(1\u03c0x + 3) - 2)^2 + 3(-2sin(1\u03c0x + 3) - 2) - 4) - 1| - 2 and g(x) = (-1(-5x^2 - 1x + 3) - 3)/(-1(-5x^2 - 1x + 3) - 1) between the vertical lines x = -3.1 and x = -3.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2|(3(2|x - 1|)^2 - 4(2|x - 1|) + 5) - 3| and g(x) = -3cos(2\u03c0(1|x - 1| + 2) + 1) + 2 from x = 0.9 to x = 1.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3|(-1sin(3\u03c0(1x^2 + 3) - 2) + 1) - 3| + 1 and g(x) = -3|((2x)/(2x - 1)) + 1| - 1 between the vertical lines x = 2.2 and x = 2.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3(-1sin(1\u03c0((-2x + 2)/(1x))) - 2), g(x) = -3|(-5x - 3) - 2|, x = -0.7, and x = -0.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2|(-3(3e^(-2x) - 3) - 1) - 2| and g(x) = -1(1|x - 2| - 3)^2 - 4(1|x - 2| - 3) - 5 between the vertical lines x = 0.1 and x = 0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1((-2((-3x + 1)/(1x)))/(-2((-3x + 1)/(1x)) + 3))^2 - 1((-2((-3x + 1)/(1x)))/(-2((-3x + 1)/(1x)) + 3)) + 2, g(x) = 2(1e^(2x))^2 - 4(1e^(2x)) - 4, x = 0.2, and x = 0.30000000000000004. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-0.4", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -5(-1|(-2|x + 2| - 2)| + 3) - 1 and g(x) = (-1(3|x - 3| - 3) - 2)/(-1(3|x - 3| - 3) + 3) between the vertical lines x = -1.2 and x = 0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1((3(-1x + 3) - 3)/(-2(-1x + 3)))^2 + 2((3(-1x + 3) - 3)/(-2(-1x + 3))) - 5 and g(x) = (2(-2sin(2\u03c0x - 1) - 2) + 3)/(-2(-2sin(2\u03c0x - 1) - 2) - 1) between the vertical lines x = 1.0 and x = 1.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3|((-1((3x + 3)/(3x + 2)) - 2)/(-1((3x + 3)/(3x + 2)) - 1)) - 2| + 2 and g(x) = -3sin(3\u03c0((-3x + 3)/(-1x - 1)) - 3) - 3 between the vertical lines x = -0.9 and x = -0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1((2(-1x^2 + 3x - 1) - 2)/(-1(-1x^2 + 3x - 1) + 3))^2 - 4((2(-1x^2 + 3x - 1) - 2)/(-1(-1x^2 + 3x - 1) + 3)) - 4 and g(x) = (3(2|x + 1| + 2) + 1)/(1(2|x + 1| + 2) + 2) from x = -0.3 to x = 3.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-1(-2|(-3|x + 2| + 3) + 2| - 2) + 1)/(-1(-2|(-3|x + 2| + 3) + 2| - 2) + 2) and g(x) = 2cos(3\u03c0(2|x + 2| + 2) - 1) + 2 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}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (3(2|(2x + 2) + 1| - 1) - 1)/(1(2|(2x + 2) + 1| - 1)), g(x) = 1(-5x - 1) - 1, x = -1.7, and x = -1.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-3(1(2|x + 2| + 1) - 5) + 3)/(-2(1(2|x + 2| + 1) - 5) + 1) and g(x) = (-1(-2sin(2\u03c0x + 1) - 2) - 1)/(2(-2sin(2\u03c0x + 1) - 2) + 3) between the vertical lines x = -3.6 and x = -3.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-2(-2|(2x^2 + 3x - 4)| + 2) + 2)/(-3(-2|(2x^2 + 3x - 4)| + 2)), g(x) = -3((-2x + 1)/(-2x - 2))^2 + 5((-2x + 1)/(-2x - 2)) - 1, x = -2.5, and x = -2.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2((-2(1cos(1\u03c0x - 2) + 1) - 1)/(2(1cos(1\u03c0x - 2) + 1) - 1)) - 2, g(x) = (1(-3x + 2) - 2)/(1(-3x + 2)), x = 1.1, and x = 2.