{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 3(-2|(4(-3sin(1\u03c0((-3(-4x^2 + 5x + 3) + 1)/(-2(-4x^2 + 5x + 3) - 3)) - 2) + 1)^2 - 5(-3sin(1\u03c0((-3(-4x^2 + 5x + 3) + 1)/(-2(-4x^2 + 5x + 3) - 3)) - 2) + 1) + 3) - 2| + 2) + 1 and g(x) = -1|(1(3cos(2\u03c0(-1|(2|x| - 1) + 2| - 2) - 3) - 3) - 4) - 3| - 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": "8.6", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-2(-1|(-3e^(-1(4(1|(3x^2 - 1x + 5) - 3| - 1)^2 - 2(1|(3x^2 - 1x + 5) - 3| - 1) - 4)) + 3) + 3| + 3) + 3)/(-3(-1|(-3e^(-1(4(1|(3x^2 - 1x + 5) - 3| - 1)^2 - 2(1|(3x^2 - 1x + 5) - 3| - 1) - 4)) + 3) + 3| + 3)) and g(x) = -2|(3(1|((2(-1x^2 + 5x - 1) + 2)/(2(-1x^2 + 5x - 1) - 3)) - 2| - 2) - 2)| 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": "1.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (2(1((2((-2(3(1|x + 2| - 1)^2 + 4(1|x + 2| - 1) + 1) + 1)/(3(3(1|x + 2| - 1)^2 + 4(1|x + 2| - 1) + 1) + 2)) - 2)/(2((-2(3(1|x + 2| - 1)^2 + 4(1|x + 2| - 1) + 1) + 1)/(3(3(1|x + 2| - 1)^2 + 4(1|x + 2| - 1) + 1) + 2)) - 1)) + 5) - 1)/(2(1((2((-2(3(1|x + 2| - 1)^2 + 4(1|x + 2| - 1) + 1) + 1)/(3(3(1|x + 2| - 1)^2 + 4(1|x + 2| - 1) + 1) + 2)) - 2)/(2((-2(3(1|x + 2| - 1)^2 + 4(1|x + 2| - 1) + 1) + 1)/(3(3(1|x + 2| - 1)^2 + 4(1|x + 2| - 1) + 1) + 2)) - 1)) + 5) - 3), g(x) = 1sin(1\u03c0(-5(-3|(-4(4x^2 - 2x - 5) + 5) + 2| - 3)^2 - 4) - 1) + 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (1(2|(-2|(-1e^(1(-3|(1x^2 - 2x - 4) - 2|))) - 2| + 2) + 3| - 3) + 3)/(3(2|(-2|(-1e^(1(-3|(1x^2 - 2x - 4) - 2|))) - 2| + 2) + 3| - 3) - 2) and g(x) = -2(-5(-2sin(1\u03c0(-2|(-2|x + 1|) - 3| - 3) + 2) + 1) - 4)^2 - 3(-5(-2sin(1\u03c0(-2|(-2|x + 1|) - 3| - 3) + 2) + 1) - 4) + 1 from x = 2.8 to x = 2.9. 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(2|(3cos(1\u03c0((-3x - 1)/(-1x + 3)) - 1) - 2) + 2| + 2) - 1)/(3(2|(3cos(1\u03c0((-3x - 1)/(-1x + 3)) - 1) - 2) + 2| + 2) + 1)))/(1((-3(2|(3cos(1\u03c0((-3x - 1)/(-1x + 3)) - 1) - 2) + 2| + 2) - 1)/(3(2|(3cos(1\u03c0((-3x - 1)/(-1x + 3)) - 1) - 2) + 2| + 2) + 1)) + 2)) + 2| + 3 and g(x) = 2(-3sin(2\u03c0((-1((3((3x)/(3x + 2)) + 2)/(3((3x)/(3x + 2)) - 2)) - 2)/(3((3((3x)/(3x + 2)) + 2)/(3((3x)/(3x + 2)) - 2)) + 2)) + 3) - 3)^2 - 2(-3sin(2\u03c0((-1((3((3x)/(3x + 2)) + 2)/(3((3x)/(3x + 2)) - 2)) - 2)/(3((3((3x)/(3x + 2)) + 2)/(3((3x)/(3x + 2)) - 2)) + 2)) + 3) - 3) - 2 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": "2.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -5((-1(1|(-1|(-4(1x^2 - 1) - 1) - 2| + 1) + 3| - 3) - 2)/(1(1|(-1|(-4(1x^2 - 1) - 1) - 2| + 1) + 3| - 3))) - 4 and g(x) = -1|(5(3|(1((-1x - 1)/(-3x + 2))^2 - 5((-1x - 1)/(-3x + 2)) + 3) - 1| + 2) - 2)| - 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": "68.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-2(-3(2|(1((-2((3x + 3)/(-1x)) - 1)/(2((3x + 3)/(-1x)) - 3))^2 + 5) - 3|) + 2) + 1)/(1(-3(2|(1((-2((3x + 3)/(-1x)) - 1)/(2((3x + 3)/(-1x)) - 3))^2 + 5) - 3|) + 2) - 3), g(x) = (-1((-1(1|(-3(-2|x - 3|)^2 - 5(-2|x - 3|) - 1) + 2|) - 1)/(3(1|(-3(-2|x - 3|)^2 - 5(-2|x - 3|) - 1) + 2|))) + 3)/(3((-1(1|(-3(-2|x - 3|)^2 - 5(-2|x - 3|) - 1) + 2|) - 1)/(3(1|(-3(-2|x - 3|)^2 - 5(-2|x - 3|) - 1) + 2|)))), x = 2.2, 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": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1cos(1\u03c0(3(2|(1((1((-1x - 3)/(1x)) + 2)/(-2((-1x - 3)/(1x)) + 3))^2 + 5) - 3|) - 5) - 2) + 2 and g(x) = 1(-1((2(2(5x - 4) - 3) - 1)/(-3(2(5x - 4) - 3) - 3)) - 1)^2 + 1(-1((2(2(5x - 4) - 3) - 1)/(-3(2(5x - 4) - 3) - 3)) - 1) - 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": "-0.8", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1((1(5((1(-3|((-3x - 3)/(-1x)) + 3| - 2) - 2)/(2(-3|((-3x - 3)/(-1x)) + 3| - 2) - 1))^2 + 3((1(-3|((-3x - 3)/(-1x)) + 3| - 2) - 2)/(2(-3|((-3x - 3)/(-1x)) + 3| - 2) - 1)) + 1) + 2)/(2(5((1(-3|((-3x - 3)/(-1x)) + 3| - 2) - 2)/(2(-3|((-3x - 3)/(-1x)) + 3| - 2) - 1))^2 + 3((1(-3|((-3x - 3)/(-1x)) + 3| - 2) - 2)/(2(-3|((-3x - 3)/(-1x)) + 3| - 2) - 1)) + 1) - 1))^2 + 5((1(5((1(-3|((-3x - 3)/(-1x)) + 3| - 2) - 2)/(2(-3|((-3x - 3)/(-1x)) + 3| - 2) - 1))^2 + 3((1(-3|((-3x - 3)/(-1x)) + 3| - 2) - 2)/(2(-3|((-3x - 3)/(-1x)) + 3| - 2) - 1)) + 1) + 2)/(2(5((1(-3|((-3x - 3)/(-1x)) + 3| - 2) - 2)/(2(-3|((-3x - 3)/(-1x)) + 3| - 2) - 1))^2 + 3((1(-3|((-3x - 3)/(-1x)) + 3| - 2) - 2)/(2(-3|((-3x - 3)/(-1x)) + 3| - 2) - 1)) + 1) - 1)) - 4, g(x) = (-1(1(-4(-2|(-1x^2 + 2x + 2) - 3| - 1) + 5)^2 - 5(-4(-2|(-1x^2 + 2x + 2) - 3| - 1) + 5) + 1) - 2)/(-3(1(-4(-2|(-1x^2 + 2x + 2) - 3| - 1) + 5)^2 - 5(-4(-2|(-1x^2 + 2x + 2) - 3| - 1) + 5) + 1) + 4), 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": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 3|((3(2(2e^(1((2(1|x + 1| + 3) - 2)/(3(1|x + 1| + 3) + 3))) + 2)^2 + 5(2e^(1((2(1|x + 1| + 3) - 2)/(3(1|x + 1| + 3) + 3))) + 2) - 3) - 2)/(-3(2(2e^(1((2(1|x + 1| + 3) - 2)/(3(1|x + 1| + 3) + 3))) + 2)^2 + 5(2e^(1((2(1|x + 1| + 3) - 2)/(3(1|x + 1| + 3) + 3))) + 2) - 3) + 2))| - 3 and g(x) = 3|(-1((-3(3(1x^2 + 3x + 1)^2 + 2(1x^2 + 3x + 1) - 1) + 3)/(2(3(1x^2 + 3x + 1)^2 + 2(1x^2 + 3x + 1) - 1) - 1))) - 3| - 3 between the vertical lines x = -0.4 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": "Determine the area of the region enclosed by the graphs of f(x) = 2(-3((-1(-4((3(4x + 5))/(-3(4x + 5) - 2))^2 - 2((3(4x + 5))/(-3(4x + 5) - 2)) + 5) - 1)/(-2(-4((3(4x + 5))/(-3(4x + 5) - 2))^2 - 2((3(4x + 5))/(-3(4x + 5) - 2)) + 5) + 1)) + 5) and g(x) = 3((-2((-2(-1|(3x^2 + 1) - 2| - 1) - 3)/(-3(-1|(3x^2 + 1) - 2| - 1) + 2)))/(1((-2(-1|(3x^2 + 1) - 2| - 1) - 3)/(-3(-1|(3x^2 + 1) - 2| - 1) + 2))))^2 - 4((-2((-2(-1|(3x^2 + 1) - 2| - 1) - 3)/(-3(-1|(3x^2 + 1) - 2| - 1) + 2)))/(1((-2(-1|(3x^2 + 1) - 2| - 1) - 3)/(-3(-1|(3x^2 + 1) - 2| - 1) + 2)))) - 1 between the vertical lines x = -1.8 and x = -1.3. 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": "Find the area of the region bounded by the curves f(x) = 5(5(2|(2(-3(-2x - 4) - 4) - 3)| - 3))^2 - 4, g(x) = -1|(3(2((-2(-1x - 4) + 3)/(-2(-1x - 4) - 2))^2 - 5((-2(-1x - 4) + 3)/(-2(-1x - 4) - 2))) + 4)| + 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": "6.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1((-2(2|((-2(-2cos(2\u03c0(-1x^2 - 2)) - 2) - 3)/(-3(-2cos(2\u03c0(-1x^2 - 2)) - 2) - 1)) + 2| + 3) + 3)/(-1(2|((-2(-2cos(2\u03c0(-1x^2 - 2)) - 2) - 3)/(-3(-2cos(2\u03c0(-1x^2 - 2)) - 2) - 1)) + 2| + 3) + 2)) - 3 and g(x) = 2(-5(4(2|(2x^2 - 5x - 4) + 2| - 2)^2 - 5) - 1) + 4 between the vertical lines x = 2.9 and x = 3.1. 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) = (2(-1((1(1((3((-2x - 1)/(2x - 1)))/(-1((-2x - 1)/(2x - 1)) - 3))^2 - 5((3((-2x - 1)/(2x - 1)))/(-1((-2x - 1)/(2x - 1)) - 3)) + 4) - 2)/(-1(1((3((-2x - 1)/(2x - 1)))/(-1((-2x - 1)/(2x - 1)) - 3))^2 - 5((3((-2x - 1)/(2x - 1)))/(-1((-2x - 1)/(2x - 1)) - 3)) + 4) + 2)) - 4) + 3)/(1(-1((1(1((3((-2x - 1)/(2x - 1)))/(-1((-2x - 1)/(2x - 1)) - 3))^2 - 5((3((-2x - 1)/(2x - 1)))/(-1((-2x - 1)/(2x - 1)) - 3)) + 4) - 2)/(-1(1((3((-2x - 1)/(2x - 1)))/(-1((-2x - 1)/(2x - 1)) - 3))^2 - 5((3((-2x - 1)/(2x - 1)))/(-1((-2x - 1)/(2x - 1)) - 3)) + 4) + 2)) - 4)) and g(x) = -3sin(1\u03c0(1(4(-3(1|x + 1| + 3) - 2) + 3) + 3) - 3) - 2 from x = 2.8 to x = 3.0. 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": "Find the area of the region bounded by the curves f(x) = (-3((-2(1(-1(1|(1x^2 - 3x + 1) - 2| + 3) + 4)^2 + 4(-1(1|(1x^2 - 3x + 1) - 2| + 3) + 4) - 1) - 1)/(-1(1(-1(1|(1x^2 - 3x + 1) - 2| + 3) + 4)^2 + 4(-1(1|(1x^2 - 3x + 1) - 2| + 3) + 4) - 1) + 2)))/(1((-2(1(-1(1|(1x^2 - 3x + 1) - 2| + 3) + 4)^2 + 4(-1(1|(1x^2 - 3x + 1) - 2| + 3) + 4) - 1) - 1)/(-1(1(-1(1|(1x^2 - 3x + 1) - 2| + 3) + 4)^2 + 4(-1(1|(1x^2 - 3x + 1) - 2| + 3) + 4) - 1) + 2))), g(x) = -3|(-3(4(-2e^(2(-5x^2 + 4x + 2)) + 2) + 1)^2 + 5(4(-2e^(2(-5x^2 + 4x + 2)) + 2) + 1) - 2) - 1| + 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": "11.4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (1(-1|(-2(-3(2cos(3\u03c0(2|x - 3| + 3) - 3) + 2) + 3) + 3) - 2|))/(-1(-1|(-2(-3(2cos(3\u03c0(2|x - 3| + 3) - 3) + 2) + 3) + 3) - 2|) - 2) and g(x) = 3(-2|(-1|(2|(5x + 5) - 3| + 2) - 1|) + 2| - 1)^2 - 1(-2|(-1|(2|(5x + 5) - 3| + 2) - 1|) + 2| - 1) - 2 from x = -0.5 to x = -0.4. 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(-1|((1((1(1e^(1x) - 3) + 2)/(1(1e^(1x) - 3))) + 3)/(3((1(1e^(1x) - 3) + 2)/(1(1e^(1x) - 3))) - 2)) + 3| - 1)) - 2|, g(x) = (-3(5(2|((1(-2sin(1\u03c0x + 1) + 2) - 2)/(-2(-2sin(1\u03c0x + 1) + 2) - 3)) - 1| - 2)^2 - 2(2|((1(-2sin(1\u03c0x + 1) + 2) - 2)/(-2(-2sin(1\u03c0x + 1) + 2) - 3)) - 1| - 2) - 5))/(-1(5(2|((1(-2sin(1\u03c0x + 1) + 2) - 2)/(-2(-2sin(1\u03c0x + 1) + 2) - 3)) - 1| - 2)^2 - 2(2|((1(-2sin(1\u03c0x + 1) + 2) - 2)/(-2(-2sin(1\u03c0x + 1) + 2) - 3)) - 1| - 2) - 5) + 2), x = 2.3, 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": "41.8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -4((-2(-4(3(-2|(1|x - 1| - 2) + 1| + 3) + 2) + 5) + 2)/(1(-4(3(-2|(1|x - 1| - 2) + 1| + 3) + 2) + 5))) + 3 and g(x) = -2(1|(-1((1(2x^2 + 4x - 5))/(2(2x^2 + 4x - 5) + 3)) - 5) - 3| - 3)^2 + 4(1|(-1((1(2x^2 + 4x - 5))/(2(2x^2 + 4x - 5) + 3)) - 5) - 3| - 3) - 4 from x = -1.6 to x = 3.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "289.9", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3|(1(1(2|((-2(-5x^2 - 1x + 1) + 3)/(-2(-5x^2 - 1x + 1) + 3)) - 2| + 2)) + 2)|, g(x) = (2(-5((2(1(-3e^(-1x) + 1)^2 + 3(-3e^(-1x) + 1) - 3) - 2)/(3(1(-3e^(-1x) + 1)^2 + 3(-3e^(-1x) + 1) - 3) - 2))^2 - 1((2(1(-3e^(-1x) + 1)^2 + 3(-3e^(-1x) + 1) - 3) - 2)/(3(1(-3e^(-1x) + 1)^2 + 3(-3e^(-1x) + 1) - 3) - 2)) + 2) + 2)/(1(-5((2(1(-3e^(-1x) + 1)^2 + 3(-3e^(-1x) + 1) - 3) - 2)/(3(1(-3e^(-1x) + 1)^2 + 3(-3e^(-1x) + 1) - 3) - 2))^2 - 1((2(1(-3e^(-1x) + 1)^2 + 3(-3e^(-1x) + 1) - 3) - 2)/(3(1(-3e^(-1x) + 1)^2 + 3(-3e^(-1x) + 1) - 3) - 2)) + 2)), x = -0.6, 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": "85.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2|(4(1|(-2cos(1\u03c0(1|((-3x + 3)/(2x)) - 3| - 3) - 3) - 3) + 3|)^2 + 5(1|(-2cos(1\u03c0(1|((-3x + 3)/(2x)) - 3| - 3) - 3) - 3) + 3|) - 5) - 2| - 3 and g(x) = -1(4((2((1(-5x - 3) - 1)/(-2(-5x - 3) + 3)) + 1)/(-1((1(-5x - 3) - 1)/(-2(-5x - 3) + 3)) + 2)) + 5)^2 - 1(4((2((1(-5x - 3) - 1)/(-2(-5x - 3) + 3)) + 1)/(-1((1(-5x - 3) - 1)/(-2(-5x - 3) + 3)) + 2)) + 5) - 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": "1.5", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-1(1(-1(-4((3(2cos(3\u03c0x - 1)) + 2)/(-2(2cos(3\u03c0x - 1)) + 3)) + 3) - 4)^2 - 2(-1(-4((3(2cos(3\u03c0x - 1)) + 2)/(-2(2cos(3\u03c0x - 1)) + 3)) + 3) - 4) - 4) + 1)/(3(1(-1(-4((3(2cos(3\u03c0x - 1)) + 2)/(-2(2cos(3\u03c0x - 1)) + 3)) + 3) - 4)^2 - 2(-1(-4((3(2cos(3\u03c0x - 1)) + 2)/(-2(2cos(3\u03c0x - 1)) + 3)) + 3) - 4) - 4) + 1), g(x) = (-1(-3|((2(1(2x^2 + 2x - 2)^2 + 1(2x^2 + 2x - 2) - 3) + 1)/(2(1(2x^2 + 2x - 2)^2 + 1(2x^2 + 2x - 2) - 3))) - 3| + 1) + 3)/(-2(-3|((2(1(2x^2 + 2x - 2)^2 + 1(2x^2 + 2x - 2) - 3) + 1)/(2(1(2x^2 + 2x - 2)^2 + 1(2x^2 + 2x - 2) - 3))) - 3| + 1) + 3), 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) = (3(-3|(2|(1|(5((2x)/(2x - 3)) - 4) - 2| - 1) + 1| + 1) - 3| + 3) + 2)/(-3(-3|(2|(1|(5((2x)/(2x - 3)) - 4) - 2| - 1) + 1| + 1) - 3| + 3) + 2), g(x) = 2((1(1(2(-2x^2 + 1x - 2) - 1)) + 1)/(-2(1(2(-2x^2 + 1x - 2) - 1)) + 1)), x = -1.3, 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) = (2(-1e^(-1(-1(-1|(2|(-2|x| - 2) + 2| + 2) + 2| + 3)^2 - 4(-1|(2|(-2|x| - 2) + 2| + 2) + 2| + 3) + 5)) - 1) + 2)/(-2(-1e^(-1(-1(-1|(2|(-2|x| - 2) + 2| + 2) + 2| + 3)^2 - 4(-1|(2|(-2|x| - 2) + 2| + 2) + 2| + 3) + 5)) - 1) - 3) and g(x) = (3((-2((1((-2(2|x + 3| - 3))/(-3(2|x + 3| - 3) - 2)) - 2)/(1((-2(2|x + 3| - 3))/(-3(2|x + 3| - 3) - 2)) + 2)) - 3)/(2((1((-2(2|x + 3| - 3))/(-3(2|x + 3| - 3) - 2)) - 2)/(1((-2(2|x + 3| - 3))/(-3(2|x + 3| - 3) - 2)) + 2)) - 1)) - 3)/(3((-2((1((-2(2|x + 3| - 3))/(-3(2|x + 3| - 3) - 2)) - 2)/(1((-2(2|x + 3| - 3))/(-3(2|x + 3| - 3) - 2)) + 2)) - 3)/(2((1((-2(2|x + 3| - 3))/(-3(2|x + 3| - 3) - 2)) - 2)/(1((-2(2|x + 3| - 3))/(-3(2|x + 3| - 3) - 2)) + 2)) - 1))) from x = -4.6 to x = -1.4. 