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "25.9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2(1(-5x - 3) - 5)^2 + 2(1(-5x - 3) - 5) - 3 and g(x) = -1cos(3\u03c0(5x + 5) + 1) from x = -1.8 to x = -1.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2cos(1\u03c0(-5(1x^2 - 2x - 4)) + 1) + 1 and g(x) = 4(-2sin(1\u03c0x + 2) + 3)^2 - 5 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}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2(4(3sin(1\u03c0x - 3) - 2) + 2) - 1 and g(x) = (-2(1e^(-1x) + 3) + 2)/(2(1e^(-1x) + 3)) 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}", "role": "user"}], "ground_truth": "28.9", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (3((2(4x + 5) - 1)/(1(4x + 5))) - 3)/(-2((2(4x + 5) - 1)/(1(4x + 5))) - 2), g(x) = 3(3sin(3\u03c0x + 3) + 1) + 2, x = -1.2, and x = -1.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -5(2|(4x^2 - 1x - 4)| - 1) + 2, g(x) = -1(1|x + 1|) + 4, x = -0.9, and x = -0.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2(1|(-1cos(2\u03c0x - 1) - 3)| + 1) + 5, g(x) = (-3(-2|x|) - 3)/(-2(-2|x|) - 1), x = -0.4, and x = 0.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "23.6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-2(1|((-1x + 2)/(2x + 1)) + 2| - 1))/(1(1|((-1x + 2)/(2x + 1)) + 2| - 1) - 3) and g(x) = (-1(-5x^2 - 1x - 5))/(-1(-5x^2 - 1x - 5) - 3) from x = -0.8 to x = 1.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "23.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -3(-2(-1|x - 3| - 3) + 5) + 2, g(x) = (-1(-3cos(1\u03c0x - 1)) - 3)/(-2(-3cos(1\u03c0x - 1)) + 3), x = -1.0, and x = -0.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "43.4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-3(1cos(1\u03c0(1x + 5) + 2) - 2) - 2)/(-1(1cos(1\u03c0(1x + 5) + 2) - 2) - 3) and g(x) = (1(-1e^(-1x) - 2) + 1)/(-1(-1e^(-1x) - 2)) from x = 4.3 to x = 4.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2((-2(3|x + 3| + 2))/(-3(3|x + 3| + 2) - 3))^2 - 1((-2(3|x + 3| + 2))/(-3(3|x + 3| + 2) - 3)) + 1, g(x) = -3cos(1\u03c0(-2|x - 3|) + 3) - 1, x = 4.1, and x = 4.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3|((-2(3|x - 1|) + 1)/(-2(3|x - 1|) - 1)) - 1| + 2, g(x) = -3(-4x - 1)^2 + 2(-4x - 1) + 3, x = -0.5, and x = -0.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2|(2sin(1\u03c0(-5x + 2) - 2) + 3) - 2| + 2, g(x) = 1(1cos(2\u03c0x + 3) - 1) + 2, x = 2.1, and x = 2.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-1(-5((-3x + 2)/(2x))^2 - 1((-3x + 2)/(2x))) + 1)/(-3(-5((-3x + 2)/(2x))^2 - 1((-3x + 2)/(2x))) - 3) and g(x) = (2(1x + 5) + 3)/(3(1x + 5) + 2) from x = 0.5 to x = 1.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1|(1((2x + 3)/(-1x))^2 - 5((2x + 3)/(-1x)) + 3) + 2| - 3 and g(x) = -1|((1x)/(-1x - 1)) + 2| - 3 from x = -1.2 to x = -0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "54.8", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (2(2((-1x + 1)/(3x + 1))^2 + 5((-1x + 1)/(3x + 1)) - 2) + 1)/(1(2((-1x + 1)/(3x + 1))^2 + 5((-1x + 1)/(3x + 1)) - 2) - 3), g(x) = (-1(-2cos(2\u03c0x) + 3) + 1)/(-3(-2cos(2\u03c0x) + 3) - 2), x = -0.5, and x = 0.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (1(3(-2x - 4) - 2) + 3)/(-2(3(-2x - 4) - 2) - 2) and g(x) = 2sin(1\u03c0(-4x^2 + 3x - 1)) - 1 between the vertical lines x = -3.2 and x = -3.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3(2|(1x - 3) + 1| - 1)^2 + 4(2|(1x - 3) + 1| - 1) + 1 and g(x) = 1cos(2\u03c0(-1|x + 2|) - 1) - 1 between the vertical lines x = 1.7 and x = 2.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.6", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2cos(3\u03c0(-2|(4x + 3) - 2| + 1) - 2) - 1, g(x) = 1(1x + 4) - 2, x = -1.5, and x = -1.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -3(2(5x^2 - 1x - 4)^2 + 5(5x^2 - 1x - 4) + 3), g(x) = (2(-4x^2 + 4x + 4) + 1)/(-3(-4x^2 + 4x + 4) + 4), x = 0.8, and x = 0.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (2(-4(-3x - 5)^2 + 1(-3x - 5)) - 2)/(2(-4(-3x - 5)^2 + 1(-3x - 5)) + 3), g(x) = -3e^(2(5x)) - 2, x = -1.8, and x = -1.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -3cos(3\u03c0((-3(-2|x - 2| + 1) - 1)/(-3(-2|x - 2| + 1) - 2))) - 1, g(x) = (-3((-3x + 2)/(-1x - 2)) - 2)/(-1((-3x + 2)/(-1x - 2)) + 2), x = 1.1, and x = 1.2000000000000002. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 4((3((-1x - 1)/(-3x - 1)) - 2)/(-3((-1x - 1)/(-3x - 1)) - 3)) - 5 and g(x) = -3(-4x^2 + 5x + 3)^2 - 2(-4x^2 + 5x + 3) + 5 between the vertical lines x = 1.5 and x = 1.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1((1(2sin(3\u03c0x - 2)) - 1)/(-1(2sin(3\u03c0x - 2))))^2 - 4((1(2sin(3\u03c0x - 2)) - 1)/(-1(2sin(3\u03c0x - 2)))) + 2, g(x) = 1|(-1cos(2\u03c0x - 1) - 1) + 3| - 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}", "role": "user"}], "ground_truth": "4.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (1((1(-3cos(2\u03c0x + 2) - 2) - 2)/(3(-3cos(2\u03c0x + 2) - 2) + 3)) + 2)/(3((1(-3cos(2\u03c0x + 2) - 2) - 2)/(3(-3cos(2\u03c0x + 2) - 2) + 3)) - 2), g(x) = -1|((-2x + 3)/(-2x - 3)) + 3| + 2, x = -1.4, and x = -1.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-1(1sin(1\u03c0((-2x)/(-3x + 2)) - 2)) + 1)/(-2(1sin(1\u03c0((-2x)/(-3x + 2)) - 2)) + 1), g(x) = -4(2x + 5) - 1, x = -2.7, and x = 1.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "62.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1sin(3\u03c0(-5(4x - 5) + 5) - 2) - 1 and g(x) = 1((1x - 1)/(1x + 1))^2 - 4((1x - 1)/(1x + 1)) + 2 between the vertical lines x = -4.2 and x = -4.1000000000000005. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1(1|(2cos(1\u03c0x - 1) - 3)| - 2) + 3 and g(x) = 1|(2x + 1) - 2| between the vertical lines x = 1.0 and x = 2.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 5(-3|(-1|x - 3|) + 3| + 3) - 2, g(x) = (1(-2cos(1\u03c0x + 1) + 3) + 1)/(-1(-2cos(1\u03c0x + 1) + 3) + 2), x = -2.7, and x = -2.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 4(-2(-2|x| - 1)^2 - 5(-2|x| - 1) - 3) + 2, g(x) = -2e^(-1(-2x + 2)) + 1, x = -0.4, and x = 0.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1(3(-5x + 2) - 3) - 1 and g(x) = 3(2|x - 1| - 1)^2 - 2(2|x - 1| - 1) + 1 between the vertical lines x = 0.3 and x = 3.