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": "Calculate the area enclosed between the functions f(x) = (-2(-5((-3(2((3(4x - 2) + 3)/(1(4x - 2) - 2))^2 - 5((3(4x - 2) + 3)/(1(4x - 2) - 2)) - 4) - 2)/(1(2((3(4x - 2) + 3)/(1(4x - 2) - 2))^2 - 5((3(4x - 2) + 3)/(1(4x - 2) - 2)) - 4) - 2)) + 3) - 1)/(1(-5((-3(2((3(4x - 2) + 3)/(1(4x - 2) - 2))^2 - 5((3(4x - 2) + 3)/(1(4x - 2) - 2)) - 4) - 2)/(1(2((3(4x - 2) + 3)/(1(4x - 2) - 2))^2 - 5((3(4x - 2) + 3)/(1(4x - 2) - 2)) - 4) - 2)) + 3) - 2) and g(x) = 1((-3(3cos(3\u03c0(-3(-2|x - 1| + 2) - 4) + 3) - 1) - 1)/(2(3cos(3\u03c0(-3(-2|x - 1| + 2) - 4) + 3) - 1) + 2)) + 4 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": "0.7", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (1(-3(3(-3((3(3sin(3\u03c0x + 3) - 1) - 3)/(1(3sin(3\u03c0x + 3) - 1) + 3))^2 - 4((3(3sin(3\u03c0x + 3) - 1) - 3)/(1(3sin(3\u03c0x + 3) - 1) + 3)) - 1) + 1) + 3) - 3)/(-2(-3(3(-3((3(3sin(3\u03c0x + 3) - 1) - 3)/(1(3sin(3\u03c0x + 3) - 1) + 3))^2 - 4((3(3sin(3\u03c0x + 3) - 1) - 3)/(1(3sin(3\u03c0x + 3) - 1) + 3)) - 1) + 1) + 3) - 2) and g(x) = -2|(-1sin(2\u03c0((-3((-1((-1x + 2)/(-2x - 1)) + 3)/(2((-1x + 2)/(-2x - 1)) + 2)) + 2)/(-3((-1((-1x + 2)/(-2x - 1)) + 3)/(2((-1x + 2)/(-2x - 1)) + 2)) - 2)) + 1)) - 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": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1((-1(-1(-3(-3(-1|x + 3|)^2 - 1(-1|x + 3|) + 3) + 5) - 2) - 2)/(2(-1(-3(-3(-1|x + 3|)^2 - 1(-1|x + 3|) + 3) + 5) - 2) + 3)) + 1, g(x) = (1(3(-3|((2((-2x)/(-3x + 4)) + 1)/(1((-2x)/(-3x + 4)) + 1))| - 2)^2 - 4(-3|((2((-2x)/(-3x + 4)) + 1)/(1((-2x)/(-3x + 4)) + 1))| - 2) + 5))/(-3(3(-3|((2((-2x)/(-3x + 4)) + 1)/(1((-2x)/(-3x + 4)) + 1))| - 2)^2 - 4(-3|((2((-2x)/(-3x + 4)) + 1)/(1((-2x)/(-3x + 4)) + 1))| - 2) + 5) + 4), x = -3.8, 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": "3.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2(1(1(1|((2(-3x + 5) - 2)/(-1(-3x + 5) - 1)) - 2| - 3)^2 - 3(1|((2(-3x + 5) - 2)/(-1(-3x + 5) - 1)) - 2| - 3) - 4) + 1)^2 - 1(1(1(1|((2(-3x + 5) - 2)/(-1(-3x + 5) - 1)) - 2| - 3)^2 - 3(1|((2(-3x + 5) - 2)/(-1(-3x + 5) - 1)) - 2| - 3) - 4) + 1) + 1 and g(x) = -1(-1|(4((-2((2x + 2)/(-3x + 4)) - 3)/(2((2x + 2)/(-3x + 4)) + 3)) + 5) - 1|) + 5 between the vertical lines x = 2.4 and x = 2.5. 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": "Determine the area of the region enclosed by the graphs of f(x) = 1|(-3cos(3\u03c0((2(2|(-1(-2|x - 1| + 3)^2 + 5(-2|x - 1| + 3) - 5)| + 3) - 1)/(1(2|(-1(-2|x - 1| + 3)^2 + 5(-2|x - 1| + 3) - 5)| + 3) - 3)) - 1) - 2) - 3| + 3 and g(x) = 1((-2(-4(-3(-2x^2 - 1x + 2) + 5) - 3) + 2)/(1(-4(-3(-2x^2 - 1x + 2) + 5) - 3) - 3))^2 - 5((-2(-4(-3(-2x^2 - 1x + 2) + 5) - 3) + 2)/(1(-4(-3(-2x^2 - 1x + 2) + 5) - 3) - 3)) + 1 between the vertical lines x = 0.2 and x = 0.30000000000000004. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "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(3(3(3(-2|x| - 1)^2 - 1(-2|x| - 1) - 5)) + 3) + 2) + 1| + 2 and g(x) = 1(2cos(1\u03c0(-2(5(3x^2 + 3x - 5) - 4) + 5) + 3) + 2) - 4 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": "1.9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (3(4(-4(2(2sin(2\u03c0((2x + 2)/(-1x)) + 3) - 1) + 3)^2 - 3(2(2sin(2\u03c0((2x + 2)/(-1x)) + 3) - 1) + 3) + 5)^2 - 4(-4(2(2sin(2\u03c0((2x + 2)/(-1x)) + 3) - 1) + 3)^2 - 3(2(2sin(2\u03c0((2x + 2)/(-1x)) + 3) - 1) + 3) + 5) - 1) + 3)/(-2(4(-4(2(2sin(2\u03c0((2x + 2)/(-1x)) + 3) - 1) + 3)^2 - 3(2(2sin(2\u03c0((2x + 2)/(-1x)) + 3) - 1) + 3) + 5)^2 - 4(-4(2(2sin(2\u03c0((2x + 2)/(-1x)) + 3) - 1) + 3)^2 - 3(2(2sin(2\u03c0((2x + 2)/(-1x)) + 3) - 1) + 3) + 5) - 1) + 1) and g(x) = 1cos(2\u03c0(-1(-2|(1(4x + 4) + 4) + 3| + 1) + 3) + 2) + 3 from x = -3.9 to x = -3.8. 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((-3((1((1((-2(5x^2 + 1x - 5) - 3)/(-2(5x^2 + 1x - 5) + 1)) - 2)/(-2((-2(5x^2 + 1x - 5) - 3)/(-2(5x^2 + 1x - 5) + 1)) + 3)) - 3)/(1((1((-2(5x^2 + 1x - 5) - 3)/(-2(5x^2 + 1x - 5) + 1)) - 2)/(-2((-2(5x^2 + 1x - 5) - 3)/(-2(5x^2 + 1x - 5) + 1)) + 3)) - 2)) - 2)/(-1((1((1((-2(5x^2 + 1x - 5) - 3)/(-2(5x^2 + 1x - 5) + 1)) - 2)/(-2((-2(5x^2 + 1x - 5) - 3)/(-2(5x^2 + 1x - 5) + 1)) + 3)) - 3)/(1((1((-2(5x^2 + 1x - 5) - 3)/(-2(5x^2 + 1x - 5) + 1)) - 2)/(-2((-2(5x^2 + 1x - 5) - 3)/(-2(5x^2 + 1x - 5) + 1)) + 3)) - 2)) - 2)) + 1, g(x) = 5(3e^(-1((1((-1(1|x| + 3) - 2)/(3(1|x| + 3))) - 2)/(3((-1(1|x| + 3) - 2)/(3(1|x| + 3))) + 1))) + 1) + 3, 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": "4.4", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 4((3((-3(-2((3(2|x + 2| + 3) + 2)/(-3(2|x + 2| + 3) + 2))^2 + 2((3(2|x + 2| + 3) + 2)/(-3(2|x + 2| + 3) + 2)) - 3) - 2)/(1(-2((3(2|x + 2| + 3) + 2)/(-3(2|x + 2| + 3) + 2))^2 + 2((3(2|x + 2| + 3) + 2)/(-3(2|x + 2| + 3) + 2)) - 3))) - 1)/(3((-3(-2((3(2|x + 2| + 3) + 2)/(-3(2|x + 2| + 3) + 2))^2 + 2((3(2|x + 2| + 3) + 2)/(-3(2|x + 2| + 3) + 2)) - 3) - 2)/(1(-2((3(2|x + 2| + 3) + 2)/(-3(2|x + 2| + 3) + 2))^2 + 2((3(2|x + 2| + 3) + 2)/(-3(2|x + 2| + 3) + 2)) - 3))) + 1)) + 5, g(x) = 5(2sin(2\u03c0((-1((-2(2x + 4) - 3)/(-1(2x + 4) - 2)) - 3)/(1((-2(2x + 4) - 3)/(-1(2x + 4) - 2)) - 3))) + 1)^2 + 3(2sin(2\u03c0((-1((-2(2x + 4) - 3)/(-1(2x + 4) - 2)) - 3)/(1((-2(2x + 4) - 3)/(-1(2x + 4) - 2)) - 3))) + 1) - 1, x = -3.0, 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": "1.6", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1(-1(1cos(1\u03c0((2(1(-2x^2 - 1x - 4) + 5) + 3)/(-1(1(-2x^2 - 1x - 4) + 5) - 3))) - 1) + 4)^2 - 3(-1(1cos(1\u03c0((2(1(-2x^2 - 1x - 4) + 5) + 3)/(-1(1(-2x^2 - 1x - 4) + 5) - 3))) - 1) + 4) + 5 and g(x) = -3|(-2|(3|(-2cos(1\u03c0(3|x + 1| - 2) + 3) - 2) - 1| - 1) - 3| - 3) + 3| + 2 between the vertical lines x = 3.2 and x = 3.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8.7", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2(-2|(2(1(-2(2x + 1) + 1)^2 + 1(-2(2x + 1) + 1) - 1)^2 - 3(1(-2(2x + 1) + 1)^2 + 1(-2(2x + 1) + 1) - 1) + 4) - 1| + 2)^2 - 4(-2|(2(1(-2(2x + 1) + 1)^2 + 1(-2(2x + 1) + 1) - 1)^2 - 3(1(-2(2x + 1) + 1)^2 + 1(-2(2x + 1) + 1) - 1) + 4) - 1| + 2) - 1, g(x) = (-1((2(-1e^(2(-5(-3x + 2)^2 - 3(-3x + 2) + 1)) + 1) - 1)/(3(-1e^(2(-5(-3x + 2)^2 - 3(-3x + 2) + 1)) + 1))) - 1)/(1((2(-1e^(2(-5(-3x + 2)^2 - 3(-3x + 2) + 1)) + 1) - 1)/(3(-1e^(2(-5(-3x + 2)^2 - 3(-3x + 2) + 1)) + 1))) + 3), 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -4(-2|(2sin(1\u03c0((-3((3((-2x - 2)/(3x - 1)))/(3((-2x - 2)/(3x - 1)) - 2)) + 3)/(2((3((-2x - 2)/(3x - 1)))/(3((-2x - 2)/(3x - 1)) - 2)) - 1)) + 2) - 3)| + 2)^2 + 3(-2|(2sin(1\u03c0((-3((3((-2x - 2)/(3x - 1)))/(3((-2x - 2)/(3x - 1)) - 2)) + 3)/(2((3((-2x - 2)/(3x - 1)))/(3((-2x - 2)/(3x - 1)) - 2)) - 1)) + 2) - 3)| + 2) + 5, g(x) = 5(-2|((-1(2cos(3\u03c0(5x - 5) + 1) - 3))/(2(2cos(3\u03c0(5x - 5) + 1) - 3) - 1)) + 1| - 3) - 2, x = -3.4, 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": "6.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1((-3(2(-3|((3((1x + 2)/(-3x - 3)) - 2)/(-2((1x + 2)/(-3x - 3)) + 3)) + 2| - 3)^2 - 2(-3|((3((1x + 2)/(-3x - 3)) - 2)/(-2((1x + 2)/(-3x - 3)) + 3)) + 2| - 3) - 4) + 1)/(2(2(-3|((3((1x + 2)/(-3x - 3)) - 2)/(-2((1x + 2)/(-3x - 3)) + 3)) + 2| - 3)^2 - 2(-3|((3((1x + 2)/(-3x - 3)) - 2)/(-2((1x + 2)/(-3x - 3)) + 3)) + 2| - 3) - 4) + 3)) + 5 and g(x) = 2|((1((3((-3((-2x + 1)/(2x - 3)) - 2)/(2((-2x + 1)/(2x - 3)))) - 3)/(-2((-3((-2x + 1)/(2x - 3)) - 2)/(2((-2x + 1)/(2x - 3)))) - 1)) + 2)/(1((3((-3((-2x + 1)/(2x - 3)) - 2)/(2((-2x + 1)/(2x - 3)))) - 3)/(-2((-3((-2x + 1)/(2x - 3)) - 2)/(2((-2x + 1)/(2x - 3)))) - 1)) + 3)) + 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 4(-5(2(1|(3(-1x + 4) - 2) + 1|)^2 + 1(1|(3(-1x + 4) - 2) + 1|) - 5) - 1) - 5 and g(x) = -3cos(2\u03c0(1|(1|(-1((3x - 1)/(-3x + 4)) + 3) - 1| + 1) + 2| - 3) - 1) - 2 from x = 3.2 to x = 4.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "49.7", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 4(-1|(-1|((1(5(1sin(3\u03c0x - 2) + 2)^2 - 5(1sin(3\u03c0x - 2) + 2) + 1) + 2)/(1(5(1sin(3\u03c0x - 2) + 2)^2 - 5(1sin(3\u03c0x - 2) + 2) + 1) - 3)) + 2| - 3) + 2| + 3) - 1, g(x) = 2cos(1\u03c0(-2|(-1(-4(5x^2 + 5x) - 5)^2 + 5(-4(5x^2 + 5x) - 5) + 1)| + 1) - 1), x = -3.2, 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": "8.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2((-2(3|(1|(-1(-1|x - 3| - 3) + 5)|) - 2| + 2) + 2)/(2(3|(1|(-1(-1|x - 3| - 3) + 5)|) - 2| + 2) + 1))^2 + 3((-2(3|(1|(-1(-1|x - 3| - 3) + 5)|) - 2| + 2) + 2)/(2(3|(1|(-1(-1|x - 3| - 3) + 5)|) - 2| + 2) + 1)), g(x) = -5(2cos(2\u03c0((2(-4((3x - 3)/(-3x))^2 + 3((3x - 3)/(-3x)) - 4))/(-1(-4((3x - 3)/(-3x))^2 + 3((3x - 3)/(-3x)) - 4) - 2)) - 1) - 2) - 5, 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (1(-1(-5(-1cos(1\u03c0(5(-4x - 3) + 2) + 2) - 3)^2 + 5(-1cos(1\u03c0(5(-4x - 3) + 2) + 2) - 3)) - 2) - 1)/(1(-1(-5(-1cos(1\u03c0(5(-4x - 3) + 2) + 2) - 3)^2 + 5(-1cos(1\u03c0(5(-4x - 3) + 2) + 2) - 3)) - 2) + 3), g(x) = (-2(1|(-2((3(1|x + 2| - 2) - 3)/(-2(1|x + 2| - 2) - 3))^2 + 2((3(1|x + 2| - 2) - 3)/(-2(1|x + 2| - 2) - 3)) + 4) + 1|) + 2)/(2(1|(-2((3(1|x + 2| - 2) - 3)/(-2(1|x + 2| - 2) - 3))^2 + 2((3(1|x + 2| - 2) - 3)/(-2(1|x + 2| - 2) - 3)) + 4) + 1|) - 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": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-1((-2(1(4(-2(3|x + 2|)^2 - 4(3|x + 2|) + 2)^2 + 2(-2(3|x + 2|)^2 - 4(3|x + 2|) + 2) - 5) - 3) + 1)/(-1(1(4(-2(3|x + 2|)^2 - 4(3|x + 2|) + 2)^2 + 2(-2(3|x + 2|)^2 - 4(3|x + 2|) + 2) - 5) - 3))) - 2)/(-1((-2(1(4(-2(3|x + 2|)^2 - 4(3|x + 2|) + 2)^2 + 2(-2(3|x + 2|)^2 - 4(3|x + 2|) + 2) - 5) - 3) + 1)/(-1(1(4(-2(3|x + 2|)^2 - 4(3|x + 2|) + 2)^2 + 2(-2(3|x + 2|)^2 - 4(3|x + 2|) + 2) - 5) - 3))) + 2), g(x) = -2((2(-4(-5(-5x + 4)^2 - 1(-5x + 4) - 3) + 2) - 2)/(3(-4(-5(-5x + 4)^2 - 1(-5x + 4) - 3) + 2) - 1)) - 1, 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": "3.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2(1(3e^(-1(2|(2(-2x^2 + 4x + 2)^2 - 1(-2x^2 + 4x + 2) - 5)| + 2)) - 2) + 4)^2 + 4(1(3e^(-1(2|(2(-2x^2 + 4x + 2)^2 - 1(-2x^2 + 4x + 2) - 5)| + 2)) - 2) + 4) - 3, g(x) = -2cos(2\u03c0(-5((2(2|((2x)/(3x + 3)) - 3| - 3) - 2)/(-3(2|((2x)/(3x + 3)) - 3| - 3) + 1))^2 + 1((2(2|((2x)/(3x + 3)) - 3| - 3) - 2)/(-3(2|((2x)/(3x + 3)) - 3| - 3) + 1)) - 2) - 1) - 2, 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((-3(3|(-3|(-2((2x - 2)/(-1x - 2)) - 3)| + 2) - 3| - 3) - 3)/(3(3|(-3|(-2((2x - 2)/(-1x - 2)) - 3)| + 2) - 3| - 3))))/(-3((-3(3|(-3|(-2((2x - 2)/(-1x - 2)) - 3)| + 2) - 3| - 3) - 3)/(3(3|(-3|(-2((2x - 2)/(-1x - 2)) - 3)| + 2) - 3| - 3))) - 2), g(x) = 5(-2sin(3\u03c0((-3((-1(-1x^2 - 5x - 4) + 2)/(-3(-1x^2 - 5x - 4) + 4)) + 3)/(-3((-1(-1x^2 - 5x - 4) + 2)/(-3(-1x^2 - 5x - 4) + 4)) + 1)) - 2) - 2), x = -4.6, 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": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 5(1((3(2sin(3\u03c0((2(-4x^2 - 2x + 1))/(-1(-4x^2 - 2x + 1) + 3)) + 1) - 1) + 3)/(3(2sin(3\u03c0((2(-4x^2 - 2x + 1))/(-1(-4x^2 - 2x + 1) + 3)) + 1) - 1) + 2))^2 + 2) + 4 and g(x) = -5(-3(-2(-1(-4x - 4)^2 + 2(-4x - 4) + 2) + 5)^2 - 5(-2(-1(-4x - 4)^2 + 2(-4x - 4) + 2) + 5) - 4) - 4 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": "1.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (1(4(1(-1(-2cos(1\u03c0(1x - 2) - 2) - 2) + 2) - 1)^2 - 5(1(-1(-2cos(1\u03c0(1x - 2) - 2) - 2) + 2) - 1) + 2) - 1)/(2(4(1(-1(-2cos(1\u03c0(1x - 2) - 2) - 2) + 2) - 1)^2 - 5(1(-1(-2cos(1\u03c0(1x - 2) - 2) - 2) + 2) - 1) + 2) - 3) and g(x) = -5(4(-5(1|((-1x + 3)/(-2x - 1)) - 3| - 1) + 5)^2 - 5(-5(1|((-1x + 3)/(-2x - 1)) - 3| - 1) + 5) + 5) + 5 from x = -4.2 to x = -2.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "52.8", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1(2((-1(-1(-3|(3|x|)| - 1)^2 - 4(-3|(3|x|)| - 1) - 2) - 2)/(3(-1(-3|(3|x|)| - 1)^2 - 4(-3|(3|x|)| - 1) - 2) - 2)) + 5)^2 - 5(2((-1(-1(-3|(3|x|)| - 1)^2 - 4(-3|(3|x|)| - 1) - 2) - 2)/(3(-1(-3|(3|x|)| - 1)^2 - 4(-3|(3|x|)| - 1) - 2) - 2)) + 5) - 1, g(x) = (-2(3((-1((2(3cos(1\u03c0x + 3) - 2) - 1)/(1(3cos(1\u03c0x + 3) - 2) - 3)))/(1((2(3cos(1\u03c0x + 3) - 2) - 1)/(1(3cos(1\u03c0x + 3) - 2) - 3)) + 2))) + 3)/(-3(3((-1((2(3cos(1\u03c0x + 3) - 2) - 1)/(1(3cos(1\u03c0x + 3) - 2) - 3)))/(1((2(3cos(1\u03c0x + 3) - 2) - 1)/(1(3cos(1\u03c0x + 3) - 2) - 3)) + 2))) + 2), 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": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 4(1|(-3cos(2\u03c0((2(5(-3|x + 3|)^2 + 2(-3|x + 3|) + 2) - 1)/(1(5(-3|x + 3|)^2 + 2(-3|x + 3|) + 2) + 2)) - 3) + 2)| - 1) - 3 and g(x) = -2(-2|(-2sin(1\u03c0(-3|(1|x - 1|)| - 1) + 3) + 3) + 3| + 3) - 3 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": "1.