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "50.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1(-1(2cos(2\u03c0x - 3) - 3)^2 - 1(2cos(2\u03c0x - 3) - 3) + 4)^2 - 4(-1(2cos(2\u03c0x - 3) - 3)^2 - 1(2cos(2\u03c0x - 3) - 3) + 4) + 3 and g(x) = 1(-2cos(3\u03c0x + 3) + 1) + 3 between the vertical lines x = 2.4 and x = 2.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3(-3|(-3|x| + 2) - 2| + 2)^2 + 2(-3|(-3|x| + 2) - 2| + 2) - 5, g(x) = -3cos(2\u03c0(3x - 3) - 3) - 3, x = 0.2, and x = 0.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2(2e^(-2((-1x + 2)/(2x + 1))) - 2) - 3, g(x) = 3cos(3\u03c0(-5x) + 3) + 2, x = -0.0, and x = 0.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (2(5(1|x + 2| - 2)^2 - 3))/(-1(5(1|x + 2| - 2)^2 - 3) - 1) and g(x) = -2e^(-2(-3x - 4)) - 3 from x = -4.0 to x = -0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41.4", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (1(-3|((1x - 3)/(-2x - 1)) + 1| - 2))/(3(-3|((1x - 3)/(-2x - 1)) + 1| - 2) - 1), g(x) = -5(-2cos(1\u03c0x - 2) - 2)^2 + 4(-2cos(1\u03c0x - 2) - 2) + 4, x = -0.6, and x = -0.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3|((-1((-2x + 2)/(3x - 2)) + 2)/(-3((-2x + 2)/(3x - 2)) - 1)) + 2| - 3, g(x) = (-3(-5x^2 + 5x))/(-1(-5x^2 + 5x) + 3), x = 0.9, and x = 1.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3((1(3x - 3) - 3)/(-3(3x - 3) + 4))^2 - 2((1(3x - 3) - 3)/(-3(3x - 3) + 4)) - 3, g(x) = 3cos(1\u03c0((-3x + 3)/(-2x - 3)) - 1) - 3, x = -1.3, and x = -1.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1(-5(2|x + 3|) + 5) - 1, g(x) = -1|((1x)/(1x + 1)) - 2| + 2, x = -3.3, and x = -2.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1|(-3|(5x + 4) + 1| + 2) - 1| + 2 and g(x) = -3sin(1\u03c0(4x - 5) + 3) + 3 from x = -1.0 to x = -0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (2(-2cos(1\u03c0((-1x + 3)/(-2x + 3)) + 1) - 1) + 1)/(2(-2cos(1\u03c0((-1x + 3)/(-2x + 3)) + 1) - 1) + 2), g(x) = (-1(1e^(2x) + 1) - 1)/(2(1e^(2x) + 1) + 1), x = 2.0, and x = 4.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-2(-3(2e^(1x))^2 - 3(2e^(1x)) + 2) - 1)/(3(-3(2e^(1x))^2 - 3(2e^(1x)) + 2) - 2), g(x) = -3cos(1\u03c0(1x^2 + 5x - 3)), x = 0.3, and x = 0.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1sin(2\u03c0(-1(1|x + 1| + 1) - 1)) + 2, g(x) = 2|(3|x - 3| - 3) - 1| + 1, x = 4.3, and x = 4.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 4(-4(1|x + 3| - 1) - 3)^2 - 4(-4(1|x + 3| - 1) - 3) - 4 and g(x) = 1|(2x + 5) + 2| - 1 from x = -3.4 to x = -2.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3(5(3sin(1\u03c0x - 1) - 1) - 4) - 2, g(x) = (-2(1|x + 2| + 2) - 3)/(-1(1|x + 2| + 2)), x = 3.1, and x = 4.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "67.4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1|((2(-4x - 5) + 1)/(-3(-4x - 5) - 2))| - 1 and g(x) = -1(1e^(1x) - 2)^2 - 2(1e^(1x) - 2) - 5 from x = -1.1 to x = -1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (2(1(1x + 4) - 4) - 3)/(2(1(1x + 4) - 4) - 1) and g(x) = -2|(1|x + 3| + 3) - 3| + 3 between the vertical lines x = -3.9 and x = -2.