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2(3((2(-3(-1((3x)/(2x + 3))^2 + 5((3x)/(2x + 3)) + 4)) - 3)/(3(-3(-1((3x)/(2x + 3))^2 + 5((3x)/(2x + 3)) + 4)) - 1))^2 - 2((2(-3(-1((3x)/(2x + 3))^2 + 5((3x)/(2x + 3)) + 4)) - 3)/(3(-3(-1((3x)/(2x + 3))^2 + 5((3x)/(2x + 3)) + 4)) - 1)) + 2) + 1 and g(x) = 2|(-1|((-3(5(-1x + 1) + 1) - 3)/(1(5(-1x + 1) + 1))) - 2| + 2) + 2| between the vertical lines x = 1.3 and 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": "Find the area of the region bounded by the curves f(x) = (-2((-1(-2(-3cos(1\u03c0((-1(4x + 5))/(2(4x + 5))) - 1) + 2) + 2))/(-2(-2(-3cos(1\u03c0((-1(4x + 5))/(2(4x + 5))) - 1) + 2) + 2) + 1)) + 1)/(2((-1(-2(-3cos(1\u03c0((-1(4x + 5))/(2(4x + 5))) - 1) + 2) + 2))/(-2(-2(-3cos(1\u03c0((-1(4x + 5))/(2(4x + 5))) - 1) + 2) + 2) + 1)) - 1), g(x) = 2(-4(-2(-3(1|x - 3|) + 4) - 1) + 5) - 3, x = 1.3, 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": "133.4", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1((-1(2|(1|((2(3x^2 + 4x - 3))/(-1(3x^2 + 4x - 3) + 2)) - 3| + 1)| + 2) + 3)/(3(2|(1|((2(3x^2 + 4x - 3))/(-1(3x^2 + 4x - 3) + 2)) - 3| + 1)| + 2) + 2))^2 - 2((-1(2|(1|((2(3x^2 + 4x - 3))/(-1(3x^2 + 4x - 3) + 2)) - 3| + 1)| + 2) + 3)/(3(2|(1|((2(3x^2 + 4x - 3))/(-1(3x^2 + 4x - 3) + 2)) - 3| + 1)| + 2) + 2)) - 1, g(x) = -5(-3((1(-3sin(3\u03c0((1x + 1)/(-1x - 2)) + 1) - 1) - 1)/(3(-3sin(3\u03c0((1x + 1)/(-1x - 2)) + 1) - 1) + 2)) - 5)^2 + 3(-3((1(-3sin(3\u03c0((1x + 1)/(-1x - 2)) + 1) - 1) - 1)/(3(-3sin(3\u03c0((1x + 1)/(-1x - 2)) + 1) - 1) + 2)) - 5) + 4, x = -2.4, 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": "26.6", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2|(2|(-3|((-3(1(1x - 2)^2 + 3) + 2)/(1(1(1x - 2)^2 + 3) + 2)) - 3| - 2) + 3| + 1) - 3| + 3, g(x) = (2(1|(-2|((3((-2x + 1)/(1x + 1)) - 3)/(1((-2x + 1)/(1x + 1)) + 1)) - 3|) + 3| - 3) + 1)/(-2(1|(-2|((3((-2x + 1)/(1x + 1)) - 3)/(1((-2x + 1)/(1x + 1)) + 1)) - 3|) + 3| - 3) - 3), 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": "41.6", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-1(-1((-1((-3(2|(3|x - 1| - 1) + 2| - 3))/(-1(2|(3|x - 1| - 1) + 2| - 3) + 2)) + 3)/(2((-3(2|(3|x - 1| - 1) + 2| - 3))/(-1(2|(3|x - 1| - 1) + 2| - 3) + 2))))^2 + 4((-1((-3(2|(3|x - 1| - 1) + 2| - 3))/(-1(2|(3|x - 1| - 1) + 2| - 3) + 2)) + 3)/(2((-3(2|(3|x - 1| - 1) + 2| - 3))/(-1(2|(3|x - 1| - 1) + 2| - 3) + 2)))) + 3) - 3)/(-2(-1((-1((-3(2|(3|x - 1| - 1) + 2| - 3))/(-1(2|(3|x - 1| - 1) + 2| - 3) + 2)) + 3)/(2((-3(2|(3|x - 1| - 1) + 2| - 3))/(-1(2|(3|x - 1| - 1) + 2| - 3) + 2))))^2 + 4((-1((-3(2|(3|x - 1| - 1) + 2| - 3))/(-1(2|(3|x - 1| - 1) + 2| - 3) + 2)) + 3)/(2((-3(2|(3|x - 1| - 1) + 2| - 3))/(-1(2|(3|x - 1| - 1) + 2| - 3) + 2)))) + 3) + 3) and g(x) = -1cos(3\u03c0(5(4(-1|((3x - 2)/(2x + 1))| - 2)^2 + 3(-1|((3x - 2)/(2x + 1))| - 2))^2 + 5)) - 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": "Determine the area of the region enclosed by the graphs of f(x) = (-3((-2((2(-5(-5(-5x^2 - 3x + 5)^2 + 4(-5x^2 - 3x + 5) + 2) - 5) - 2)/(2(-5(-5(-5x^2 - 3x + 5)^2 + 4(-5x^2 - 3x + 5) + 2) - 5) + 3)) + 3)/(2((2(-5(-5(-5x^2 - 3x + 5)^2 + 4(-5x^2 - 3x + 5) + 2) - 5) - 2)/(2(-5(-5(-5x^2 - 3x + 5)^2 + 4(-5x^2 - 3x + 5) + 2) - 5) + 3)) + 2)) + 1)/(-3((-2((2(-5(-5(-5x^2 - 3x + 5)^2 + 4(-5x^2 - 3x + 5) + 2) - 5) - 2)/(2(-5(-5(-5x^2 - 3x + 5)^2 + 4(-5x^2 - 3x + 5) + 2) - 5) + 3)) + 3)/(2((2(-5(-5(-5x^2 - 3x + 5)^2 + 4(-5x^2 - 3x + 5) + 2) - 5) - 2)/(2(-5(-5(-5x^2 - 3x + 5)^2 + 4(-5x^2 - 3x + 5) + 2) - 5) + 3)) + 2)) + 4) and g(x) = -2(2(2(2|((-1x + 3)/(3x + 3)) + 3| - 3)^2 - 2) - 5)^2 - 5(2(2(2|((-1x + 3)/(3x + 3)) + 3| - 3)^2 - 2) - 5) - 1 between the vertical lines x = -1.4 and x = -1.3. 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": "Determine the area of the region enclosed by the graphs of f(x) = -5((2(-3|(1(-3|(2|x - 2| + 2) - 3| - 1)^2 + 1(-3|(2|x - 2| + 2) - 3| - 1) - 1) - 2| + 1) - 1)/(1(-3|(1(-3|(2|x - 2| + 2) - 3| - 1)^2 + 1(-3|(2|x - 2| + 2) - 3| - 1) - 1) - 2| + 1) + 3)) - 2 and g(x) = (-2(-2|((-3(-1cos(1\u03c0(1x - 2) + 1) + 3) + 2)/(-2(-1cos(1\u03c0(1x - 2) + 1) + 3) + 3)) + 2| - 2) - 1)/(-1(-2|((-3(-1cos(1\u03c0(1x - 2) + 1) + 3) + 2)/(-2(-1cos(1\u03c0(1x - 2) + 1) + 3) + 3)) + 2| - 2) - 3) between the vertical lines x = 2.3 and x = 2.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "26.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (1(3(-5((-3(1(2|x| + 3)^2 + 4(2|x| + 3) + 4) - 1)/(2(1(2|x| + 3)^2 + 4(2|x| + 3) + 4) + 2)) + 2)) - 2)/(-3(3(-5((-3(1(2|x| + 3)^2 + 4(2|x| + 3) + 4) - 1)/(2(1(2|x| + 3)^2 + 4(2|x| + 3) + 4) + 2)) + 2)) - 3) and g(x) = -2e^(1((-2((2(-1|(5x^2 + 3x - 1)|) + 1)/(-1(-1|(5x^2 + 3x - 1)|) - 2)) + 3)/(-3((2(-1|(5x^2 + 3x - 1)|) + 1)/(-1(-1|(5x^2 + 3x - 1)|) - 2)) - 3))) + 1 from x = 0.1 to 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) = (3(-2(5(1|(-1|(-1|x - 1| - 1) + 1| - 3) - 1| + 2)^2 - 3(1|(-1|(-1|x - 1| - 1) + 1| - 3) - 1| + 2) - 5)^2 + 3(5(1|(-1|(-1|x - 1| - 1) + 1| - 3) - 1| + 2)^2 - 3(1|(-1|(-1|x - 1| - 1) + 1| - 3) - 1| + 2) - 5) + 3) - 3)/(1(-2(5(1|(-1|(-1|x - 1| - 1) + 1| - 3) - 1| + 2)^2 - 3(1|(-1|(-1|x - 1| - 1) + 1| - 3) - 1| + 2) - 5)^2 + 3(5(1|(-1|(-1|x - 1| - 1) + 1| - 3) - 1| + 2)^2 - 3(1|(-1|(-1|x - 1| - 1) + 1| - 3) - 1| + 2) - 5) + 3) - 2) and g(x) = -3(1e^(1(4((2(5x + 2) + 2)/(1(5x + 2) + 3))^2 + 4((2(5x + 2) + 2)/(1(5x + 2) + 3)))) - 1)^2 - 4(1e^(1(4((2(5x + 2) + 2)/(1(5x + 2) + 3))^2 + 4((2(5x + 2) + 2)/(1(5x + 2) + 3)))) - 1) + 2 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": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -5(-3|((-2(1(3sin(2\u03c0(-2|x| + 2) + 3) + 2)^2 - 2(3sin(2\u03c0(-2|x| + 2) + 3) + 2) + 1) + 3)/(-3(1(3sin(2\u03c0(-2|x| + 2) + 3) + 2)^2 - 2(3sin(2\u03c0(-2|x| + 2) + 3) + 2) + 1) - 1)) + 3| - 1)^2 + 3(-3|((-2(1(3sin(2\u03c0(-2|x| + 2) + 3) + 2)^2 - 2(3sin(2\u03c0(-2|x| + 2) + 3) + 2) + 1) + 3)/(-3(1(3sin(2\u03c0(-2|x| + 2) + 3) + 2)^2 - 2(3sin(2\u03c0(-2|x| + 2) + 3) + 2) + 1) - 1)) + 3| - 1) - 4 and g(x) = -2|(3(-1(-1(-3cos(1\u03c0x - 2) - 2)^2 - 3(-3cos(1\u03c0x - 2) - 2) - 2)^2 - 3(-1(-3cos(1\u03c0x - 2) - 2)^2 - 3(-3cos(1\u03c0x - 2) - 2) - 2)) - 2) + 2| - 3 from x = -3.0 to x = -2.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "270.9", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2|((2(3|(-1|(2(1x^2 - 2x + 2)^2 + 3(1x^2 - 2x + 2) - 5) + 2| + 1) + 2| - 1) - 3)/(1(3|(-1|(2(1x^2 - 2x + 2)^2 + 3(1x^2 - 2x + 2) - 5) + 2| + 1) + 2| - 1)))|, g(x) = -1|(4(4(-2|(4x - 5) + 2| - 1)^2 + 5(-2|(4x - 5) + 2| - 1) + 4)^2 + 4(4(-2|(4x - 5) + 2| - 1)^2 + 5(-2|(4x - 5) + 2| - 1) + 4) + 1)| - 3, x = 0.7, and x = 0.7999999999999999. 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(-2((1(-3|(5(-4x^2 - 3x - 4)^2 + 3(-4x^2 - 3x - 4) - 3) - 3| + 2))/(-3(-3|(5(-4x^2 - 3x - 4)^2 + 3(-4x^2 - 3x - 4) - 3) - 3| + 2) - 2))^2 - 4((1(-3|(5(-4x^2 - 3x - 4)^2 + 3(-4x^2 - 3x - 4) - 3) - 3| + 2))/(-3(-3|(5(-4x^2 - 3x - 4)^2 + 3(-4x^2 - 3x - 4) - 3) - 3| + 2) - 2)) + 1) - 2 and g(x) = (-2(-2cos(2\u03c0(-2|((3(-1x^2 - 3x))/(-1(-1x^2 - 3x) - 3)) - 1|) + 3) - 2) + 3)/(-2(-2cos(2\u03c0(-2|((3(-1x^2 - 3x))/(-1(-1x^2 - 3x) - 3)) - 1|) + 3) - 2) - 1) between the vertical lines x = 1.1 and x = 1.2000000000000002. 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) = 1|((3(-3sin(1\u03c0(1|(-1(-1|x + 3| + 2) + 5) + 1| - 3)) - 1) + 1)/(-2(-3sin(1\u03c0(1|(-1(-1|x + 3| + 2) + 5) + 1| - 3)) - 1) + 3)) - 3| + 3 and g(x) = -3cos(2\u03c0(5((3(-1(5x - 3) + 5) + 2)/(-1(-1(5x - 3) + 5) + 3)) + 2) - 3) + 1 from x = 3.2 to x = 3.3000000000000003. 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": "Calculate the area enclosed between the functions f(x) = (-2(2(5((1(-2((3x + 2)/(2x + 2))^2 + 4((3x + 2)/(2x + 2)) + 1) - 1)/(-2(-2((3x + 2)/(2x + 2))^2 + 4((3x + 2)/(2x + 2)) + 1)))^2 - 5((1(-2((3x + 2)/(2x + 2))^2 + 4((3x + 2)/(2x + 2)) + 1) - 1)/(-2(-2((3x + 2)/(2x + 2))^2 + 4((3x + 2)/(2x + 2)) + 1))) - 4) - 4) - 3)/(2(2(5((1(-2((3x + 2)/(2x + 2))^2 + 4((3x + 2)/(2x + 2)) + 1) - 1)/(-2(-2((3x + 2)/(2x + 2))^2 + 4((3x + 2)/(2x + 2)) + 1)))^2 - 5((1(-2((3x + 2)/(2x + 2))^2 + 4((3x + 2)/(2x + 2)) + 1) - 1)/(-2(-2((3x + 2)/(2x + 2))^2 + 4((3x + 2)/(2x + 2)) + 1))) - 4) - 4) - 1) and g(x) = -1sin(2\u03c0(-3(-2((2(-2x^2 + 3x - 4) - 1)/(-2(-2x^2 + 3x - 4) + 3))^2 - 2((2(-2x^2 + 3x - 4) - 1)/(-2(-2x^2 + 3x - 4) + 3)) + 1)^2 + 4(-2((2(-2x^2 + 3x - 4) - 1)/(-2(-2x^2 + 3x - 4) + 3))^2 - 2((2(-2x^2 + 3x - 4) - 1)/(-2(-2x^2 + 3x - 4) + 3)) + 1) - 2) + 1) from x = -0.8 to x = -0.1. 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) = 2|(1(-2((2(-4(-3|x + 3| + 3) + 5))/(-2(-4(-3|x + 3| + 3) + 5) + 1))^2 + 1((2(-4(-3|x + 3| + 3) + 5))/(-2(-4(-3|x + 3| + 3) + 5) + 1)) - 3) - 1) + 1| + 1, g(x) = 2|(-1((3(2|(-4x - 4) - 1| + 3) - 1)/(3(2|(-4x - 4) - 1| + 3) - 2)) - 2)| + 2, x = -3.6, 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": "3.9", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1(2e^(2(-2(2|(1(1|x|)^2) + 1| - 1)^2 + 5)) - 3) - 4, g(x) = -1((-2(2cos(3\u03c0(-2(3x - 1))) + 2) - 3)/(2(2cos(3\u03c0(-2(3x - 1))) + 2) + 3)) + 5, 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": "331.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2(1|(5(-2|((-2(4x^2 - 4x - 5) - 1)/(3(4x^2 - 4x - 5))) + 1| + 3)^2 + 3(-2|((-2(4x^2 - 4x - 5) - 1)/(3(4x^2 - 4x - 5))) + 1| + 3) + 3) - 3|)^2 + 4(1|(5(-2|((-2(4x^2 - 4x - 5) - 1)/(3(4x^2 - 4x - 5))) + 1| + 3)^2 + 3(-2|((-2(4x^2 - 4x - 5) - 1)/(3(4x^2 - 4x - 5))) + 1| + 3) + 3) - 3|) - 3 and g(x) = 4((2(5(-1(-2|x| + 1) - 5)) + 3)/(-2(5(-1(-2|x| + 1) - 5)) + 3))^2 + 1((2(5(-1(-2|x| + 1) - 5)) + 3)/(-2(5(-1(-2|x| + 1) - 5)) + 3)) + 2 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": "43.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-1(-3|(-3(-3|(1|(-2|x - 2| + 3) + 2| - 2) + 1| + 3)^2 + 3(-3|(1|(-2|x - 2| + 3) + 2| - 2) + 1| + 3))|) - 1)/(-3(-3|(-3(-3|(1|(-2|x - 2| + 3) + 2| - 2) + 1| + 3)^2 + 3(-3|(1|(-2|x - 2| + 3) + 2| - 2) + 1| + 3))|) - 1) and g(x) = 3e^(-2(5(1(2|((-1x - 1)/(-2x - 3)) - 2| + 1)^2 - 2(2|((-1x - 1)/(-2x - 3)) - 2| + 1) - 1) + 3)) from x = 3.7 to x = 4.3. 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": "Calculate the area enclosed between the functions f(x) = (2(-3|((-1(-1sin(2\u03c0(-4(5x^2 - 5x - 1) - 1) - 1) + 2) - 1)/(-3(-1sin(2\u03c0(-4(5x^2 - 5x - 1) - 1) - 1) + 2) - 2)) + 3| - 3) + 2)/(-1(-3|((-1(-1sin(2\u03c0(-4(5x^2 - 5x - 1) - 1) - 1) + 2) - 1)/(-3(-1sin(2\u03c0(-4(5x^2 - 5x - 1) - 1) - 1) + 2) - 2)) + 3| - 3) - 2) and g(x) = 5(5(-4(1(-1|x + 1|) - 1) - 4) - 5)^2 + 3(5(-4(1(-1|x + 1|) - 1) - 4) - 5) - 3 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": "16.7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 3(5(-1(-2|(-1(-5x^2 + 3x - 2)^2 - 5(-5x^2 + 3x - 2) + 5) + 1| - 2) - 5)^2 - 2(-1(-2|(-1(-5x^2 + 3x - 2)^2 - 5(-5x^2 + 3x - 2) + 5) + 1| - 2) - 5) - 2) - 4 and g(x) = (-1((2((1(2e^(-1(2|x - 1| - 1))) - 1)/(-1(2e^(-1(2|x - 1| - 1))) - 3)) + 3)/(-3((1(2e^(-1(2|x - 1| - 1))) - 1)/(-1(2e^(-1(2|x - 1| - 1))) - 3)) + 4)) - 2)/(2((2((1(2e^(-1(2|x - 1| - 1))) - 1)/(-1(2e^(-1(2|x - 1| - 1))) - 3)) + 3)/(-3((1(2e^(-1(2|x - 1| - 1))) - 1)/(-1(2e^(-1(2|x - 1| - 1))) - 3)) + 4)) - 1) 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": "6.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2|(4(-2e^(1(-2|(5(5x^2 - 1x + 5)^2 + 4(5x^2 - 1x + 5) + 3) - 3|)) - 2)^2 + 5(-2e^(1(-2|(5(5x^2 - 1x + 5)^2 + 4(5x^2 - 1x + 5) + 3) - 3|)) - 2) + 1)| - 2 and g(x) = -3|(-3(4(-3((-1x)/(-2x + 3)) - 2) + 2)^2 + 5(4(-3((-1x)/(-2x + 3)) - 2) + 2) - 1) + 1| - 2 from x = 0.7 to x = 0.9. 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": "Find the area of the region bounded by the curves f(x) = -3|(2sin(1\u03c0(-5(2|(2|(5x^2 + 1x - 4) - 1| - 2) - 3| + 3)^2 + 4(2|(2|(5x^2 + 1x - 4) - 1| - 2) - 3| + 3) - 4) - 3) + 3) - 3| + 3, g(x) = -3(3sin(3\u03c0(3((3(2|x - 1| - 3) - 3)/(3(2|x - 1| - 3) - 2))) - 3) - 2)^2 + 2(3sin(3\u03c0(3((3(2|x - 1| - 3) - 3)/(3(2|x - 1| - 3) - 2))) - 3) - 2) + 4, 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1|((-1(-1|(-3(5((1x - 1)/(1x - 2)) + 1)^2 + 5(5((1x - 1)/(1x - 2)) + 1) + 5) - 1| + 3) - 1)/(-3(-1|(-3(5((1x - 1)/(1x - 2)) + 1)^2 + 5(5((1x - 1)/(1x - 2)) + 1) + 5) - 1| + 3) - 1)) + 1| + 3 and g(x) = 1(-3((1(3sin(1\u03c0(1x^2 + 2x + 2) - 3) + 1) - 2)/(-3(3sin(1\u03c0(1x^2 + 2x + 2) - 3) + 1) - 1))^2 - 3((1(3sin(1\u03c0(1x^2 + 2x + 2) - 3) + 1) - 2)/(-3(3sin(1\u03c0(1x^2 + 2x + 2) - 3) + 1) - 1)) + 1) + 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": "62.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2|(-3e^(2(-3(-1(-1|(1|x - 2| + 3) - 1| + 1)^2 - 2(-1|(1|x - 2| + 3) - 1| + 1) + 1) - 1))) - 2| - 2, g(x) = 1(5((3(3(-2|x - 3| + 2)^2 + 4(-2|x - 3| + 2) - 4) + 2)/(2(3(-2|x - 3| + 2)^2 + 4(-2|x - 3| + 2) - 4) - 1)) + 5) + 1, x = 1.0, 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": "21.8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1|((-3(-3|(-3(-1((-3x - 3)/(-1x + 2))^2 - 2((-3x - 3)/(-1x + 2)) - 1)^2 + 3(-1((-3x - 3)/(-1x + 2))^2 - 2((-3x - 3)/(-1x + 2)) - 1) - 4) + 2| + 1) + 3)/(-1(-3|(-3(-1((-3x - 3)/(-1x + 2))^2 - 2((-3x - 3)/(-1x + 2)) - 1)^2 + 3(-1((-3x - 3)/(-1x + 2))^2 - 2((-3x - 3)/(-1x + 2)) - 1) - 4) + 2| + 1) - 2)) + 2| + 2 and g(x) = 1(-3sin(2\u03c0(-4(-3|(1|x - 3|) + 3| - 1) - 1) + 3) - 1)^2 + 3(-3sin(2\u03c0(-4(-3|(1|x - 3|) + 3| - 1) - 1) + 3) - 1) - 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": "0.7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2|(1|(2((3((3(-4x^2 - 5x - 3) + 3)/(-1(-4x^2 - 5x - 3) + 2)) + 3)/(3((3(-4x^2 - 5x - 3) + 3)/(-1(-4x^2 - 5x - 3) + 2)) - 2)) - 4) + 2| - 1) + 3| - 1 and g(x) = -3|(4(-3(-1(2x^2 - 1x + 2)^2 + 2(2x^2 - 1x + 2) + 5) - 4) + 2) + 1| + 3 from x = -0.7 to x = 1.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "294.