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -3(2|((-3x + 3)/(2x + 3)) - 1| - 1)^2 - 5(2|((-3x + 3)/(2x + 3)) - 1| - 1) - 5, g(x) = -2cos(2\u03c0(-1|x - 3| - 1)) - 3, x = -0.2, and x = 0.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (1(3cos(3\u03c0((3x - 2)/(1x)) + 2)) + 2)/(2(3cos(3\u03c0((3x - 2)/(1x)) + 2)) + 2), g(x) = 2|(-2e^(1x) + 2) + 3|, x = 0.1, and x = 0.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2sin(2\u03c0(1(1|x + 1| - 2)^2 - 3(1|x + 1| - 2) + 5) - 1) + 3 and g(x) = -3(3x - 5) - 1 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}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1((-1((3x + 1)/(2x - 1)))/(-1((3x + 1)/(2x - 1)) - 2)) - 1 and g(x) = -5(3cos(3\u03c0x + 1) - 1) + 2 from x = 2.5 to x = 2.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1sin(2\u03c0((-1(2|x - 1| - 1) - 3)/(-2(2|x - 1| - 1) - 3)) + 3) - 3 and g(x) = -2|(-3x - 1)| + 1 from x = -0.9 to x = 0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.6", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -3(-5(-5x - 1)^2 + 3(-5x - 1)) - 5, g(x) = 1|((-2x - 1)/(-2x - 3)) - 1|, x = -0.4, and x = -0.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 4(-3(-1x + 5) + 2)^2 + 2(-3(-1x + 5) + 2) - 2 and g(x) = (3(-3sin(2\u03c0x + 1) - 1))/(-2(-3sin(2\u03c0x + 1) - 1) - 1) between the vertical lines x = 3.8 and x = 4.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2(-5(2sin(1\u03c0x))^2 + 5(2sin(1\u03c0x)) + 2) - 1, g(x) = -3|((2x - 2)/(-3x)) + 2| + 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}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2(1(5x - 4)^2 - 1(5x - 4)), g(x) = (1(-1cos(3\u03c0x - 2) + 2) + 2)/(2(-1cos(3\u03c0x - 2) + 2) + 3), x = 0.8, and x = 1.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3(-3|(-4x^2 + 5)|)^2 + 3(-3|(-4x^2 + 5)|) - 4, g(x) = 1((2x)/(-3x + 2))^2 + 1((2x)/(-3x + 2)) + 5, x = 0.7, and x = 1.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "23.9", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2sin(3\u03c0(1((-1x - 3)/(1x - 2)) + 4) - 2) - 3 and g(x) = -1(1e^(1x) + 3) + 3 between the vertical lines x = 1.6 and x = 1.7000000000000002. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 4(2|(-2cos(3\u03c0x + 2) - 1) + 1|) - 1 and g(x) = -1(3e^(-2x) - 3)^2 - 5(3e^(-2x) - 3) - 5 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}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2cos(2\u03c0(-1(-2|x - 3| - 2)^2 + 3(-2|x - 3| - 2) - 3) - 1) + 3 and g(x) = (2((2x + 3)/(-1x - 2)) + 2)/(-2((2x + 3)/(-1x - 2)) + 3) from x = -1.6 to x = -1.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3(2cos(1\u03c0(-1x + 5) + 2) - 2) - 1 and g(x) = 2|(2x) - 3| - 3 between the vertical lines x = 4.3 and x = 4.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2|((1(-3|x + 1|))/(1(-3|x + 1|) - 3)) + 2| + 2 and g(x) = (-1(-3x^2 - 1x + 4) + 3)/(1(-3x^2 - 1x + 4) + 1) between the vertical lines x = -1.7 and x = 1.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "23.4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1|((-2(3x + 3) - 3)/(2(3x + 3) - 3)) + 3| - 1 and g(x) = 4(2x^2 + 1x - 1) - 4 from x = -0.4 to x = 0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.6", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 5((3(-2|x + 3| + 1) - 1)/(-3(-2|x + 3| + 1) - 2)) + 2 and g(x) = 5(-3cos(3\u03c0x + 3) - 1)^2 - 2(-3cos(3\u03c0x + 3) - 1) + 1 between the vertical lines x = -3.8 and x = -3.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (3(5(2x^2 - 3x - 5)^2 - 3(2x^2 - 3x - 5) - 5) - 2)/(2(5(2x^2 - 3x - 5)^2 - 3(2x^2 - 3x - 5) - 5) + 2) and g(x) = -3e^(2(-4x - 3)) + 1 from x = 2.3 to x = 2.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1((-2(2x^2 - 3x - 5) + 2)/(-1(2x^2 - 3x - 5) - 1)) + 3 and g(x) = -4(2cos(1\u03c0x) + 2)^2 + 4(2cos(1\u03c0x) + 2) + 5 from x = -4.6 to x = -3.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "27.7", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 5(3(3x + 5)^2 + 2(3x + 5) - 2) - 5, g(x) = (-3(3x - 4) + 3)/(-2(3x - 4) - 1), x = -2.2, and x = -1.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 4(1(-1e^(-1x) + 3)^2 + 4(-1e^(-1x) + 3) - 2)^2 + 5(1(-1e^(-1x) + 3)^2 + 4(-1e^(-1x) + 3) - 2) - 5 and g(x) = 4(-2x - 4) + 3 between the vertical lines x = -1.9 and x = -1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "53.6", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (1(-1|(3sin(3\u03c0x - 3) + 1) + 2| + 2) - 1)/(-3(-1|(3sin(3\u03c0x - 3) + 1) + 2| + 2) + 4), g(x) = 1|(1cos(3\u03c0x + 2) + 3) + 3| + 2, x = 3.6, and x = 4.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1(1(2sin(2\u03c0x))^2 - 5(2sin(2\u03c0x)) + 5)^2 - 3(1(2sin(2\u03c0x))^2 - 5(2sin(2\u03c0x)) + 5) + 3 and g(x) = -1(-2|x - 3| + 3)^2 - 5(-2|x - 3| + 3) + 5 between the vertical lines x = -0.5 and x = 0.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "75.7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3|(-5(-1x^2 - 2x + 5)^2 - 2(-1x^2 - 2x + 5) + 1)| and g(x) = -2|(-4x^2 + 4x + 5) + 1| + 3 from x = 1.6 to x = 1.7000000000000002. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1(2cos(3\u03c0(1x^2 - 1x - 1) + 1) - 2) + 1 and g(x) = -3e^(-2(3|x - 1| - 1)) + 3 from x = -4.0 to x = -3.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2(-3cos(1\u03c0((-3x - 1)/(3x - 2)) - 1)) - 5 and g(x) = -2sin(2\u03c0(1x + 2) + 2) - 1 from x = -0.3 to x = 0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-2(-2((1x - 1)/(1x + 2))^2 - 1((1x - 1)/(1x + 2)) + 2) + 2)/(2(-2((1x - 1)/(1x + 2))^2 - 1((1x - 1)/(1x + 2)) + 2) + 1) and g(x) = -1sin(3\u03c0(1|x + 2| + 3)) - 2 between the vertical lines x = -2.2 and x = -2.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2(-1(1e^(-2x) + 1) + 5)^2 - 1(-1(1e^(-2x) + 1) + 5) + 4, g(x) = 3e^(-1(1x^2 - 2x - 1)) + 3, x = -0.7, and x = -0.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (2(-4((-2x - 2)/(1x)) - 4) - 3)/(1(-4((-2x - 2)/(1x)) - 4)) and g(x) = 3|(-3|x| + 2)| + 2 between the vertical lines x = -1.9 and x = -0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1(-3sin(3\u03c0(-1x^2 + 1x + 4) - 3)) + 4, g(x) = (1(3x + 5) - 3)/(3(3x + 5) + 2), x = -2.2, and x = -2.