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -5(-3cos(3\u03c0((2(-3((-1(-2x^2 + 2x - 4))/(-3(-2x^2 + 2x - 4) + 1))^2 + 2((-1(-2x^2 + 2x - 4))/(-3(-2x^2 + 2x - 4) + 1)) - 3) - 2)/(-1(-3((-1(-2x^2 + 2x - 4))/(-3(-2x^2 + 2x - 4) + 1))^2 + 2((-1(-2x^2 + 2x - 4))/(-3(-2x^2 + 2x - 4) + 1)) - 3) + 2)) + 3)) and g(x) = 2((-3(-4((1(-5x + 5) - 1)/(2(-5x + 5) - 1)) - 3) - 1)/(-2(-4((1(-5x + 5) - 1)/(2(-5x + 5) - 1)) - 3) - 1))^2 + 1((-3(-4((1(-5x + 5) - 1)/(2(-5x + 5) - 1)) - 3) - 1)/(-2(-4((1(-5x + 5) - 1)/(2(-5x + 5) - 1)) - 3) - 1)) + 3 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1|(3sin(1\u03c0(-5(1|((2((-2x - 2)/(-3x - 2)) + 3)/(-1((-2x - 2)/(-3x - 2)) + 3)) + 3| + 2) - 1) - 3) - 3) + 3| - 1 and g(x) = (-3((1(3|(-3|(-2|x - 1|) + 2| - 1) + 2| + 3) + 3)/(2(3|(-3|(-2|x - 1|) + 2| - 1) + 2| + 3) + 2)) + 1)/(1((1(3|(-3|(-2|x - 1|) + 2| - 1) + 2| + 3) + 3)/(2(3|(-3|(-2|x - 1|) + 2| - 1) + 2| + 3) + 2)) - 2) between the vertical lines x = -3 and x = 3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19.8", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -4((-3(-4((2((2((1x - 1)/(1x + 1)) - 3)/(2((1x - 1)/(1x + 1)) - 3)) - 2)/(-3((2((1x - 1)/(1x + 1)) - 3)/(2((1x - 1)/(1x + 1)) - 3)) - 2)) - 5) + 1)/(-1(-4((2((2((1x - 1)/(1x + 1)) - 3)/(2((1x - 1)/(1x + 1)) - 3)) - 2)/(-3((2((1x - 1)/(1x + 1)) - 3)/(2((1x - 1)/(1x + 1)) - 3)) - 2)) - 5) - 2)) + 3, g(x) = (-1(-2(-2(-1(-3cos(1\u03c0x + 2) + 3) + 2) - 3)^2 + 5) + 2)/(1(-2(-2(-1(-3cos(1\u03c0x + 2) + 3) + 2) - 3)^2 + 5)), x = -4.2, 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": "19.9", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1(-2|(1sin(3\u03c0(-1|((-3(2|x - 3| - 3) - 1)/(-2(2|x - 3| - 3) - 1)) - 3| + 3) + 3) + 1) + 3| + 2)^2 - 3(-2|(1sin(3\u03c0(-1|((-3(2|x - 3| - 3) - 1)/(-2(2|x - 3| - 3) - 1)) - 3| + 3) + 3) + 1) + 3| + 2) - 2 and g(x) = -1((-2(5((-1(-5x + 2) - 2)/(3(-5x + 2) + 2))^2 + 1((-1(-5x + 2) - 2)/(3(-5x + 2) + 2)) + 1) - 1)/(-1(5((-1(-5x + 2) - 2)/(3(-5x + 2) + 2))^2 + 1((-1(-5x + 2) - 2)/(3(-5x + 2) + 2)) + 1) + 2)) - 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": "1.7", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -4(-3(2(-1((-2(1x + 3) - 1)/(-1(1x + 3) - 3))^2 + 4((-2(1x + 3) - 1)/(-1(1x + 3) - 3)) + 5) + 3)^2 + 1(2(-1((-2(1x + 3) - 1)/(-1(1x + 3) - 3))^2 + 4((-2(1x + 3) - 1)/(-1(1x + 3) - 3)) + 5) + 3) + 1) - 3, g(x) = -1((-3(-5(2(2|x|)^2 - 5(2|x|) + 3) + 1) + 3)/(-2(-5(2(2|x|)^2 - 5(2|x|) + 3) + 1) + 1)) - 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": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1|((-3(-3|((-2(1(4x + 2) + 1))/(2(1(4x + 2) + 1) - 1)) + 1|) + 1)/(-2(-3|((-2(1(4x + 2) + 1))/(2(1(4x + 2) + 1) - 1)) + 1|) + 1)) + 3| + 2 and g(x) = 3((-1((3(-3(2x^2 - 1x - 5)^2 + 3) + 3)/(1(-3(2x^2 - 1x - 5)^2 + 3) - 2)) + 2)/(1((3(-3(2x^2 - 1x - 5)^2 + 3) + 3)/(1(-3(2x^2 - 1x - 5)^2 + 3) - 2)))) - 4 between the vertical lines x = -1.6 and x = -1.1. 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) = -3sin(2\u03c0(1(2|((-3(-5(5x + 5)^2 + 3(5x + 5) + 2))/(3(-5(5x + 5)^2 + 3(5x + 5) + 2))) + 2|)^2 + 3(2|((-3(-5(5x + 5)^2 + 3(5x + 5) + 2))/(3(-5(5x + 5)^2 + 3(5x + 5) + 2))) + 2|) - 3) - 3) + 1, g(x) = (3(3(-5(-2(-5x - 2)^2 - 4(-5x - 2) + 4)^2 - 2(-2(-5x - 2)^2 - 4(-5x - 2) + 4) + 1)^2 + 4(-5(-2(-5x - 2)^2 - 4(-5x - 2) + 4)^2 - 2(-2(-5x - 2)^2 - 4(-5x - 2) + 4) + 1) - 5) - 3)/(3(3(-5(-2(-5x - 2)^2 - 4(-5x - 2) + 4)^2 - 2(-2(-5x - 2)^2 - 4(-5x - 2) + 4) + 1)^2 + 4(-5(-2(-5x - 2)^2 - 4(-5x - 2) + 4)^2 - 2(-2(-5x - 2)^2 - 4(-5x - 2) + 4) + 1) - 5) + 2), 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": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2|(-1(-4((2(-2sin(2\u03c0((-1x - 1)/(1x + 2)) - 2) + 1) + 2)/(-3(-2sin(2\u03c0((-1x - 1)/(1x + 2)) - 2) + 1) + 2)) - 4) + 3)| + 2, g(x) = 4(-3|((2((-2(1x + 5) + 1)/(-1(1x + 5) - 1)) + 1)/(1((-2(1x + 5) + 1)/(-1(1x + 5) - 1)) - 3)) + 1|) + 2, 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": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-3(-3|(2(2(2sin(1\u03c0(-4x) - 3) - 2) + 5) - 4)| + 3) - 1)/(-1(-3|(2(2(2sin(1\u03c0(-4x) - 3) - 2) + 5) - 4)| + 3) + 2), g(x) = (-2(-2|((3(2(4x + 1) - 5))/(2(2(4x + 1) - 5) - 3)) + 2|) + 2)/(-2(-2|((3(2(4x + 1) - 5))/(2(2(4x + 1) - 5) - 3)) + 2|) + 3), x = -0.2, 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": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1|((-3((2(2|(2|(3|x + 3| - 1) - 3| + 1) - 3| + 2) + 3)/(-3(2|(2|(3|x + 3| - 1) - 3| + 1) - 3| + 2) + 4)) + 1)/(1((2(2|(2|(3|x + 3| - 1) - 3| + 1) - 3| + 2) + 3)/(-3(2|(2|(3|x + 3| - 1) - 3| + 1) - 3| + 2) + 4)) + 3))| and g(x) = 4(1|(-3|((-1(-3x - 5) + 3)/(2(-3x - 5) - 1)) + 2| + 3) + 1| - 1)^2 + 1(1|(-3|((-1(-3x - 5) + 3)/(2(-3x - 5) - 1)) + 2| + 3) + 1| - 1) - 5 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": "2.8", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1sin(3\u03c0((2(-1(-3|(3(4x^2 - 5) - 2) - 2| - 1) - 5) + 3)/(3(-1(-3|(3(4x^2 - 5) - 2) - 2| - 1) - 5) + 3)) + 2) - 3, g(x) = -3cos(3\u03c0(3|(1|(-2(-3|x - 1| - 3)^2 - 2(-3|x - 1| - 3)) + 1| + 3) - 2|)) - 1, 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": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 3((2(2(1(1((-3x + 2)/(-1x))^2 + 5((-3x + 2)/(-1x)) + 2) - 1)^2 - 3(1(1((-3x + 2)/(-1x))^2 + 5((-3x + 2)/(-1x)) + 2) - 1) - 3) + 3)/(1(2(1(1((-3x + 2)/(-1x))^2 + 5((-3x + 2)/(-1x)) + 2) - 1)^2 - 3(1(1((-3x + 2)/(-1x))^2 + 5((-3x + 2)/(-1x)) + 2) - 1) - 3) + 3)) - 4 and g(x) = 3(-1((-3((2(1sin(2\u03c0x - 2) + 1) + 1)/(-1(1sin(2\u03c0x - 2) + 1) + 3)) - 2)/(-1((2(1sin(2\u03c0x - 2) + 1) + 1)/(-1(1sin(2\u03c0x - 2) + 1) + 3)))) + 4) + 3 between the vertical lines x = 3.3 and x = 3.8. 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(3sin(1\u03c0(-3|(-3(2|(4x + 1)| + 1)^2 + 2(2|(4x + 1)| + 1) - 1) - 2| + 2))) - 3)/(3(3sin(1\u03c0(-3|(-3(2|(4x + 1)| + 1)^2 + 2(2|(4x + 1)| + 1) - 1) - 2| + 2))) - 2) and g(x) = -1((2(5((1(-4x^2 - 3) - 1)/(-1(-4x^2 - 3))) + 3) + 3)/(-3(5((1(-4x^2 - 3) - 1)/(-1(-4x^2 - 3))) + 3) + 2))^2 + 1((2(5((1(-4x^2 - 3) - 1)/(-1(-4x^2 - 3))) + 3) + 3)/(-3(5((1(-4x^2 - 3) - 1)/(-1(-4x^2 - 3))) + 3) + 2)) - 4 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -4((-1((3((-1(-1|(-2|x + 2| + 1) - 2| - 2))/(-2(-1|(-2|x + 2| + 1) - 2| - 2))) - 2)/(2((-1(-1|(-2|x + 2| + 1) - 2| - 2))/(-2(-1|(-2|x + 2| + 1) - 2| - 2))))) - 2)/(-2((3((-1(-1|(-2|x + 2| + 1) - 2| - 2))/(-2(-1|(-2|x + 2| + 1) - 2| - 2))) - 2)/(2((-1(-1|(-2|x + 2| + 1) - 2| - 2))/(-2(-1|(-2|x + 2| + 1) - 2| - 2))))) + 3)) + 3 and g(x) = -2(1sin(3\u03c0((-1(1(-3x - 5)^2 - 1(-3x - 5) + 4) + 2)/(-1(1(-3x - 5)^2 - 1(-3x - 5) + 4))) - 2) - 1)^2 - 1(1sin(3\u03c0((-1(1(-3x - 5)^2 - 1(-3x - 5) + 4) + 2)/(-1(1(-3x - 5)^2 - 1(-3x - 5) + 4))) - 2) - 1) + 5 from x = -2.1 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) = -1((3((1(-3e^(-2((1(1x - 2) + 2)/(-2(1x - 2) - 3))) + 3) - 3)/(1(-3e^(-2((1(1x - 2) + 2)/(-2(1x - 2) - 3))) + 3))))/(-3((1(-3e^(-2((1(1x - 2) + 2)/(-2(1x - 2) - 3))) + 3) - 3)/(1(-3e^(-2((1(1x - 2) + 2)/(-2(1x - 2) - 3))) + 3))) - 2)) - 1, g(x) = 1(-3sin(3\u03c0((-1(-1|(1x + 5) - 3| + 2) + 3)/(-3(-1|(1x + 5) - 3| + 2) - 3)) + 2) + 2)^2 - 5(-3sin(3\u03c0((-1(-1|(1x + 5) - 3| + 2) + 3)/(-3(-1|(1x + 5) - 3| + 2) - 3)) + 2) + 2) - 5, x = -3.7, 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": "25.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1(1((2((-3(-1(3x^2 - 5x - 1)^2 + 2(3x^2 - 5x - 1) - 2) - 1)/(2(-1(3x^2 - 5x - 1)^2 + 2(3x^2 - 5x - 1) - 2) + 1)) - 1)/(-2((-3(-1(3x^2 - 5x - 1)^2 + 2(3x^2 - 5x - 1) - 2) - 1)/(2(-1(3x^2 - 5x - 1)^2 + 2(3x^2 - 5x - 1) - 2) + 1)) - 2)) + 3) + 2 and g(x) = 3|((-2(2|(-1|(2x + 1) - 3| + 1) + 3|) + 1)/(-3(2|(-1|(2x + 1) - 3| + 1) + 3|))) + 2| from x = -1.0 to x = -0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 3(3sin(3\u03c0(2|(2(-3((-2x + 1)/(2x - 3)) - 2)^2 - 4(-3((-2x + 1)/(2x - 3)) - 2) - 5) + 2| + 2)) - 2) + 1 and g(x) = 1|(-2|((1(-1|(-1x + 5) - 1| - 1) - 1)/(1(-1|(-1x + 5) - 1| - 1) + 2)) + 2| - 1) - 2| - 2 between the vertical lines x = 4.0 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": "Determine the area of the region enclosed by the graphs of f(x) = -2|(-1|((-2(1(2(-3x + 3) - 5) - 3))/(-3(1(2(-3x + 3) - 5) - 3) - 3)) - 2| - 2) - 2| - 3 and g(x) = -1((-1(3(-4(4x - 3)^2 + 5) - 2) + 2)/(-3(3(-4(4x - 3)^2 + 5) - 2) - 2)) - 1 between the vertical lines x = 0.5 and x = 1.0. Round 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) = -3(3|(-2|((1(3((2x + 2)/(1x))) - 3)/(1(3((2x + 2)/(1x))) + 3)) + 2| + 2) + 1| + 2) + 1 and g(x) = -2|(-1|(2(-3((1x)/(2x - 1))^2 - 5((1x)/(2x - 1))) + 5) - 2|) - 1| + 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": "-10.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3sin(2\u03c0(-1|(4(-2(-1(2|x - 2| - 3)^2 + 3(2|x - 2| - 3) - 1) + 5) - 5) - 3| + 2) + 2) - 2, g(x) = -2|(-3|((-1((3((-2x - 3)/(-2x + 3)) + 1)/(-2((-2x - 3)/(-2x + 3)) + 3)) - 3)/(-2((3((-2x - 3)/(-2x + 3)) + 1)/(-2((-2x - 3)/(-2x + 3)) + 3)))) + 1| + 1) - 2| + 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-2((-3((-3(-2cos(2\u03c0(-4((-2x + 1)/(-2x - 3))^2 - 3((-2x + 1)/(-2x - 3)) - 4) + 1) + 2) + 3)/(-2(-2cos(2\u03c0(-4((-2x + 1)/(-2x - 3))^2 - 3((-2x + 1)/(-2x - 3)) - 4) + 1) + 2) + 3)) - 2)/(2((-3(-2cos(2\u03c0(-4((-2x + 1)/(-2x - 3))^2 - 3((-2x + 1)/(-2x - 3)) - 4) + 1) + 2) + 3)/(-2(-2cos(2\u03c0(-4((-2x + 1)/(-2x - 3))^2 - 3((-2x + 1)/(-2x - 3)) - 4) + 1) + 2) + 3)) - 1)) + 2)/(-2((-3((-3(-2cos(2\u03c0(-4((-2x + 1)/(-2x - 3))^2 - 3((-2x + 1)/(-2x - 3)) - 4) + 1) + 2) + 3)/(-2(-2cos(2\u03c0(-4((-2x + 1)/(-2x - 3))^2 - 3((-2x + 1)/(-2x - 3)) - 4) + 1) + 2) + 3)) - 2)/(2((-3(-2cos(2\u03c0(-4((-2x + 1)/(-2x - 3))^2 - 3((-2x + 1)/(-2x - 3)) - 4) + 1) + 2) + 3)/(-2(-2cos(2\u03c0(-4((-2x + 1)/(-2x - 3))^2 - 3((-2x + 1)/(-2x - 3)) - 4) + 1) + 2) + 3)) - 1)) - 1) and g(x) = -3((3(-1e^(1(-3((2x - 1)/(-2x - 1)) + 4)) - 2) - 2)/(-1(-1e^(1(-3((2x - 1)/(-2x - 1)) + 4)) - 2) - 2))^2 - 1((3(-1e^(1(-3((2x - 1)/(-2x - 1)) + 4)) - 2) - 2)/(-1(-1e^(1(-3((2x - 1)/(-2x - 1)) + 4)) - 2) - 2)) - 1 from x = 3.7 to x = 5.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 4(1(1|(1|(1cos(1\u03c0(5x - 5) - 2) + 1) - 1| - 3) - 1| + 2)^2 - 5(1|(1|(1cos(1\u03c0(5x - 5) - 2) + 1) - 1| - 3) - 1| + 2)) - 2 and g(x) = 2|(-2e^(1((1(5(2|x - 1| + 3)^2 + 1(2|x - 1| + 3) + 3) + 3)/(-2(5(2|x - 1| + 3)^2 + 1(2|x - 1| + 3) + 3) + 3))) - 1) - 3| - 2 from x = -2.7 to 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) = -2(5(-3((1(3cos(2\u03c0(-4x - 3) + 3) + 3) + 3)/(3(3cos(2\u03c0(-4x - 3) + 3) + 3) - 2))^2 + 1)^2 - 3) + 2 and g(x) = 1cos(1\u03c0(1|((2(-1((2x + 3)/(-2x + 3))^2 - 1))/(-1(-1((2x + 3)/(-2x + 3))^2 - 1) + 3)) - 1| - 1) + 3) - 2 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": "0.9", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-2(3cos(3\u03c0(5(-4(4(-1x^2 + 4x - 5) + 1) + 2)^2 - 2(-4(4(-1x^2 + 4x - 5) + 1) + 2) + 4) + 1) + 3) - 1)/(3(3cos(3\u03c0(5(-4(4(-1x^2 + 4x - 5) + 1) + 2)^2 - 2(-4(4(-1x^2 + 4x - 5) + 1) + 2) + 4) + 1) + 3)), g(x) = (1((-1(3|(5(3x - 1)^2 - 1(3x - 1) - 1) - 1| - 2) - 1)/(2(3|(5(3x - 1)^2 - 1(3x - 1) - 1) - 1| - 2) + 1)) - 1)/(2((-1(3|(5(3x - 1)^2 - 1(3x - 1) - 1) - 1| - 2) - 1)/(2(3|(5(3x - 1)^2 - 1(3x - 1) - 1) - 1| - 2) + 1))), 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": "1.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2|((2(2(1((1(-2x - 1) - 1)/(-2(-2x - 1) - 1))) - 1) + 3)/(-2(2(1((1(-2x - 1) - 1)/(-2(-2x - 1) - 1))) - 1) + 3))| - 1 and g(x) = (2(2cos(2\u03c0(-1|(-1|(-2|x - 2| + 2) + 1| + 3) + 3| - 1) + 1) + 1) - 2)/(3(2cos(2\u03c0(-1|(-1|(-2|x - 2| + 2) + 1| + 3) + 3| - 1) + 1) + 1) - 2) from x = 3.2 to x = 3.4. 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) = -1|((-3(4((2(2(2x + 4)^2 - 5(2x + 4) + 5) - 2)/(-1(2(2x + 4)^2 - 5(2x + 4) + 5) + 2))^2 + 1((2(2(2x + 4)^2 - 5(2x + 4) + 5) - 2)/(-1(2(2x + 4)^2 - 5(2x + 4) + 5) + 2)) - 5) - 3)/(2(4((2(2(2x + 4)^2 - 5(2x + 4) + 5) - 2)/(-1(2(2x + 4)^2 - 5(2x + 4) + 5) + 2))^2 + 1((2(2(2x + 4)^2 - 5(2x + 4) + 5) - 2)/(-1(2(2x + 4)^2 - 5(2x + 4) + 5) + 2)) - 5) - 1)) - 1| - 1 and g(x) = -3|(-2(1|(1(-4x)^2 - 3(-4x) - 3) + 1| + 1) + 3)| - 2 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-1(3((-3((1(5(-1x^2 + 4x)^2 - 4(-1x^2 + 4x) - 4) - 3)/(1(5(-1x^2 + 4x)^2 - 4(-1x^2 + 4x) - 4) + 3)) + 1)/(-2((1(5(-1x^2 + 4x)^2 - 4(-1x^2 + 4x) - 4) - 3)/(1(5(-1x^2 + 4x)^2 - 4(-1x^2 + 4x) - 4) + 3)) + 3))^2 - 4((-3((1(5(-1x^2 + 4x)^2 - 4(-1x^2 + 4x) - 4) - 3)/(1(5(-1x^2 + 4x)^2 - 4(-1x^2 + 4x) - 4) + 3)) + 1)/(-2((1(5(-1x^2 + 4x)^2 - 4(-1x^2 + 4x) - 4) - 3)/(1(5(-1x^2 + 4x)^2 - 4(-1x^2 + 4x) - 4) + 3)) + 3)) + 4) + 3)/(-3(3((-3((1(5(-1x^2 + 4x)^2 - 4(-1x^2 + 4x) - 4) - 3)/(1(5(-1x^2 + 4x)^2 - 4(-1x^2 + 4x) - 4) + 3)) + 1)/(-2((1(5(-1x^2 + 4x)^2 - 4(-1x^2 + 4x) - 4) - 3)/(1(5(-1x^2 + 4x)^2 - 4(-1x^2 + 4x) - 4) + 3)) + 3))^2 - 4((-3((1(5(-1x^2 + 4x)^2 - 4(-1x^2 + 4x) - 4) - 3)/(1(5(-1x^2 + 4x)^2 - 4(-1x^2 + 4x) - 4) + 3)) + 1)/(-2((1(5(-1x^2 + 4x)^2 - 4(-1x^2 + 4x) - 4) - 3)/(1(5(-1x^2 + 4x)^2 - 4(-1x^2 + 4x) - 4) + 3)) + 3)) + 4) + 4) and g(x) = 4(1(2((-2(2|x + 1| - 3) + 2)/(1(2|x + 1| - 3))) + 3)^2 - 5(2((-2(2|x + 1| - 3) + 2)/(1(2|x + 1| - 3))) + 3) + 1) - 1 between the vertical lines x = -4.3 and x = -2.8. Round 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) = -2|((-3((-3(-1e^(-2((1((-3x)/(-2x - 1)) + 3)/(-1((-3x)/(-2x - 1)) + 2))) + 3) - 1)/(-3(-1e^(-2((1((-3x)/(-2x - 1)) + 3)/(-1((-3x)/(-2x - 1)) + 2))) + 3))) + 2)/(3((-3(-1e^(-2((1((-3x)/(-2x - 1)) + 3)/(-1((-3x)/(-2x - 1)) + 2))) + 3) - 1)/(-3(-1e^(-2((1((-3x)/(-2x - 1)) + 3)/(-1((-3x)/(-2x - 1)) + 2))) + 3))) - 2)) - 1| and g(x) = 3sin(3\u03c0(-3(3((-3(-4x + 1) - 3)/(2(-4x + 1))) + 2) + 4) - 3) - 1 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": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3(-3(-2|(1(3(2x^2 - 4x - 4)^2 - 1(2x^2 - 4x - 4) - 3) + 2) - 3| + 1) + 1) - 2, g(x) = 3(1e^(-1(1|(1|((1x + 1)/(3x - 2)) - 3| + 1) + 3| + 3)) + 2) - 3, 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": "2.