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -4((3(2x + 4) - 1)/(-1(2x + 4) - 1))^2 - 3((3(2x + 4) - 1)/(-1(2x + 4) - 1)) + 4, g(x) = 3cos(1\u03c0(-3x - 5) + 1) + 2, x = -1.4, and x = -1.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-2(5(-3|x - 1| + 1)) - 3)/(3(5(-3|x - 1| + 1))) and g(x) = (1((-3x + 3)/(-2x)))/(-2((-3x + 3)/(-2x)) - 1) from x = 0.2 to x = 0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2(-3sin(3\u03c0(1|x + 1| - 1) + 3) - 2) + 5 and g(x) = (1(-1x - 2) + 1)/(1(-1x - 2)) between the vertical lines x = -3.4 and x = -3.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 5((2((-3x + 3)/(3x - 1)) + 1)/(3((-3x + 3)/(3x - 1)))) - 4 and g(x) = 3(3|x + 1| - 3)^2 - 3(3|x + 1| - 3) - 2 from x = 0.5 to x = 0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1sin(1\u03c0(2(1|x + 1| - 1)^2 + 4(1|x + 1| - 1) - 2) + 2) - 3 and g(x) = -5(2x - 1)^2 - 5(2x - 1) - 2 from x = -0.0 to x = 0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1((-1((-2x + 1)/(-2x + 3)) - 3)/(-2((-2x + 1)/(-2x + 3)) - 2)) + 4 and g(x) = (-2(2x) + 2)/(2(2x) + 1) between the vertical lines x = -0.1 and x = 1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11.6", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1(2sin(3\u03c0(1x - 2) - 3))^2 - 1(2sin(3\u03c0(1x - 2) - 3)) + 5 and g(x) = -3(-2sin(2\u03c0x) - 1)^2 + 4(-2sin(2\u03c0x) - 1) + 3 between the vertical lines x = -2.1 and x = -1.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3sin(3\u03c0(-3(-2|x - 1| - 1) + 1) + 2) + 1 and g(x) = 3(-2|x - 1| + 3) + 2 from x = -0.3 to x = -0.19999999999999998. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1sin(2\u03c0(-1((1x + 3)/(1x)) + 2) + 2), g(x) = -1|(3e^(1x) - 3) - 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}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 4(1(4x - 1)) + 2, g(x) = (3(1|x| - 3) - 3)/(2(1|x| - 3) - 1), x = 0.2, and x = 3.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "95.9", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (1((2(2x + 3))/(-2(2x + 3) - 2)) + 3)/(-1((2(2x + 3))/(-2(2x + 3) - 2)) + 2) and g(x) = -3e^(-1((3x + 3)/(1x + 3))) + 3 between the vertical lines x = -1.8 and x = -0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1(1|(-1|x - 1| + 2) + 3| + 1)^2 - 5(1|(-1|x - 1| + 2) + 3| + 1) + 5 and g(x) = 5(2|x - 2| - 1) + 3 from x = 0.8 to x = 2.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6.8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3|(-2cos(2\u03c0(-5x - 1)) - 2) - 1| - 1 and g(x) = -4(-2|x| + 3)^2 + 1(-2|x| + 3) + 4 from x = 2.3 to x = 2.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1(4(-1|x - 2| + 2) - 5) + 2 and g(x) = (-2((1x - 1)/(-2x + 3)) + 3)/(2((1x - 1)/(-2x + 3)) - 3) from x = 0.5 to x = 3.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (1(2|(-3sin(2\u03c0x) - 2) + 1| - 3) - 2)/(2(2|(-3sin(2\u03c0x) - 2) + 1| - 3)) and g(x) = 1e^(-2((2x - 1)/(-2x + 1))) from x = 1.6 to x = 1.