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -5((-1(2|(-5(3e^(-1(1|x - 1|)) - 1)^2 + 1(3e^(-1(1|x - 1|)) - 1) - 1)|) - 2)/(2(2|(-5(3e^(-1(1|x - 1|)) - 1)^2 + 1(3e^(-1(1|x - 1|)) - 1) - 1)|) - 1)) - 4 and g(x) = 1(-1|(-3(-3(-5x + 1)^2 - 3(-5x + 1) + 2) - 2) - 2|)^2 + 4(-1|(-3(-3(-5x + 1)^2 - 3(-5x + 1) + 2) - 2) - 2|) - 2 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": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -3(-2((2(-3|((-3((2x + 3)/(-1x + 2)) + 3)/(-3((2x + 3)/(-1x + 2)) + 1)) - 1|) - 2)/(2(-3|((-3((2x + 3)/(-1x + 2)) + 3)/(-3((2x + 3)/(-1x + 2)) + 1)) - 1|) - 1)) + 4)^2 - 3(-2((2(-3|((-3((2x + 3)/(-1x + 2)) + 3)/(-3((2x + 3)/(-1x + 2)) + 1)) - 1|) - 2)/(2(-3|((-3((2x + 3)/(-1x + 2)) + 3)/(-3((2x + 3)/(-1x + 2)) + 1)) - 1|) - 1)) + 4) - 5, g(x) = -3|((-2((-2((2(2|x - 3|) - 2)/(3(2|x - 3|) - 1)) - 3)/(-1((2(2|x - 3|) - 2)/(3(2|x - 3|) - 1)) - 1)) + 2)/(1((-2((2(2|x - 3|) - 2)/(3(2|x - 3|) - 1)) - 3)/(-1((2(2|x - 3|) - 2)/(3(2|x - 3|) - 1)) - 1)))) + 2| - 1, x = 2.8, 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": "2.8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-3(-3cos(2\u03c0((-2((-3(4(3x^2 - 1x - 5)^2 - 5(3x^2 - 1x - 5) + 3) + 2)/(-1(4(3x^2 - 1x - 5)^2 - 5(3x^2 - 1x - 5) + 3) - 3)) - 3)/(1((-3(4(3x^2 - 1x - 5)^2 - 5(3x^2 - 1x - 5) + 3) + 2)/(-1(4(3x^2 - 1x - 5)^2 - 5(3x^2 - 1x - 5) + 3) - 3)) - 3))) - 1) + 3)/(1(-3cos(2\u03c0((-2((-3(4(3x^2 - 1x - 5)^2 - 5(3x^2 - 1x - 5) + 3) + 2)/(-1(4(3x^2 - 1x - 5)^2 - 5(3x^2 - 1x - 5) + 3) - 3)) - 3)/(1((-3(4(3x^2 - 1x - 5)^2 - 5(3x^2 - 1x - 5) + 3) + 2)/(-1(4(3x^2 - 1x - 5)^2 - 5(3x^2 - 1x - 5) + 3) - 3)) - 3))) - 1) + 1) and g(x) = -3(-2|(4(-4((-2x + 1)/(-2x - 1))^2 + 5((-2x + 1)/(-2x - 1)) - 3)^2 + 4)| + 2) + 3 from x = 1.0 to x = 1.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "50.8", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (2(-2(-4(-3(-4(5x^2 - 5x - 2) + 2)^2 - 2(-4(5x^2 - 5x - 2) + 2))^2 - 2(-3(-4(5x^2 - 5x - 2) + 2)^2 - 2(-4(5x^2 - 5x - 2) + 2)) + 2) + 4) + 1)/(-3(-2(-4(-3(-4(5x^2 - 5x - 2) + 2)^2 - 2(-4(5x^2 - 5x - 2) + 2))^2 - 2(-3(-4(5x^2 - 5x - 2) + 2)^2 - 2(-4(5x^2 - 5x - 2) + 2)) + 2) + 4) - 3) and g(x) = -3(1(-2(-2|(-2x^2 + 5x)| + 3))^2 - 5(-2(-2|(-2x^2 + 5x)| + 3)) - 3)^2 + 4(1(-2(-2|(-2x^2 + 5x)| + 3))^2 - 5(-2(-2|(-2x^2 + 5x)| + 3)) - 3) - 2 between the vertical lines x = 2.7 and x = 3.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40.7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-1((2(1(-2|(5(1x - 3))|)^2 + 2(-2|(5(1x - 3))|) + 2))/(-1(1(-2|(5(1x - 3))|)^2 + 2(-2|(5(1x - 3))|) + 2) - 1)) + 2)/(-1((2(1(-2|(5(1x - 3))|)^2 + 2(-2|(5(1x - 3))|) + 2))/(-1(1(-2|(5(1x - 3))|)^2 + 2(-2|(5(1x - 3))|) + 2) - 1)) + 2) and g(x) = (-2((2(1(1sin(2\u03c0((3x + 2)/(2x + 3))) + 1)) - 1)/(-2(1(1sin(2\u03c0((3x + 2)/(2x + 3))) + 1)))))/(-3((2(1(1sin(2\u03c0((3x + 2)/(2x + 3))) + 1)) - 1)/(-2(1(1sin(2\u03c0((3x + 2)/(2x + 3))) + 1)))) + 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2cos(3\u03c0(-5(4(1((-3(2|x + 2| + 3) + 1)/(2(2|x + 2| + 3) + 3)) + 4)^2 - 3(1((-3(2|x + 2| + 3) + 1)/(2(2|x + 2| + 3) + 3)) + 4) + 2) + 2) - 1) - 1 and g(x) = 3cos(2\u03c0(-4(2|(-4(2|x| - 2)^2 + 5(2|x| - 2) - 2) + 1| - 1)^2 + 4) - 3) + 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": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2(-4(-3(3(1cos(2\u03c0((3x + 3)/(-2x)) - 3) - 1)^2 - 4(1cos(2\u03c0((3x + 3)/(-2x)) - 3) - 1) + 1)^2 + 4(3(1cos(2\u03c0((3x + 3)/(-2x)) - 3) - 1)^2 - 4(1cos(2\u03c0((3x + 3)/(-2x)) - 3) - 1) + 1)) + 3) + 2, g(x) = 4(-5(-2|(-5(-1x^2 - 3x) + 2) + 2| + 2)^2) + 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": "313.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2|(-1|(3((2((1((3x + 3)/(2x - 1)) + 1)/(-3((3x + 3)/(2x - 1)) - 1)) - 3)/(2((1((3x + 3)/(2x - 1)) + 1)/(-3((3x + 3)/(2x - 1)) - 1)) - 1)) + 3) + 2| + 3) - 2| + 3 and g(x) = 3(2(-1cos(2\u03c0(1((-3x - 3)/(2x + 2)) - 4) + 3) - 2)^2 + 5(-1cos(2\u03c0(1((-3x - 3)/(2x + 2)) - 4) + 3) - 2) + 1) - 3 from x = -0.6 to x = -0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "46.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2cos(2\u03c0(-2|(-1(-1(-4(3x^2 - 3x - 2)^2) + 1) + 2) - 1|) + 2) - 2, g(x) = -3|((3(1sin(1\u03c0(-5(-2x - 2)^2 + 5(-2x - 2) + 5) - 3) + 2) + 2)/(-2(1sin(1\u03c0(-5(-2x - 2)^2 + 5(-2x - 2) + 5) - 3) + 2))) + 3| - 2, 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": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -3(2|((-1(-2(2|(1|x| + 1) - 3|) + 4) + 2)/(-2(-2(2|(1|x| + 1) - 3|) + 4) - 2)) - 2|) - 2, g(x) = -3e^(-2(3|(1|(1|((2x - 1)/(-2x + 3)) - 3| - 2) - 2| - 3) + 2| - 3)) - 1, x = -3.4, 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": "103.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 3|(-2|(5((-2((-1(2|x + 2| - 3) + 3)/(-2(2|x + 2| - 3) - 1)) - 2)/(-1((-1(2|x + 2| - 3) + 3)/(-2(2|x + 2| - 3) - 1)) + 3))^2 + 4((-2((-1(2|x + 2| - 3) + 3)/(-2(2|x + 2| - 3) - 1)) - 2)/(-1((-1(2|x + 2| - 3) + 3)/(-2(2|x + 2| - 3) - 1)) + 3)) + 2) - 2|) - 2| - 3 and g(x) = 1(3(3(2sin(2\u03c0(2|x + 1| + 3) - 3) + 2)^2 + 5) - 4) + 2 from x = -3.6 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((-3(-2((-1((2(-2|x - 3| - 1) + 1)/(1(-2|x - 3| - 1) + 3)) + 1)/(1((2(-2|x - 3| - 1) + 1)/(1(-2|x - 3| - 1) + 3)))) - 1))/(2(-2((-1((2(-2|x - 3| - 1) + 1)/(1(-2|x - 3| - 1) + 3)) + 1)/(1((2(-2|x - 3| - 1) + 1)/(1(-2|x - 3| - 1) + 3)))) - 1))) - 3)/(2((-3(-2((-1((2(-2|x - 3| - 1) + 1)/(1(-2|x - 3| - 1) + 3)) + 1)/(1((2(-2|x - 3| - 1) + 1)/(1(-2|x - 3| - 1) + 3)))) - 1))/(2(-2((-1((2(-2|x - 3| - 1) + 1)/(1(-2|x - 3| - 1) + 3)) + 1)/(1((2(-2|x - 3| - 1) + 1)/(1(-2|x - 3| - 1) + 3)))) - 1)))), g(x) = 2|((-1(-4((-3((-1x + 3)/(3x - 2)) + 3)/(-3((-1x + 3)/(3x - 2)) - 1))^2 + 3((-3((-1x + 3)/(3x - 2)) + 3)/(-3((-1x + 3)/(3x - 2)) - 1)) + 3) - 2)/(3(-4((-3((-1x + 3)/(3x - 2)) + 3)/(-3((-1x + 3)/(3x - 2)) - 1))^2 + 3((-3((-1x + 3)/(3x - 2)) + 3)/(-3((-1x + 3)/(3x - 2)) - 1)) + 3) - 2)) - 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": "2.9", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1((1(2|(2|(1|((1x)/(-3x + 2)) + 2| + 2) + 3|) - 3| - 3) - 1)/(-2(2|(2|(1|((1x)/(-3x + 2)) + 2| + 2) + 3|) - 3| - 3)))^2 + 2((1(2|(2|(1|((1x)/(-3x + 2)) + 2| + 2) + 3|) - 3| - 3) - 1)/(-2(2|(2|(1|((1x)/(-3x + 2)) + 2| + 2) + 3|) - 3| - 3))) + 1, g(x) = -5(3(1cos(3\u03c0((-2(-1|x + 1|) - 2)/(-2(-1|x + 1|) + 3)) + 1) + 1) - 2) + 1, x = -1.4, 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": "2.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 4((3(-2((-2((-2(-1x - 1))/(2(-1x - 1) + 1)))/(-1((-2(-1x - 1))/(2(-1x - 1) + 1)) - 1)) + 4) - 2)/(-1(-2((-2((-2(-1x - 1))/(2(-1x - 1) + 1)))/(-1((-2(-1x - 1))/(2(-1x - 1) + 1)) - 1)) + 4) - 2)), g(x) = -3|((2(-3|(1(-5x^2 - 3x + 3) + 2) - 3| + 3) + 2)/(-2(-3|(1(-5x^2 - 3x + 3) + 2) - 3| + 3) - 3))| - 2, x = -1.2, and x = -1.0999999999999999. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.5", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-1(-3(4((-2((-2(5x^2 - 2))/(-2(5x^2 - 2) + 3)) - 3)/(-3((-2(5x^2 - 2))/(-2(5x^2 - 2) + 3)) - 3)) - 4) - 4) - 2)/(2(-3(4((-2((-2(5x^2 - 2))/(-2(5x^2 - 2) + 3)) - 3)/(-3((-2(5x^2 - 2))/(-2(5x^2 - 2) + 3)) - 3)) - 4) - 4) - 3), g(x) = -2|(-1|(1|((-2(2|x|) + 2)/(2(2|x|) + 2)) - 2| + 1) - 2| - 2) + 1| - 2, x = -0.8, 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": "9.4", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-1(-1|(-4(-1cos(2\u03c0(-1((-3x - 1)/(2x - 1))^2 + 1((-3x - 1)/(2x - 1)) - 3) + 3)) + 3) + 3|) + 2)/(-1(-1|(-4(-1cos(2\u03c0(-1((-3x - 1)/(2x - 1))^2 + 1((-3x - 1)/(2x - 1)) - 3) + 3)) + 3) + 3|)), g(x) = 1|(1(-3sin(1\u03c0(4(-3x^2 + 3x + 4)^2 - 4(-3x^2 + 3x + 4)) - 1) + 3)^2 - 4(-3sin(1\u03c0(4(-3x^2 + 3x + 4)^2 - 4(-3x^2 + 3x + 4)) - 1) + 3) - 3) + 2| + 1, 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": "Determine the area of the region enclosed by the graphs of f(x) = 3e^(-1((-1(5(1(3(-3x + 5) - 2) - 5) + 3) + 1)/(3(5(1(3(-3x + 5) - 2) - 5) + 3) + 2))) and g(x) = (2(-4((1(-2|(-2sin(3\u03c0x - 1) - 1)| + 1) - 1)/(-2(-2|(-2sin(3\u03c0x - 1) - 1)| + 1) + 1))^2 + 1((1(-2|(-2sin(3\u03c0x - 1) - 1)| + 1) - 1)/(-2(-2|(-2sin(3\u03c0x - 1) - 1)| + 1) + 1)) - 1) + 1)/(-2(-4((1(-2|(-2sin(3\u03c0x - 1) - 1)| + 1) - 1)/(-2(-2|(-2sin(3\u03c0x - 1) - 1)| + 1) + 1))^2 + 1((1(-2|(-2sin(3\u03c0x - 1) - 1)| + 1) - 1)/(-2(-2|(-2sin(3\u03c0x - 1) - 1)| + 1) + 1)) - 1) - 3) between the vertical lines x = 2.5 and x = 2.7. 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) = -3sin(1\u03c0(2|(-3|((2(-4((3x + 2)/(-1x + 2)) - 3) - 3)/(-2(-4((3x + 2)/(-1x + 2)) - 3) - 1)) - 1| - 2) - 3|) + 3) - 2 and g(x) = (1((-1(2sin(3\u03c0(-1((-2x + 2)/(3x - 2))^2 + 3((-2x + 2)/(3x - 2)) + 3) + 1) + 1))/(-2(2sin(3\u03c0(-1((-2x + 2)/(3x - 2))^2 + 3((-2x + 2)/(3x - 2)) + 3) + 1) + 1) + 3)) + 1)/(2((-1(2sin(3\u03c0(-1((-2x + 2)/(3x - 2))^2 + 3((-2x + 2)/(3x - 2)) + 3) + 1) + 1))/(-2(2sin(3\u03c0(-1((-2x + 2)/(3x - 2))^2 + 3((-2x + 2)/(3x - 2)) + 3) + 1) + 1) + 3)) + 1) from x = -1.4 to 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": "Find the area of the region bounded by the curves f(x) = -3|(3(-1|(-2((3((-1x + 1)/(-2x + 3)) + 3)/(3((-1x + 1)/(-2x + 3)) - 2)) + 1)| + 3) + 2) - 3| + 1, g(x) = -3(-2e^(-2(2|(5(3x^2 + 2x + 1) + 4) - 2| + 3)) + 1)^2 + 3(-2e^(-2(2|(5(3x^2 + 2x + 1) + 4) - 2| + 3)) + 1) - 2, x = 1.1, 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-2(3e^(2(4(-1|(1|(1x^2 + 4x + 4)| + 1) - 3| - 3) + 5)) - 2) - 3)/(-3(3e^(2(4(-1|(1|(1x^2 + 4x + 4)| + 1) - 3| - 3) + 5)) - 2) - 1) and g(x) = (-2(1|(-1(-3sin(2\u03c0(1|x - 1| + 2) + 2) + 2)^2 + 5(-3sin(2\u03c0(1|x - 1| + 2) + 2) + 2) - 3)|) + 1)/(-2(1|(-1(-3sin(2\u03c0(1|x - 1| + 2) + 2) + 2)^2 + 5(-3sin(2\u03c0(1|x - 1| + 2) + 2) + 2) - 3)|)) between the vertical lines x = -1.8 and x = -1.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (3(2cos(1\u03c0(2|(4((-2(-2x^2 - 2x) + 3)/(1(-2x^2 - 2x)))) + 3|) + 3) - 2) - 3)/(-3(2cos(1\u03c0(2|(4((-2(-2x^2 - 2x) + 3)/(1(-2x^2 - 2x)))) + 3|) + 3) - 2) - 3), g(x) = 1((-2((1(-2(1|x + 3| + 1) - 2) - 3)/(2(-2(1|x + 3| + 1) - 2) + 2)))/(-2((1(-2(1|x + 3| + 1) - 2) - 3)/(2(-2(1|x + 3| + 1) - 2) + 2)) - 2))^2 + 5((-2((1(-2(1|x + 3| + 1) - 2) - 3)/(2(-2(1|x + 3| + 1) - 2) + 2)))/(-2((1(-2(1|x + 3| + 1) - 2) - 3)/(2(-2(1|x + 3| + 1) - 2) + 2)) - 2)), 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": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-3((-3(3(3|(2(1x - 4) + 3)| + 3)^2 + 3(3|(2(1x - 4) + 3)| + 3) - 5) - 2)/(-2(3(3|(2(1x - 4) + 3)| + 3)^2 + 3(3|(2(1x - 4) + 3)| + 3) - 5) + 3)) + 3)/(-3((-3(3(3|(2(1x - 4) + 3)| + 3)^2 + 3(3|(2(1x - 4) + 3)| + 3) - 5) - 2)/(-2(3(3|(2(1x - 4) + 3)| + 3)^2 + 3(3|(2(1x - 4) + 3)| + 3) - 5) + 3)) + 1) and g(x) = 4(2cos(2\u03c0(1(-5(4x + 3) - 2)) + 2) - 1)^2 - 4(2cos(2\u03c0(1(-5(4x + 3) - 2)) + 2) - 1) + 1 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": "1.7", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 4((1(-3(-2((3(-4x - 3) + 3)/(3(-4x - 3) + 3)) - 1)^2 + 1(-2((3(-4x - 3) + 3)/(3(-4x - 3) + 3)) - 1) + 1) + 1)/(-3(-3(-2((3(-4x - 3) + 3)/(3(-4x - 3) + 3)) - 1)^2 + 1(-2((3(-4x - 3) + 3)/(3(-4x - 3) + 3)) - 1) + 1)))^2 - 5((1(-3(-2((3(-4x - 3) + 3)/(3(-4x - 3) + 3)) - 1)^2 + 1(-2((3(-4x - 3) + 3)/(3(-4x - 3) + 3)) - 1) + 1) + 1)/(-3(-3(-2((3(-4x - 3) + 3)/(3(-4x - 3) + 3)) - 1)^2 + 1(-2((3(-4x - 3) + 3)/(3(-4x - 3) + 3)) - 1) + 1))) + 3 and g(x) = -2(-2(-1(-3((2x - 3)/(2x)) - 2) + 3)^2 + 3(-1(-3((2x - 3)/(2x)) - 2) + 3) + 4) between the vertical lines x = 0.5 and x = 0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.4", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 5(-1((-2(1(-2(1e^(-1x) - 1) - 1) + 3) - 2)/(1(1(-2(1e^(-1x) - 1) - 1) + 3) + 3))^2 + 3((-2(1(-2(1e^(-1x) - 1) - 1) + 3) - 2)/(1(1(-2(1e^(-1x) - 1) - 1) + 3) + 3)) - 1)^2 - 5(-1((-2(1(-2(1e^(-1x) - 1) - 1) + 3) - 2)/(1(1(-2(1e^(-1x) - 1) - 1) + 3) + 3))^2 + 3((-2(1(-2(1e^(-1x) - 1) - 1) + 3) - 2)/(1(1(-2(1e^(-1x) - 1) - 1) + 3) + 3)) - 1) - 5, g(x) = 4(-3cos(1\u03c0(1(-4(1|x|)^2 - 5(1|x|) - 4)^2 + 3(-4(1|x|)^2 - 5(1|x|) - 4) - 2) + 2) - 2)^2 - 5, 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": "3.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -3|(-2(1sin(2\u03c0((-1((-2(-2|x - 3|) + 3)/(1(-2|x - 3|) + 2)) - 2)/(2((-2(-2|x - 3|) + 3)/(1(-2|x - 3|) + 2)) + 1))) - 3)^2 - 2(1sin(2\u03c0((-1((-2(-2|x - 3|) + 3)/(1(-2|x - 3|) + 2)) - 2)/(2((-2(-2|x - 3|) + 3)/(1(-2|x - 3|) + 2)) + 1))) - 3) + 2) - 2| + 1, g(x) = 1(-3|((3(-1(-3x + 4) - 3))/(-1(-1(-3x + 4) - 3) + 2)) - 3| - 3) - 1, x = 2.8, 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": "290.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-1((-1(-3cos(1\u03c0((1(2((1x - 3)/(-2x)) + 5) - 2)/(-2(2((1x - 3)/(-2x)) + 5) - 3)) + 2) - 3) - 3)/(2(-3cos(1\u03c0((1(2((1x - 3)/(-2x)) + 5) - 2)/(-2(2((1x - 3)/(-2x)) + 5) - 3)) + 2) - 3) - 1)) + 1)/(-1((-1(-3cos(1\u03c0((1(2((1x - 3)/(-2x)) + 5) - 2)/(-2(2((1x - 3)/(-2x)) + 5) - 3)) + 2) - 3) - 3)/(2(-3cos(1\u03c0((1(2((1x - 3)/(-2x)) + 5) - 2)/(-2(2((1x - 3)/(-2x)) + 5) - 3)) + 2) - 3) - 1)) + 2) and g(x) = 1(3(3|(3(3|x - 3| - 2)^2 - 2(3|x - 3| - 2) - 4) - 1| - 2)^2 + 5(3|(3(3|x - 3| - 2)^2 - 2(3|x - 3| - 2) - 4) - 1| - 2))^2 - 5(3(3|(3(3|x - 3| - 2)^2 - 2(3|x - 3| - 2) - 4) - 1| - 2)^2 + 5(3|(3(3|x - 3| - 2)^2 - 2(3|x - 3| - 2) - 4) - 1| - 2)) between the vertical lines x = 2.6 and x = 2.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6.9", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1(3(2(2(-4(1x + 5) + 2)^2 - 5(-4(1x + 5) + 2) + 1)^2 - 2(2(-4(1x + 5) + 2)^2 - 5(-4(1x + 5) + 2) + 1) + 1)^2 - 3(2(2(-4(1x + 5) + 2)^2 - 5(-4(1x + 5) + 2) + 1)^2 - 2(2(-4(1x + 5) + 2)^2 - 5(-4(1x + 5) + 2) + 1) + 1) - 5) + 1, g(x) = (2((-1(1sin(2\u03c0((1(-1x - 4) - 3)/(3(-1x - 4) - 1)) - 3) + 2))/(1(1sin(2\u03c0((1(-1x - 4) - 3)/(3(-1x - 4) - 1)) - 3) + 2) - 2)) - 3)/(1((-1(1sin(2\u03c0((1(-1x - 4) - 3)/(3(-1x - 4) - 1)) - 3) + 2))/(1(1sin(2\u03c0((1(-1x - 4) - 3)/(3(-1x - 4) - 1)) - 3) + 2) - 2)) + 2), x = -4.6, 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": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2|(1(-1(2|(-2|(-2cos(2\u03c0x + 3) + 2)|) - 3|) + 5)^2 - 3(-1(2|(-2|(-2cos(2\u03c0x + 3) + 2)|) - 3|) + 5) - 5) + 1| + 3 and g(x) = 5(4(3cos(1\u03c0(-3(-3x^2 + 3x - 4) - 2) - 2) - 2) - 3) - 5 between the vertical lines x = 0.7 and x = 1.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "227.9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3((-3(4((2(-1|(-2|x + 3| - 1) + 2|) - 3)/(3(-1|(-2|x + 3| - 1) + 2|) + 1))))/(-3(4((2(-1|(-2|x + 3| - 1) + 2|) - 3)/(3(-1|(-2|x + 3| - 1) + 2|) + 1))) - 1)) - 2 and g(x) = -5(4(3((-2(2sin(1\u03c0x - 3) - 1))/(-1(2sin(1\u03c0x - 3) - 1) + 2))^2 - 2((-2(2sin(1\u03c0x - 3) - 1))/(-1(2sin(1\u03c0x - 3) - 1) + 2)) - 5) - 2) + 4 from x = 1.3 to x = 1.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40.6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2e^(-2(1((-3(2|(-4((-2x - 2)/(1x - 3))) + 3|) - 2)/(1(2|(-4((-2x - 2)/(1x - 3))) + 3|) - 3))^2 + 2((-3(2|(-4((-2x - 2)/(1x - 3))) + 3|) - 2)/(1(2|(-4((-2x - 2)/(1x - 3))) + 3|) - 3)) - 4)) and g(x) = 1cos(2\u03c0(-5((-1(1|(3x - 1) + 2| + 3) - 3)/(2(1|(3x - 1) + 2| + 3) - 1)) - 5) - 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": "3.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (1(1|(-2|(-3((-2(-5x^2 - 4x - 1))/(3(-5x^2 - 4x - 1) + 2)) - 5)| - 3)| + 3) + 3)/(-2(1|(-2|(-3((-2(-5x^2 - 4x - 1))/(3(-5x^2 - 4x - 1) + 2)) - 5)| - 3)| + 3) - 3) and g(x) = 2cos(3\u03c0(-4(3|(5(5x + 5)^2 - 1(5x + 5) - 4) - 1| + 3)^2 - 2(3|(5(5x + 5)^2 - 1(5x + 5) - 4) - 1| + 3)) + 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3(1(-4((1((2(3x + 3) + 1)/(-1(3x + 3) + 2)) - 3)/(3((2(3x + 3) + 1)/(-1(3x + 3) + 2)) + 3)) + 3)^2 - 1(-4((1((2(3x + 3) + 1)/(-1(3x + 3) + 2)) - 3)/(3((2(3x + 3) + 1)/(-1(3x + 3) + 2)) + 3)) + 3) - 1) - 3, g(x) = 2((1(3|(-2sin(3\u03c0((1x)/(1x)) - 2) - 3) + 3| - 1) - 3)/(2(3|(-2sin(3\u03c0((1x)/(1x)) - 2) - 3) + 3| - 1) - 1))^2 + 5((1(3|(-2sin(3\u03c0((1x)/(1x)) - 2) - 3) + 3| - 1) - 3)/(2(3|(-2sin(3\u03c0((1x)/(1x)) - 2) - 3) + 3| - 1) - 1)) - 4, x = -0.3, 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": "3.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -5(2|((-1(4(-4(2|x - 2| - 2) + 3) - 1) - 1)/(1(4(-4(2|x - 2| - 2) + 3) - 1) - 3)) + 3| - 3)^2 + 4(2|((-1(4(-4(2|x - 2| - 2) + 3) - 1) - 1)/(1(4(-4(2|x - 2| - 2) + 3) - 1) - 3)) + 3| - 3) + 5, g(x) = -5((1(2|((-1(-3x - 5))/(1(-3x - 5) + 3)) - 3| + 1))/(2(2|((-1(-3x - 5))/(1(-3x - 5) + 3)) - 3| + 1)))^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": "1.7", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2sin(1\u03c0((-3(-1((-1(5((3x + 3)/(2x)) + 2))/(-2(5((3x + 3)/(2x)) + 2) + 3))^2 + 1((-1(5((3x + 3)/(2x)) + 2))/(-2(5((3x + 3)/(2x)) + 2) + 3)) - 5) - 3)/(-2(-1((-1(5((3x + 3)/(2x)) + 2))/(-2(5((3x + 3)/(2x)) + 2) + 3))^2 + 1((-1(5((3x + 3)/(2x)) + 2))/(-2(5((3x + 3)/(2x)) + 2) + 3)) - 5) - 1)) - 3) - 1, g(x) = (1(1(4(-4(3x - 5) + 2) + 3)^2 + 2(4(-4(3x - 5) + 2) + 3) + 2) - 2)/(-2(1(4(-4(3x - 5) + 2) + 3)^2 + 2(4(-4(3x - 5) + 2) + 3) + 2) + 3), 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) = (-2(-4(-1(5(-1e^(1(-3|x - 2|)) - 1) + 2) - 2) - 4) - 2)/(-2(-4(-1(5(-1e^(1(-3|x - 2|)) - 1) + 2) - 2) - 4) + 3) and g(x) = (-1(2|(-1|((3(2|x - 3|) - 2)/(-2(2|x - 3|) + 3)) - 2| + 2) - 2| - 2) - 3)/(-2(2|(-1|((3(2|x - 3|) - 2)/(-2(2|x - 3|) + 3)) - 2| + 2) - 2| - 2) + 3) between the vertical lines x = 3.7 and x = 4.0. 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(-3(3|((-2(1sin(1\u03c0x) - 2) + 3)/(-2(1sin(1\u03c0x) - 2) - 1)) - 3|)^2 + 3(3|((-2(1sin(1\u03c0x) - 2) + 3)/(-2(1sin(1\u03c0x) - 2) - 1)) - 3|) - 3) + 1)/(-1(-3(3|((-2(1sin(1\u03c0x) - 2) + 3)/(-2(1sin(1\u03c0x) - 2) - 1)) - 3|)^2 + 3(3|((-2(1sin(1\u03c0x) - 2) + 3)/(-2(1sin(1\u03c0x) - 2) - 1)) - 3|) - 3) + 2))^2 - 5((1(-3(3|((-2(1sin(1\u03c0x) - 2) + 3)/(-2(1sin(1\u03c0x) - 2) - 1)) - 3|)^2 + 3(3|((-2(1sin(1\u03c0x) - 2) + 3)/(-2(1sin(1\u03c0x) - 2) - 1)) - 3|) - 3) + 1)/(-1(-3(3|((-2(1sin(1\u03c0x) - 2) + 3)/(-2(1sin(1\u03c0x) - 2) - 1)) - 3|)^2 + 3(3|((-2(1sin(1\u03c0x) - 2) + 3)/(-2(1sin(1\u03c0x) - 2) - 1)) - 3|) - 3) + 2)) - 5, g(x) = -1(-3|(1cos(2\u03c0((-3(2|x| - 2) - 2)/(-2(2|x| - 2))) - 3)) + 3| + 3)^2 - 4(-3|(1cos(2\u03c0((-3(2|x| - 2) - 2)/(-2(2|x| - 2))) - 3)) + 3| + 3) - 4, 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": "1.9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 3(1|(2|((-2(1(1|x| - 3) + 2) + 1)/(1(1(1|x| - 3) + 2) - 2)) + 1| - 1) - 1| - 2)^2 - 1(1|(2|((-2(1(1|x| - 3) + 2) + 1)/(1(1(1|x| - 3) + 2) - 2)) + 1| - 1) - 1| - 2) - 3 and g(x) = 1(-1(2(1(-1|x - 1| - 3) - 5) + 2) - 5)^2 + 2 from x = 2.6 to x = 3.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2131.5", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -3cos(1\u03c0((2(5(4((-3(4x + 3) - 1)/(2(4x + 3) + 2))^2 + 5((-3(4x + 3) - 1)/(2(4x + 3) + 2)))^2 - 5(4((-3(4x + 3) - 1)/(2(4x + 3) + 2))^2 + 5((-3(4x + 3) - 1)/(2(4x + 3) + 2))) - 2) + 3)/(3(5(4((-3(4x + 3) - 1)/(2(4x + 3) + 2))^2 + 5((-3(4x + 3) - 1)/(2(4x + 3) + 2)))^2 - 5(4((-3(4x + 3) - 1)/(2(4x + 3) + 2))^2 + 5((-3(4x + 3) - 1)/(2(4x + 3) + 2))) - 2) - 2))) - 1, g(x) = -3cos(3\u03c0(3|((-3(-5((-3x - 1)/(-1x - 2))^2 - 2((-3x - 1)/(-1x - 2)) + 1) + 1)/(1(-5((-3x - 1)/(-1x - 2))^2 - 2((-3x - 1)/(-1x - 2)) + 1) + 2)) + 1| - 3) - 1) + 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (2(-3(1(-5((2(3|x + 2|) + 3)/(-2(3|x + 2|) + 3))^2 - 3((2(3|x + 2|) + 3)/(-2(3|x + 2|) + 3)) + 2) + 3)^2 - 4(1(-5((2(3|x + 2|) + 3)/(-2(3|x + 2|) + 3))^2 - 3((2(3|x + 2|) + 3)/(-2(3|x + 2|) + 3)) + 2) + 3) - 1) - 3)/(2(-3(1(-5((2(3|x + 2|) + 3)/(-2(3|x + 2|) + 3))^2 - 3((2(3|x + 2|) + 3)/(-2(3|x + 2|) + 3)) + 2) + 3)^2 - 4(1(-5((2(3|x + 2|) + 3)/(-2(3|x + 2|) + 3))^2 - 3((2(3|x + 2|) + 3)/(-2(3|x + 2|) + 3)) + 2) + 3) - 1) + 1) and g(x) = (1(-1sin(1\u03c0(-3|(2|(-3x - 2) - 3| + 1) + 2| - 2) + 2) + 3) + 2)/(2(-1sin(1\u03c0(-3|(2|(-3x - 2) - 3| + 1) + 2| - 2) + 2) + 3) - 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": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (1((1(-5(2((-3(-1e^(-1x) + 2) + 1)/(-2(-1e^(-1x) + 2) - 2))^2 - 3((-3(-1e^(-1x) + 2) + 1)/(-2(-1e^(-1x) + 2) - 2)) - 5) - 3) - 2)/(1(-5(2((-3(-1e^(-1x) + 2) + 1)/(-2(-1e^(-1x) + 2) - 2))^2 - 3((-3(-1e^(-1x) + 2) + 1)/(-2(-1e^(-1x) + 2) - 2)) - 5) - 3))) - 2)/(2((1(-5(2((-3(-1e^(-1x) + 2) + 1)/(-2(-1e^(-1x) + 2) - 2))^2 - 3((-3(-1e^(-1x) + 2) + 1)/(-2(-1e^(-1x) + 2) - 2)) - 5) - 3) - 2)/(1(-5(2((-3(-1e^(-1x) + 2) + 1)/(-2(-1e^(-1x) + 2) - 2))^2 - 3((-3(-1e^(-1x) + 2) + 1)/(-2(-1e^(-1x) + 2) - 2)) - 5) - 3))) + 3) and g(x) = (1(-3sin(2\u03c0(-3(1|(-1x - 1) - 2| - 2)^2 + 3(1|(-1x - 1) - 2| - 2) - 4) - 1) + 1) + 2)/(-2(-3sin(2\u03c0(-3(1|(-1x - 1) - 2| - 2)^2 + 3(1|(-1x - 1) - 2| - 2) - 4) - 1) + 1) + 3) between the vertical lines x = -1.7 and x = -0.8. 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": "Calculate the area enclosed between the functions f(x) = (-1(1cos(3\u03c0((-1(2(1(3x) + 1) - 5) + 2)/(-1(2(1(3x) + 1) - 5) - 3)) + 3)) - 1)/(-3(1cos(3\u03c0((-1(2(1(3x) + 1) - 5) + 2)/(-1(2(1(3x) + 1) - 5) - 3)) + 3)) - 1) and g(x) = (-1((1(-2(-1|((2x)/(-2x + 3)) - 1| + 3) - 2))/(-1(-2(-1|((2x)/(-2x + 3)) - 1| + 3) - 2) - 3)) + 2)/(1((1(-2(-1|((2x)/(-2x + 3)) - 1| + 3) - 2))/(-1(-2(-1|((2x)/(-2x + 3)) - 1| + 3) - 2) - 3))) from x = -0.5 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": "Determine the area of the region enclosed by the graphs of f(x) = 3|(1(-4(-2(-1((3x - 2)/(-3x)) - 3)^2 + 4)^2 - 1(-2(-1((3x - 2)/(-3x)) - 3)^2 + 4) - 3) - 4) + 1| - 3 and g(x) = 3|(1(-5(1(1x^2 - 4x - 1) - 2)^2 + 2(1(1x^2 - 4x - 1) - 2) + 4)^2 - 2(-5(1(1x^2 - 4x - 1) - 2)^2 + 2(1(1x^2 - 4x - 1) - 2) + 4) + 5)| - 2 between the vertical lines x = -0.9 and x = -0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "27.9", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2|(3sin(3\u03c0(-2|((-2((-3(-2|x + 2| - 3) - 1)/(2(-2|x + 2| - 3) + 1)) + 1)/(-1((-3(-2|x + 2| - 3) - 1)/(2(-2|x + 2| - 3) + 1)) - 1)) + 2| - 1) - 1) + 2)| + 1, g(x) = 1(-3|(5(-2(-5x^2 - 4x + 2)^2 + 5(-5x^2 - 4x + 2) - 3) + 5) - 2| + 1), 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": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 5((2(-1sin(3\u03c0((2((-3(-5x - 2) - 2)/(1(-5x - 2))) - 2)/(1((-3(-5x - 2) - 2)/(1(-5x - 2))) + 3)) - 3) + 1) - 2)/(1(-1sin(3\u03c0((2((-3(-5x - 2) - 2)/(1(-5x - 2))) - 2)/(1((-3(-5x - 2) - 2)/(1(-5x - 2))) + 3)) - 3) + 1) + 2))^2 + 2((2(-1sin(3\u03c0((2((-3(-5x - 2) - 2)/(1(-5x - 2))) - 2)/(1((-3(-5x - 2) - 2)/(1(-5x - 2))) + 3)) - 3) + 1) - 2)/(1(-1sin(3\u03c0((2((-3(-5x - 2) - 2)/(1(-5x - 2))) - 2)/(1((-3(-5x - 2) - 2)/(1(-5x - 2))) + 3)) - 3) + 1) + 2)) - 2 and g(x) = (-1(2|(-3(-2((3x + 3)/(2x + 2))^2 - 2((3x + 3)/(2x + 2)) - 3)^2 - 3(-2((3x + 3)/(2x + 2))^2 - 2((3x + 3)/(2x + 2)) - 3) + 5) - 3| + 3) + 2)/(1(2|(-3(-2((3x + 3)/(2x + 2))^2 - 2((3x + 3)/(2x + 2)) - 3)^2 - 3(-2((3x + 3)/(2x + 2))^2 - 2((3x + 3)/(2x + 2)) - 3) + 5) - 3| + 3) - 2) between the vertical lines x = 4.2 and x = 4.3. 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((1(1(-5(2sin(1\u03c0(-1x^2 - 3x - 2) + 1) - 1) + 2)^2 - 4(-5(2sin(1\u03c0(-1x^2 - 3x - 2) + 1) - 1) + 2) - 5))/(-3(1(-5(2sin(1\u03c0(-1x^2 - 3x - 2) + 1) - 1) + 2)^2 - 4(-5(2sin(1\u03c0(-1x^2 - 3x - 2) + 1) - 1) + 2) - 5) + 1)) + 1, g(x) = (2(3((-2(2(-3|x + 3| - 3)^2 - 4(-3|x + 3| - 3) - 3) - 1)/(2(2(-3|x + 3| - 3)^2 - 4(-3|x + 3| - 3) - 3) + 3))^2 - 2((-2(2(-3|x + 3| - 3)^2 - 4(-3|x + 3| - 3) - 3) - 1)/(2(2(-3|x + 3| - 3)^2 - 4(-3|x + 3| - 3) - 3) + 3)) + 3) + 1)/(2(3((-2(2(-3|x + 3| - 3)^2 - 4(-3|x + 3| - 3) - 3) - 1)/(2(2(-3|x + 3| - 3)^2 - 4(-3|x + 3| - 3) - 3) + 3))^2 - 2((-2(2(-3|x + 3| - 3)^2 - 4(-3|x + 3| - 3) - 3) - 1)/(2(2(-3|x + 3| - 3)^2 - 4(-3|x + 3| - 3) - 3) + 3)) + 3) - 1), x = 4.8, and x = 4.8999999999999995. 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(4(1(-5(-4(-3x^2 - 4x + 4))^2 + 2)^2 - 1(-5(-4(-3x^2 - 4x + 4))^2 + 2) - 1) + 5))/(-3(4(1(-5(-4(-3x^2 - 4x + 4))^2 + 2)^2 - 1(-5(-4(-3x^2 - 4x + 4))^2 + 2) - 1) + 5) + 2), g(x) = (1(4(1(3|(1sin(2\u03c0x + 1) + 2)|) - 1) + 2))/(-1(4(1(3|(1sin(2\u03c0x + 1) + 2)|) - 1) + 2) - 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3(1|(-1|(-5((3(3cos(3\u03c0x - 2) + 3) - 2)/(-3(3cos(3\u03c0x - 2) + 3) - 2)) - 5) + 1| + 1)| - 3) + 4 and g(x) = 1e^(2(1(2|(-4(-4x - 3) - 2) - 3|))) from x = -0.5 to x = -0.4. 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) = 1|(-2cos(1\u03c0(-4(-3((1(-1x^2 + 4x + 4) - 1)/(2(-1x^2 + 4x + 4) - 1))^2 + 4((1(-1x^2 + 4x + 4) - 1)/(2(-1x^2 + 4x + 4) - 1)))^2 + 2(-3((1(-1x^2 + 4x + 4) - 1)/(2(-1x^2 + 4x + 4) - 1))^2 + 4((1(-1x^2 + 4x + 4) - 1)/(2(-1x^2 + 4x + 4) - 1))) - 4) - 2)) + 2| - 2 and g(x) = (2(1(-3(-3(3|x + 1| - 2)^2 - 4(3|x + 1| - 2) + 1)^2 + 1(-3(3|x + 1| - 2)^2 - 4(3|x + 1| - 2) + 1) + 5) + 4))/(3(1(-3(-3(3|x + 1| - 2)^2 - 4(3|x + 1| - 2) + 1)^2 + 1(-3(3|x + 1| - 2)^2 - 4(3|x + 1| - 2) + 1) + 5) + 4) - 2) between the vertical lines x = -0.8 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": "Determine the area of the region enclosed by the graphs of f(x) = -1(-1(-3(-4(1((-3x + 1)/(-2x + 3))^2 - 3((-3x + 1)/(-2x + 3)) - 3) - 2) - 5)^2 - 4(-3(-4(1((-3x + 1)/(-2x + 3))^2 - 3((-3x + 1)/(-2x + 3)) - 3) - 2) - 5) - 5) - 3 and g(x) = (3(2|((2(1|(2x + 3) - 3| + 3) + 3)/(-3(1|(2x + 3) - 3| + 3) - 3)) + 2| + 3))/(1(2|((2(1|(2x + 3) - 3| + 3) + 3)/(-3(1|(2x + 3) - 3| + 3) - 3)) + 2| + 3) + 1) between the vertical lines x = 2.3 and x = 2.4. 