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (1(-1|(1x^2 - 4x - 2) + 3| + 2) + 3)/(-1(-1|(1x^2 - 4x - 2) + 3| + 2) - 3) and g(x) = 2sin(2\u03c0(1x + 1) - 1) - 1 from x = -4.8 to x = -4.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3|(-3|(1x^2 - 3x + 1) + 1| - 3)| - 3 and g(x) = 4(-2|x + 1| - 2) between the vertical lines x = 0.4 and x = 3.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36.9", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2|(-3|(3|x + 1| - 1) + 2| + 3) + 1| + 2, g(x) = (-2(1x + 4) + 3)/(-1(1x + 4) - 1), x = -1.0, and x = -0.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (3(-1cos(1\u03c0(1x - 4)) + 3) + 1)/(3(-1cos(1\u03c0(1x - 4)) + 3) + 3) and g(x) = 2(-4x^2 + 4x - 2) + 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}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1(-4(-1|x + 3| + 1) - 5) - 2, g(x) = 5(4x^2 + 4x - 5)^2 - 3(4x^2 + 4x - 5) - 4, x = 0.6, and x = 0.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1|(-3|(-3x - 2)| - 2) - 2| + 1 and g(x) = -2|(-1x - 4)| - 3 between the vertical lines x = -1.3 and x = 0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-3(-2|(-1|x + 1| + 1) - 1| + 2) + 2)/(-1(-2|(-1|x + 1| + 1) - 1| + 2) + 3), g(x) = -2e^(1(-1x^2 - 5x + 3)) + 2, x = 0.7, and x = 2.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -4(1(-1|x + 2| - 2)^2 + 3(-1|x + 2| - 2) - 2) - 3 and g(x) = -2((-2x - 1)/(-3x + 1))^2 + 4((-2x - 1)/(-3x + 1)) + 4 from x = 0.1 to x = 0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-14.9", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1(3|(1x + 5) - 1| - 1) + 2, g(x) = -1cos(3\u03c0(-1x^2 - 4x + 5) - 2) + 1, x = -5.0, and x = -4.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 3sin(3\u03c0(5(3x + 1)^2 + 1(3x + 1) + 2) + 2) - 3 and g(x) = 2(5x^2 + 2x - 1) + 2 between the vertical lines x = -0.1 and x = 0.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 3|(2|(2sin(3\u03c0x + 3) - 1) + 2| - 2) - 2| - 1 and g(x) = (-2(-2sin(3\u03c0x - 2) + 1) - 2)/(-1(-2sin(3\u03c0x - 2) + 1) - 2) from x = -1.4 to x = -0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -5(2(2|x + 1| - 1)^2 + 5(2|x + 1| - 1))^2 - 3(2(2|x + 1| - 1)^2 + 5(2|x + 1| - 1)) - 4, g(x) = 3(-3|x + 3| - 1) - 1, x = -1.2, and x = -0.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 5((2(-3|x| + 1) + 2)/(3(-3|x| + 1) - 2))^2 + 4((2(-3|x| + 1) + 2)/(3(-3|x| + 1) - 2)) - 3 and g(x) = 2|(-3x + 5) + 3| - 2 from x = 0.2 to x = 2.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15.9", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2|((1(5x + 5))/(2(5x + 5)))| + 1 and g(x) = -4(-2e^(1x) + 2)^2 - 2(-2e^(1x) + 2) + 4 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}", "role": "user"}], "ground_truth": "1.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 3(2|(3|x - 1| - 2) + 3| - 3) and g(x) = 5(-2|x - 2| - 1)^2 - 5(-2|x - 2| - 1) - 4 from x = 1.8 to x = 2.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1(3(-2cos(2\u03c0x + 2) - 2) + 4) and g(x) = (1(5x + 2) - 3)/(2(5x + 2)) between the vertical lines x = 3.0 and x = 3.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}