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) = 1(3(-2|(1|(4(5x + 4) - 1) + 3| + 1) - 3| + 1)^2 - 1(-2|(1|(4(5x + 4) - 1) + 3| + 1) - 3| + 1) - 4)^2 + 2(3(-2|(1|(4(5x + 4) - 1) + 3| + 1) - 3| + 1)^2 - 1(-2|(1|(4(5x + 4) - 1) + 3| + 1) - 3| + 1) - 4) - 2 and g(x) = (-1(-5(-1(3(2|x - 1| + 1)^2 - 4(2|x - 1| + 1) + 1)^2 + 4(3(2|x - 1| + 1)^2 - 4(2|x - 1| + 1) + 1) + 3)^2 - 1(-1(3(2|x - 1| + 1)^2 - 4(2|x - 1| + 1) + 1)^2 + 4(3(2|x - 1| + 1)^2 - 4(2|x - 1| + 1) + 1) + 3) - 1) - 3)/(3(-5(-1(3(2|x - 1| + 1)^2 - 4(2|x - 1| + 1) + 1)^2 + 4(3(2|x - 1| + 1)^2 - 4(2|x - 1| + 1) + 1) + 3)^2 - 1(-1(3(2|x - 1| + 1)^2 - 4(2|x - 1| + 1) + 1)^2 + 4(3(2|x - 1| + 1)^2 - 4(2|x - 1| + 1) + 1) + 3) - 1) + 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": "10.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1e^(1(-2(2|(-2(-4((2x + 3)/(-3x - 3)) + 5)^2 + 1(-4((2x + 3)/(-3x - 3)) + 5)) + 3| - 3) - 1)) - 2, g(x) = (2((-1(3|((-3(2cos(2\u03c0x - 2) - 1))/(-2(2cos(2\u03c0x - 2) - 1) + 3)) + 2| - 3) - 1)/(1(3|((-3(2cos(2\u03c0x - 2) - 1))/(-2(2cos(2\u03c0x - 2) - 1) + 3)) + 2| - 3) + 1)) - 2)/(-1((-1(3|((-3(2cos(2\u03c0x - 2) - 1))/(-2(2cos(2\u03c0x - 2) - 1) + 3)) + 2| - 3) - 1)/(1(3|((-3(2cos(2\u03c0x - 2) - 1))/(-2(2cos(2\u03c0x - 2) - 1) + 3)) + 2| - 3) + 1))), 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": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-2(1(-4(-4(3(-1x + 2) - 5)^2 + 3(3(-1x + 2) - 5) + 4))^2 + 5(-4(-4(3(-1x + 2) - 5)^2 + 3(3(-1x + 2) - 5) + 4)) + 2) - 1)/(-1(1(-4(-4(3(-1x + 2) - 5)^2 + 3(3(-1x + 2) - 5) + 4))^2 + 5(-4(-4(3(-1x + 2) - 5)^2 + 3(3(-1x + 2) - 5) + 4)) + 2) + 3) and g(x) = 4(-1|(-2|((1(2x^2 + 1x - 3) + 3)/(-2(2x^2 + 1x - 3) - 1)) + 2| + 3) - 1| + 1) - 1 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": "50.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2|(-2(4(1(1|((2x - 3)/(-3x - 3)) - 1| + 1) - 2)^2 - 5(1(1|((2x - 3)/(-3x - 3)) - 1| + 1) - 2) + 3) + 5) + 1| - 2 and g(x) = 3e^(2(-1|(1|((-1(-1x^2 - 3x + 5))/(-1(-1x^2 - 3x + 5) + 2)) - 3| + 1) - 1| + 3)) + 2 between the vertical lines x = -0.7 and x = 0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "217.4", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (1((2((2(3(-2|(2|x| - 2) + 1| + 2)^2 + 2(-2|(2|x| - 2) + 1| + 2) - 2) - 2)/(-2(3(-2|(2|x| - 2) + 1| + 2)^2 + 2(-2|(2|x| - 2) + 1| + 2) - 2) - 2)) - 1)/(1((2(3(-2|(2|x| - 2) + 1| + 2)^2 + 2(-2|(2|x| - 2) + 1| + 2) - 2) - 2)/(-2(3(-2|(2|x| - 2) + 1| + 2)^2 + 2(-2|(2|x| - 2) + 1| + 2) - 2) - 2)) + 2)))/(1((2((2(3(-2|(2|x| - 2) + 1| + 2)^2 + 2(-2|(2|x| - 2) + 1| + 2) - 2) - 2)/(-2(3(-2|(2|x| - 2) + 1| + 2)^2 + 2(-2|(2|x| - 2) + 1| + 2) - 2) - 2)) - 1)/(1((2(3(-2|(2|x| - 2) + 1| + 2)^2 + 2(-2|(2|x| - 2) + 1| + 2) - 2) - 2)/(-2(3(-2|(2|x| - 2) + 1| + 2)^2 + 2(-2|(2|x| - 2) + 1| + 2) - 2) - 2)) + 2)) - 2) and g(x) = 1(-1cos(1\u03c0((-2(3|((2x - 1)/(1x)) - 3| + 3) - 1)/(2(3|((2x - 1)/(1x)) - 3| + 3) - 1)) + 2) - 1) + 1 between the vertical lines x = -0.7 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) = (1(-1(2(-1(1|(1|x + 2| - 2) - 1| + 3)^2 + 4(1|(1|x + 2| - 2) - 1| + 3) + 3)^2 - 1(-1(1|(1|x + 2| - 2) - 1| + 3)^2 + 4(1|(1|x + 2| - 2) - 1| + 3) + 3))^2 - 2(2(-1(1|(1|x + 2| - 2) - 1| + 3)^2 + 4(1|(1|x + 2| - 2) - 1| + 3) + 3)^2 - 1(-1(1|(1|x + 2| - 2) - 1| + 3)^2 + 4(1|(1|x + 2| - 2) - 1| + 3) + 3))) + 2)/(-1(-1(2(-1(1|(1|x + 2| - 2) - 1| + 3)^2 + 4(1|(1|x + 2| - 2) - 1| + 3) + 3)^2 - 1(-1(1|(1|x + 2| - 2) - 1| + 3)^2 + 4(1|(1|x + 2| - 2) - 1| + 3) + 3))^2 - 2(2(-1(1|(1|x + 2| - 2) - 1| + 3)^2 + 4(1|(1|x + 2| - 2) - 1| + 3) + 3)^2 - 1(-1(1|(1|x + 2| - 2) - 1| + 3)^2 + 4(1|(1|x + 2| - 2) - 1| + 3) + 3))) + 3) and g(x) = -2|((3((1((-2(-5x + 5) + 3)/(-3(-5x + 5) + 4)) + 3)/(2((-2(-5x + 5) + 3)/(-3(-5x + 5) + 4)) + 3)) - 3)/(-2((1((-2(-5x + 5) + 3)/(-3(-5x + 5) + 4)) + 3)/(2((-2(-5x + 5) + 3)/(-3(-5x + 5) + 4)) + 3)) - 1)) - 1| + 1 between the vertical lines x = 2.4 and x = 2.8. 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) = -2|((-2(-4(4((-3((3x - 1)/(-3x - 3)) + 2)/(2((3x - 1)/(-3x - 3)))) - 1)^2 + 4(4((-3((3x - 1)/(-3x - 3)) + 2)/(2((3x - 1)/(-3x - 3)))) - 1) - 2) - 1)/(-1(-4(4((-3((3x - 1)/(-3x - 3)) + 2)/(2((3x - 1)/(-3x - 3)))) - 1)^2 + 4(4((-3((3x - 1)/(-3x - 3)) + 2)/(2((3x - 1)/(-3x - 3)))) - 1) - 2) + 3)) - 3| + 1 and g(x) = -3(3((-3(-1(-3sin(3\u03c0x - 2) - 2)^2 + 3(-3sin(3\u03c0x - 2) - 2) + 2) + 1)/(2(-1(-3sin(3\u03c0x - 2) - 2)^2 + 3(-3sin(3\u03c0x - 2) - 2) + 2) + 2)) + 2)^2 + 1(3((-3(-1(-3sin(3\u03c0x - 2) - 2)^2 + 3(-3sin(3\u03c0x - 2) - 2) + 2) + 1)/(2(-1(-3sin(3\u03c0x - 2) - 2)^2 + 3(-3sin(3\u03c0x - 2) - 2) + 2) + 2)) + 2) - 1 from x = 4.1 to x = 4.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "138.6", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-1(1(-5(3(-1(2sin(1\u03c0x - 3) + 1) + 1) + 4) - 5)^2 + 2(-5(3(-1(2sin(1\u03c0x - 3) + 1) + 1) + 4) - 5) + 4) - 3)/(-3(1(-5(3(-1(2sin(1\u03c0x - 3) + 1) + 1) + 4) - 5)^2 + 2(-5(3(-1(2sin(1\u03c0x - 3) + 1) + 1) + 4) - 5) + 4) - 3), g(x) = -3(5(3|((-2(-5x + 2) + 1)/(-2(-5x + 2) - 2)) - 3| - 3)^2 + 2(3|((-2(-5x + 2) + 1)/(-2(-5x + 2) - 2)) - 3| - 3) - 3) - 4, x = 0.7, and x = 0.7999999999999999. Round your answer 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) = 5(-1|(1|(4((1(-2|x - 1| - 3) - 3)/(1(-2|x - 1| - 3) + 1))^2 - 3((1(-2|x - 1| - 3) - 3)/(1(-2|x - 1| - 3) + 1)) - 4) + 3| - 3)| + 1) - 3, g(x) = -1(1|((-2(-5(1cos(2\u03c0x - 1)) + 3) - 3)/(-2(-5(1cos(2\u03c0x - 1)) + 3) + 1))| - 1) + 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": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1e^(1(-4(1((-3((2(5x^2 + 2x - 2) + 2)/(2(5x^2 + 2x - 2) + 1)))/(-3((2(5x^2 + 2x - 2) + 2)/(2(5x^2 + 2x - 2) + 1)) + 1)) + 3)^2 + 3(1((-3((2(5x^2 + 2x - 2) + 2)/(2(5x^2 + 2x - 2) + 1)))/(-3((2(5x^2 + 2x - 2) + 2)/(2(5x^2 + 2x - 2) + 1)) + 1)) + 3) + 1)) - 2 and g(x) = 1sin(3\u03c0((-3(-2|(2|((-2x)/(-3x - 3)) - 3| - 2) + 3| + 1) - 1)/(-3(-2|(2|((-2x)/(-3x - 3)) - 3| - 2) + 3| + 1) + 2)) + 2) - 1 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": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3(-1(3((-1(3e^(-1(1|x| + 1)) - 2) - 3)/(1(3e^(-1(1|x| + 1)) - 2)))^2 - 4((-1(3e^(-1(1|x| + 1)) - 2) - 3)/(1(3e^(-1(1|x| + 1)) - 2))) + 2))^2 + 2(-1(3((-1(3e^(-1(1|x| + 1)) - 2) - 3)/(1(3e^(-1(1|x| + 1)) - 2)))^2 - 4((-1(3e^(-1(1|x| + 1)) - 2) - 3)/(1(3e^(-1(1|x| + 1)) - 2))) + 2)) - 2 and g(x) = (1(3((-3((-1((-2x - 1)/(-2x - 3)) - 3)/(-2((-2x - 1)/(-2x - 3)) + 1)) + 3)/(1((-1((-2x - 1)/(-2x - 3)) - 3)/(-2((-2x - 1)/(-2x - 3)) + 1)) - 2))^2 - 4) - 3)/(2(3((-3((-1((-2x - 1)/(-2x - 3)) - 3)/(-2((-2x - 1)/(-2x - 3)) + 1)) + 3)/(1((-1((-2x - 1)/(-2x - 3)) - 3)/(-2((-2x - 1)/(-2x - 3)) + 1)) - 2))^2 - 4)) between the vertical lines x = -2.1 and x = -1.4. 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": "Calculate the area enclosed between the functions f(x) = (-3(-5(-1e^(1(-2|(-5(-4x - 5)^2 + 2(-4x - 5) + 4) + 2| - 3))) - 5) - 2)/(1(-5(-1e^(1(-2|(-5(-4x - 5)^2 + 2(-4x - 5) + 4) + 2| - 3))) - 5) - 2) and g(x) = -1cos(3\u03c0(-5(-4((2(-2|x + 2| + 1) + 2)/(-2(-2|x + 2| + 1) - 1)) - 3) + 5) + 2) - 1 from x = -4.4 to x = -4.3. 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|((1(2|((-3(-1x^2 - 2x - 1) - 1)/(2(-1x^2 - 2x - 1))) - 3|) - 2)/(-3(2|((-3(-1x^2 - 2x - 1) - 1)/(2(-1x^2 - 2x - 1))) - 3|) - 2)) + 1| + 3) + 1 and g(x) = (-3(-1|(2|(-5(-1x^2 + 4x - 3)^2 + 1(-1x^2 + 4x - 3) + 5) + 1| + 3) - 2| + 3) + 3)/(-3(-1|(2|(-5(-1x^2 + 4x - 3)^2 + 1(-1x^2 + 4x - 3) + 5) + 1| + 3) - 2| + 3) - 3) between the vertical lines x = 0.6 and x = 3.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 3(-1(2|(-1(5(2x^2 - 2x - 5)^2 + 1(2x^2 - 2x - 5) - 2)^2 - 2(5(2x^2 - 2x - 5)^2 + 1(2x^2 - 2x - 5) - 2)) - 1| + 3) + 3)^2 - 3(-1(2|(-1(5(2x^2 - 2x - 5)^2 + 1(2x^2 - 2x - 5) - 2)^2 - 2(5(2x^2 - 2x - 5)^2 + 1(2x^2 - 2x - 5) - 2)) - 1| + 3) + 3) - 4 and g(x) = (-2(-5((3(-5(2|x + 1| + 3)) - 3)/(3(-5(2|x + 1| + 3)) - 2))^2 - 3((3(-5(2|x + 1| + 3)) - 3)/(3(-5(2|x + 1| + 3)) - 2)) - 4) + 3)/(-1(-5((3(-5(2|x + 1| + 3)) - 3)/(3(-5(2|x + 1| + 3)) - 2))^2 - 3((3(-5(2|x + 1| + 3)) - 3)/(3(-5(2|x + 1| + 3)) - 2)) - 4) - 1) between the vertical lines x = -1.2 and x = -1.1. 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) = 5((1(-1cos(2\u03c0(-5(-3(3x^2 - 4x - 5)^2 - 1(3x^2 - 4x - 5) + 3)^2 + 5(-3(3x^2 - 4x - 5)^2 - 1(3x^2 - 4x - 5) + 3) + 3)) + 3) - 3)/(-3(-1cos(2\u03c0(-5(-3(3x^2 - 4x - 5)^2 - 1(3x^2 - 4x - 5) + 3)^2 + 5(-3(3x^2 - 4x - 5)^2 - 1(3x^2 - 4x - 5) + 3) + 3)) + 3) - 2)) - 1 and g(x) = (1(4((1(-4(-2|x + 2| + 3) + 1) - 3)/(3(-4(-2|x + 2| + 3) + 1)))^2 + 5((1(-4(-2|x + 2| + 3) + 1) - 3)/(3(-4(-2|x + 2| + 3) + 1))) + 1) - 1)/(3(4((1(-4(-2|x + 2| + 3) + 1) - 3)/(3(-4(-2|x + 2| + 3) + 1)))^2 + 5((1(-4(-2|x + 2| + 3) + 1) - 3)/(3(-4(-2|x + 2| + 3) + 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (3(-5(-3((3((2(-4x^2 + 1x + 4) - 3)/(-2(-4x^2 + 1x + 4) + 1)) - 1)/(2((2(-4x^2 + 1x + 4) - 3)/(-2(-4x^2 + 1x + 4) + 1)) + 2))^2 - 4((3((2(-4x^2 + 1x + 4) - 3)/(-2(-4x^2 + 1x + 4) + 1)) - 1)/(2((2(-4x^2 + 1x + 4) - 3)/(-2(-4x^2 + 1x + 4) + 1)) + 2))) - 4))/(-1(-5(-3((3((2(-4x^2 + 1x + 4) - 3)/(-2(-4x^2 + 1x + 4) + 1)) - 1)/(2((2(-4x^2 + 1x + 4) - 3)/(-2(-4x^2 + 1x + 4) + 1)) + 2))^2 - 4((3((2(-4x^2 + 1x + 4) - 3)/(-2(-4x^2 + 1x + 4) + 1)) - 1)/(2((2(-4x^2 + 1x + 4) - 3)/(-2(-4x^2 + 1x + 4) + 1)) + 2))) - 4) + 3), g(x) = 1cos(3\u03c0(-1(3(-5(-2x^2 - 2x) + 5)^2 - 1(-5(-2x^2 - 2x) + 5) - 3)^2 - 2(3(-5(-2x^2 - 2x) + 5)^2 - 1(-5(-2x^2 - 2x) + 5) - 3) - 4) + 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2e^(-1((-1(-3(-2|(2(-1x^2 + 3x) + 5)| - 3)^2 + 4(-2|(2(-1x^2 + 3x) + 5)| - 3) - 3) - 1)/(3(-3(-2|(2(-1x^2 + 3x) + 5)| - 3)^2 + 4(-2|(2(-1x^2 + 3x) + 5)| - 3) - 3) + 3))) and g(x) = (-1(2(2e^(-1(2((2x - 1)/(-2x - 3))^2 + 5((2x - 1)/(-2x - 3)) + 1)) - 2)^2 - 4(2e^(-1(2((2x - 1)/(-2x - 3))^2 + 5((2x - 1)/(-2x - 3)) + 1)) - 2) - 2) - 2)/(2(2(2e^(-1(2((2x - 1)/(-2x - 3))^2 + 5((2x - 1)/(-2x - 3)) + 1)) - 2)^2 - 4(2e^(-1(2((2x - 1)/(-2x - 3))^2 + 5((2x - 1)/(-2x - 3)) + 1)) - 2) - 2) + 1) from x = -3.0 to x = 1.0. 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": "Calculate the area enclosed between the functions f(x) = -2|(1((1(-5(1((-1x - 2)/(2x + 2)) + 2) + 2) + 1)/(2(-5(1((-1x - 2)/(2x + 2)) + 2) + 2) + 2))^2 - 1((1(-5(1((-1x - 2)/(2x + 2)) + 2) + 2) + 1)/(2(-5(1((-1x - 2)/(2x + 2)) + 2) + 2) + 2)) - 3) - 1| + 2 and g(x) = -2|(5(-3sin(3\u03c0(2|((-1x + 3)/(-1x)) + 2| - 2) - 2) - 2) - 3) + 3| + 3 from x = -1.4 to x = -1.3. 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) = -4((1(-1|(-5(3|((1x - 3)/(2x)) + 1| - 1) - 3) - 1| + 2) + 3)/(1(-1|(-5(3|((1x - 3)/(2x)) + 1| - 1) - 3) - 1| + 2)))^2 + 4((1(-1|(-5(3|((1x - 3)/(2x)) + 1| - 1) - 3) - 1| + 2) + 3)/(1(-1|(-5(3|((1x - 3)/(2x)) + 1| - 1) - 3) - 1| + 2))) - 2 and g(x) = 1(-1|((-1(-2sin(3\u03c0(1|x - 3| - 3) - 3) + 3) - 1)/(2(-2sin(3\u03c0(1|x - 3| - 3) - 3) + 3) - 3)) - 3| + 1) - 5 from x = 0.8 to x = 0.9. 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": "Find the area of the region bounded by the curves f(x) = 2e^(1((-3(3|(-3(-1|(5x - 3)| + 1)^2 - 1) + 2| - 2) + 1)/(1(3|(-3(-1|(5x - 3)| + 1)^2 - 1) + 2| - 2) - 2))) + 2, g(x) = -4(1e^(1((3((1((-2x)/(2x + 3)) - 2)/(-2((-2x)/(2x + 3)) - 2)) - 2)/(1((1((-2x)/(2x + 3)) - 2)/(-2((-2x)/(2x + 3)) - 2)) + 1))) - 1)^2 + 4, 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": "1.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (1(1|(-2sin(1\u03c0(-3|((-1(1|x + 2|) - 1)/(3(1|x + 2|) - 1)) - 3|) - 1) - 1) - 3| - 2) + 3)/(1(1|(-2sin(1\u03c0(-3|((-1(1|x + 2|) - 1)/(3(1|x + 2|) - 1)) - 3|) - 1) - 1) - 3| - 2)), g(x) = 1|(2((1(-3(2sin(1\u03c0x) + 3)^2 + 1(2sin(1\u03c0x) + 3) + 3) - 3)/(-1(-3(2sin(1\u03c0x) + 3)^2 + 1(2sin(1\u03c0x) + 3) + 3) + 2))^2 - 3((1(-3(2sin(1\u03c0x) + 3)^2 + 1(2sin(1\u03c0x) + 3) + 3) - 3)/(-1(-3(2sin(1\u03c0x) + 3)^2 + 1(2sin(1\u03c0x) + 3) + 3) + 2)) - 2)| + 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": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 3|(1(5(2(-1(5x^2 + 1) + 1) - 3)^2 + 1(2(-1(5x^2 + 1) + 1) - 3) - 2) + 3) - 3| - 3 and g(x) = 3(-4((2((1(3x + 4) - 3)/(-3(3x + 4) - 2)) + 2)/(-2((1(3x + 4) - 3)/(-3(3x + 4) - 2)) + 1)) - 5)^2 - 1(-4((2((1(3x + 4) - 3)/(-3(3x + 4) - 2)) + 2)/(-2((1(3x + 4) - 3)/(-3(3x + 4) - 2)) + 1)) - 5) between the vertical lines x = -1.2 and x = 0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-770.7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (1((2(5(-2((3(1x + 2) - 2)/(1(1x + 2))) - 1)^2 - 3(-2((3(1x + 2) - 2)/(1(1x + 2))) - 1) + 3) + 1)/(3(5(-2((3(1x + 2) - 2)/(1(1x + 2))) - 1)^2 - 3(-2((3(1x + 2) - 2)/(1(1x + 2))) - 1) + 3) + 3)) + 3)/(2((2(5(-2((3(1x + 2) - 2)/(1(1x + 2))) - 1)^2 - 3(-2((3(1x + 2) - 2)/(1(1x + 2))) - 1) + 3) + 1)/(3(5(-2((3(1x + 2) - 2)/(1(1x + 2))) - 1)^2 - 3(-2((3(1x + 2) - 2)/(1(1x + 2))) - 1) + 3) + 3)) - 3) and g(x) = 2|(1|((-3(-4(1|x + 2| - 2) + 2) - 1)/(2(-4(1|x + 2| - 2) + 2) + 3))| + 3) - 3| - 3 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": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1((-2(-3|((-3(-3e^(1((2x + 2)/(1x - 3))) + 1))/(1(-3e^(1((2x + 2)/(1x - 3))) + 1) + 2)) - 2| + 1) - 2)/(3(-3|((-3(-3e^(1((2x + 2)/(1x - 3))) + 1))/(1(-3e^(1((2x + 2)/(1x - 3))) + 1) + 2)) - 2| + 1)))^2 + 1((-2(-3|((-3(-3e^(1((2x + 2)/(1x - 3))) + 1))/(1(-3e^(1((2x + 2)/(1x - 3))) + 1) + 2)) - 2| + 1) - 2)/(3(-3|((-3(-3e^(1((2x + 2)/(1x - 3))) + 1))/(1(-3e^(1((2x + 2)/(1x - 3))) + 1) + 2)) - 2| + 1))) - 3 and g(x) = 3e^(2(-1|((-2(-3((1x - 3)/(-2x + 3)) + 1) + 2)/(-1(-3((1x - 3)/(-2x + 3)) + 1) - 1)) + 2| - 1)) 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": "342.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1(-2((2(-1|(-1|((-1x - 2)/(1x + 2)) + 3|) - 2|) + 1)/(-2(-1|(-1|((-1x - 2)/(1x + 2)) + 3|) - 2|) + 3)) - 2) - 3, g(x) = -5(4((3(-3|(3sin(1\u03c0x + 1) + 1) - 3| + 3))/(-2(-3|(3sin(1\u03c0x + 1) + 1) - 3| + 3) + 1))^2 + 3((3(-3|(3sin(1\u03c0x + 1) + 1) - 3| + 3))/(-2(-3|(3sin(1\u03c0x + 1) + 1) - 3| + 3) + 1)) + 2) + 4, x = -3.4, 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": "23.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (3(2e^(-1(-2((-1((-2((-1x)/(3x + 1)) - 2)/(2((-1x)/(3x + 1)) - 3)) + 3)/(-3((-2((-1x)/(3x + 1)) - 2)/(2((-1x)/(3x + 1)) - 3)))) - 5))) - 3)/(-1(2e^(-1(-2((-1((-2((-1x)/(3x + 1)) - 2)/(2((-1x)/(3x + 1)) - 3)) + 3)/(-3((-2((-1x)/(3x + 1)) - 2)/(2((-1x)/(3x + 1)) - 3)))) - 5))) - 3) and g(x) = -2|(-3e^(2((-3(3((-1x + 3)/(-3x + 1))^2 + 4((-1x + 3)/(-3x + 1)) - 4) + 3)/(-2(3((-1x + 3)/(-3x + 1))^2 + 4((-1x + 3)/(-3x + 1)) - 4) + 1))) - 3) + 3| + 3 between the vertical lines x = -1.7 and x = 0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "186.9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1((-1(-1|(1(3(5x^2 + 3x - 4) + 4)^2 + 5) - 1| - 2) + 3)/(3(-1|(1(3(5x^2 + 3x - 4) + 4)^2 + 5) - 1| - 2) - 1)) + 1 and g(x) = 3((-2(2sin(1\u03c0(-3|(2x^2 + 4x + 2) + 1| + 2) - 2) + 3) + 3)/(-1(2sin(1\u03c0(-3|(2x^2 + 4x + 2) + 1| + 2) - 2) + 3) - 1)) + 1 from x = -4.7 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) = (-3(-5(-1(-4((2(-5x^2 - 3x - 2) + 2)/(2(-5x^2 - 3x - 2) + 3)) + 3) - 2) + 5) + 1)/(-2(-5(-1(-4((2(-5x^2 - 3x - 2) + 2)/(2(-5x^2 - 3x - 2) + 3)) + 3) - 2) + 5) - 2), g(x) = (1(-3(2(2e^(2(-2x^2 - 2x - 3)) + 2)^2 - 2(2e^(2(-2x^2 - 2x - 3)) + 2) + 5) - 2) + 3)/(1(-3(2(2e^(2(-2x^2 - 2x - 3)) + 2)^2 - 2(2e^(2(-2x^2 - 2x - 3)) + 2) + 5) - 2)), x = -0.8, 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": "2.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 3((2(-2(2(-1(1cos(3\u03c0x + 2) - 2) - 3) + 2) + 4) - 2)/(-2(-2(2(-1(1cos(3\u03c0x + 2) - 2) - 3) + 2) + 4) + 3)) and g(x) = -1(-2|((-1(-1sin(3\u03c0(-5x^2 + 4x - 4) - 3) - 3) - 2)/(3(-1sin(3\u03c0(-5x^2 + 4x - 4) - 3) - 3) + 3)) - 1| - 1) - 3 from x = -2.6 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(2(1(1(1(3|x - 2|) - 4)^2 - 3) - 5)) + 4 and g(x) = -1|((-1(-2sin(1\u03c0(-2|(-5x^2 + 1x - 1) + 2| + 2) + 3) + 3) - 2)/(2(-2sin(1\u03c0(-2|(-5x^2 + 1x - 1) + 2| + 2) + 3) + 3))) + 2| - 3 between the vertical lines x = 4.0 and 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) = 4((-1(1(1(-2(-5x^2 - 2x + 1)^2 + 3(-5x^2 - 2x + 1) + 5) - 1) - 4) + 1)/(1(1(1(-2(-5x^2 - 2x + 1)^2 + 3(-5x^2 - 2x + 1) + 5) - 1) - 4)))^2 + 2((-1(1(1(-2(-5x^2 - 2x + 1)^2 + 3(-5x^2 - 2x + 1) + 5) - 1) - 4) + 1)/(1(1(1(-2(-5x^2 - 2x + 1)^2 + 3(-5x^2 - 2x + 1) + 5) - 1) - 4))) + 5, g(x) = (1(3(-1|(-1(2sin(3\u03c0x + 3) + 1)^2 + 4(2sin(3\u03c0x + 3) + 1) - 4) - 1| + 2)^2 + 1(-1|(-1(2sin(3\u03c0x + 3) + 1)^2 + 4(2sin(3\u03c0x + 3) + 1) - 4) - 1| + 2) - 5) + 2)/(1(3(-1|(-1(2sin(3\u03c0x + 3) + 1)^2 + 4(2sin(3\u03c0x + 3) + 1) - 4) - 1| + 2)^2 + 1(-1|(-1(2sin(3\u03c0x + 3) + 1)^2 + 4(2sin(3\u03c0x + 3) + 1) - 4) - 1| + 2) - 5)), x = 2.3, 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": "4.6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (3((-2(5(3|(-1|(2|x| + 1) - 1| + 3)| - 2) + 3) - 3)/(3(5(3|(-1|(2|x| + 1) - 1| + 3)| - 2) + 3) + 1)))/(-2((-2(5(3|(-1|(2|x| + 1) - 1| + 3)| - 2) + 3) - 3)/(3(5(3|(-1|(2|x| + 1) - 1| + 3)| - 2) + 3) + 1)) - 2) and g(x) = 2|((-1(-4(1((1x - 2)/(-2x))^2 - 3((1x - 2)/(-2x)) - 5)^2 + 1(1((1x - 2)/(-2x))^2 - 3((1x - 2)/(-2x)) - 5)) - 1)/(2(-4(1((1x - 2)/(-2x))^2 - 3((1x - 2)/(-2x)) - 5)^2 + 1(1((1x - 2)/(-2x))^2 - 3((1x - 2)/(-2x)) - 5)))) - 1| from x = -1.5 to x = 0.2. 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) = 5((-3(-1(2|(2(4x) + 5) + 2| + 1) + 5) - 1)/(1(-1(2|(2(4x) + 5) + 2| + 1) + 5) + 3))^2 + 3((-3(-1(2|(2(4x) + 5) + 2| + 1) + 5) - 1)/(1(-1(2|(2(4x) + 5) + 2| + 1) + 5) + 3)) - 5 and g(x) = (1(-3e^(-1(-5(3|(-1|x + 2| + 2) - 3| + 3) - 2)) - 1) - 1)/(1(-3e^(-1(-5(3|(-1|x + 2| + 2) - 3| + 3) - 2)) - 1) + 3) 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": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -3(1cos(3\u03c0((2(1|(1((2x)/(1x + 1))^2 + 2((2x)/(1x + 1))) + 1| - 3) - 1)/(-3(1|(1((2x)/(1x + 1))^2 + 2((2x)/(1x + 1))) + 1| - 3) + 1)) + 1) + 2)^2 - 2(1cos(3\u03c0((2(1|(1((2x)/(1x + 1))^2 + 2((2x)/(1x + 1))) + 1| - 3) - 1)/(-3(1|(1((2x)/(1x + 1))^2 + 2((2x)/(1x + 1))) + 1| - 3) + 1)) + 1) + 2) - 5, g(x) = 1(-5((3(-2|(-3e^(2x)) + 2| + 2) - 2)/(-2(-2|(-3e^(2x)) + 2| + 2))) + 5) + 4, 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": "30.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2(-1|(-1|(3(2|((1x)/(1x + 1)) - 2| - 2)^2 - 1(2|((1x)/(1x + 1)) - 2| - 2) - 1) + 3| - 1) - 1| + 1)^2 - 4(-1|(-1|(3(2|((1x)/(1x + 1)) - 2| - 2)^2 - 1(2|((1x)/(1x + 1)) - 2| - 2) - 1) + 3| - 1) - 1| + 1) - 4 and g(x) = -3|(1(-1((-2((2x + 2)/(-3x + 4)) - 2)/(2((2x + 2)/(-3x + 4)) + 3)) - 2)^2 + 3(-1((-2((2x + 2)/(-3x + 4)) - 2)/(2((2x + 2)/(-3x + 4)) + 3)) - 2) + 2) + 1| + 2 between the vertical lines x = 2.7 and x = 3.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-24.6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 4((2(-3(-5(-1(1x - 2) - 3) - 3)^2 - 3(-5(-1(1x - 2) - 3) - 3) + 5) - 2)/(-1(-3(-5(-1(1x - 2) - 3) - 3)^2 - 3(-5(-1(1x - 2) - 3) - 3) + 5) + 2)) + 3 and g(x) = -1((-1(2|(1sin(3\u03c0(1x^2 + 2x) - 3) - 3) - 1| - 3) - 2)/(2(2|(1sin(3\u03c0(1x^2 + 2x) - 3) - 3) - 1| - 3) - 1)) + 1 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": "11.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3(1|(1(2(-1((-1x - 3)/(1x))^2 - 2((-1x - 3)/(1x)) + 2)^2 + 5(-1((-1x - 3)/(1x))^2 - 2((-1x - 3)/(1x)) + 2) + 1) - 4) + 2| - 3), g(x) = 1sin(2\u03c0(1((-3(4(-1x - 2)^2 - 4(-1x - 2)) - 3)/(-1(4(-1x - 2)^2 - 4(-1x - 2)) - 2)) + 2) - 2) + 2, x = -2.0, 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": "2.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -3|((2((-1(1(5(1|x - 2|)^2 + 3(1|x - 2|))^2 - 1(5(1|x - 2|)^2 + 3(1|x - 2|)) - 3) + 3)/(-2(1(5(1|x - 2|)^2 + 3(1|x - 2|))^2 - 1(5(1|x - 2|)^2 + 3(1|x - 2|)) - 3))) + 1)/(2((-1(1(5(1|x - 2|)^2 + 3(1|x - 2|))^2 - 1(5(1|x - 2|)^2 + 3(1|x - 2|)) - 3) + 3)/(-2(1(5(1|x - 2|)^2 + 3(1|x - 2|))^2 - 1(5(1|x - 2|)^2 + 3(1|x - 2|)) - 3))) + 3)) + 2| + 3, g(x) = 1((-3((-2(2|((-1x - 1)/(-2x + 3)) + 2| - 3) - 3)/(-2(2|((-1x - 1)/(-2x + 3)) + 2| - 3) - 2)) - 2)/(1((-2(2|((-1x - 1)/(-2x + 3)) + 2| - 3) - 3)/(-2(2|((-1x - 1)/(-2x + 3)) + 2| - 3) - 2)))) - 5, x = 1.5, 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": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-2(-3cos(2\u03c0(4((-1(-3|((-3x)/(2x - 3)) + 1| - 3) - 1)/(2(-3|((-3x)/(2x - 3)) + 1| - 3) + 1))^2 - 3((-1(-3|((-3x)/(2x - 3)) + 1| - 3) - 1)/(2(-3|((-3x)/(2x - 3)) + 1| - 3) + 1)) - 5)) - 2) + 3)/(2(-3cos(2\u03c0(4((-1(-3|((-3x)/(2x - 3)) + 1| - 3) - 1)/(2(-3|((-3x)/(2x - 3)) + 1| - 3) + 1))^2 - 3((-1(-3|((-3x)/(2x - 3)) + 1| - 3) - 1)/(2(-3|((-3x)/(2x - 3)) + 1| - 3) + 1)) - 5)) - 2) + 1), g(x) = (2(1(5(-2sin(3\u03c0(-5x) - 2) - 2)^2 - 3(-2sin(3\u03c0(-5x) - 2) - 2) - 5) - 3) - 3)/(-3(1(5(-2sin(3\u03c0(-5x) - 2) - 2)^2 - 3(-2sin(3\u03c0(-5x) - 2) - 2) - 5) - 3) + 2), x = -4.4, 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": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 4(-2(-1|(3|(5(-3x + 4)^2 - 3(-3x + 4) + 1) - 2| - 1) - 3|) - 2) - 4 and g(x) = (-2(5(3|(-1(1x + 4) + 3) - 2| - 3) - 4) + 2)/(2(5(3|(-1(1x + 4) + 3) - 2| - 3) - 4) + 2) between the vertical lines x = 1.1 and x = 1.4. 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((1(3e^(1(-5(-1(4x + 3) - 4) - 4))) - 2)/(-3(3e^(1(-5(-1(4x + 3) - 4) - 4))) - 3))^2 + 3((1(3e^(1(-5(-1(4x + 3) - 4) - 4))) - 2)/(-3(3e^(1(-5(-1(4x + 3) - 4) - 4))) - 3)) - 4, g(x) = 3cos(2\u03c0(3((-2(-1(-5x - 5) + 5) - 3)/(-2(-1(-5x - 5) + 5) + 1)) + 1) - 3), 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": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -5(-2e^(-2((-2(1(-1|((-3x + 3)/(3x - 2)) - 1| + 2)^2 + 3(-1|((-3x + 3)/(3x - 2)) - 1| + 2) - 1) - 3)/(-2(1(-1|((-3x + 3)/(3x - 2)) - 1| + 2)^2 + 3(-1|((-3x + 3)/(3x - 2)) - 1| + 2) - 1) - 1))))^2 + 2(-2e^(-2((-2(1(-1|((-3x + 3)/(3x - 2)) - 1| + 2)^2 + 3(-1|((-3x + 3)/(3x - 2)) - 1| + 2) - 1) - 3)/(-2(1(-1|((-3x + 3)/(3x - 2)) - 1| + 2)^2 + 3(-1|((-3x + 3)/(3x - 2)) - 1| + 2) - 1) - 1)))) + 4 and g(x) = -3(-3cos(2\u03c0(-3|(-1|(-5x - 4) - 3|) - 3| + 2) - 3) - 2)^2 - 4(-3cos(2\u03c0(-3|(-1|(-5x - 4) - 3|) - 3| + 2) - 3) - 2) + 4 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": "1.7", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2(-4(-1sin(2\u03c0((1(-3|(-1x - 4) + 2| + 3))/(3(-3|(-1x - 4) + 2| + 3) + 2)) - 2)) + 4)^2 + 1(-4(-1sin(2\u03c0((1(-3|(-1x - 4) + 2| + 3))/(3(-3|(-1x - 4) + 2| + 3) + 2)) - 2)) + 4) + 2, g(x) = (-2((1(-4(-4(-2x + 4)^2 - 2(-2x + 4) + 3)^2 - 5(-4(-2x + 4)^2 - 2(-2x + 4) + 3) + 5) + 1)/(-3(-4(-4(-2x + 4)^2 - 2(-2x + 4) + 3)^2 - 5(-4(-2x + 4)^2 - 2(-2x + 4) + 3) + 5) + 2)) + 3)/(1((1(-4(-4(-2x + 4)^2 - 2(-2x + 4) + 3)^2 - 5(-4(-2x + 4)^2 - 2(-2x + 4) + 3) + 5) + 1)/(-3(-4(-4(-2x + 4)^2 - 2(-2x + 4) + 3)^2 - 5(-4(-2x + 4)^2 - 2(-2x + 4) + 3) + 5) + 2))), 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": "5.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3((1(2sin(1\u03c0(4((-2(-4x) - 1)/(-3(-4x)))^2 + 5((-2(-4x) - 1)/(-3(-4x))) + 1)) - 3) + 3)/(-1(2sin(1\u03c0(4((-2(-4x) - 1)/(-3(-4x)))^2 + 5((-2(-4x) - 1)/(-3(-4x))) + 1)) - 3) - 1)) and g(x) = (-1((1(2e^(1(-1(-3x^2 + 5x)^2 + 2(-3x^2 + 5x) - 4)) + 1) + 1)/(2(2e^(1(-1(-3x^2 + 5x)^2 + 2(-3x^2 + 5x) - 4)) + 1) + 1)) + 1)/(1((1(2e^(1(-1(-3x^2 + 5x)^2 + 2(-3x^2 + 5x) - 4)) + 1) + 1)/(2(2e^(1(-1(-3x^2 + 5x)^2 + 2(-3x^2 + 5x) - 4)) + 1) + 1))) 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": "30.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3(4(-2|((-1(-1|(3|x + 3| - 3) + 3| + 1) + 3)/(2(-1|(3|x + 3| - 3) + 3| + 1) - 1)) + 1| - 3)^2 - 3) - 4, g(x) = 2|(5((1(5((3x)/(-1x + 2)) - 3) - 3)/(-2(5((3x)/(-1x + 2)) - 3) - 3)) + 3) - 1| + 1, 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": "10.9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1|(-1((1(-2((-2(5x - 2) + 2)/(-2(5x - 2) - 3)) + 5) + 2)/(2(-2((-2(5x - 2) + 2)/(-2(5x - 2) - 3)) + 5)))^2 - 2((1(-2((-2(5x - 2) + 2)/(-2(5x - 2) - 3)) + 5) + 2)/(2(-2((-2(5x - 2) + 2)/(-2(5x - 2) - 3)) + 5))) + 1) - 1| - 3 and g(x) = 2|((-3(-2|(1|(1x - 5) - 3| - 1) - 1| + 2) + 3)/(2(-2|(1|(1x - 5) - 3| - 1) - 1| + 2) + 1)) + 3| + 2 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": "-0.7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2((-2(-1(-2e^(-1(-1|(-4x^2 - 5x + 1)|)))) - 3)/(1(-1(-2e^(-1(-1|(-4x^2 - 5x + 1)|)))) - 2)) + 1 and g(x) = -1|(2sin(3\u03c0((2((-3((-2x - 1)/(-2x + 3)) + 1)/(-1((-2x - 1)/(-2x + 3)) - 2)) + 1)/(1((-3((-2x - 1)/(-2x + 3)) + 1)/(-1((-2x - 1)/(-2x + 3)) - 2)) - 2)) + 3)) + 1| - 1 from x = 2.8 to 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) = -3|(1((1((3(-3(2sin(3\u03c0x - 1) - 1) - 2) - 3)/(-1(-3(2sin(3\u03c0x - 1) - 1) - 2) + 2)) + 3)/(-2((3(-3(2sin(3\u03c0x - 1) - 1) - 2) - 3)/(-1(-3(2sin(3\u03c0x - 1) - 1) - 2) + 2)) + 1)) - 2) + 1| - 3 and g(x) = -1((-2(-1e^(-1(-4(2x - 3) + 2)) + 1) + 3)/(-2(-1e^(-1(-4(2x - 3) + 2)) + 1) - 3)) - 4 from x = 0.8 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": "Determine the area of the region enclosed by the graphs of f(x) = -4(1|(-2cos(1\u03c0((2((-3(-5x^2 - 5x + 5) - 2)/(2(-5x^2 - 5x + 5) + 1)) - 1)/(-2((-3(-5x^2 - 5x + 5) - 2)/(2(-5x^2 - 5x + 5) + 1)))) + 3) - 1) - 2|)^2 + 3(1|(-2cos(1\u03c0((2((-3(-5x^2 - 5x + 5) - 2)/(2(-5x^2 - 5x + 5) + 1)) - 1)/(-2((-3(-5x^2 - 5x + 5) - 2)/(2(-5x^2 - 5x + 5) + 1)))) + 3) - 1) - 2|) and g(x) = -3((-1(-1|(-3(1|x - 1| + 3)^2 - 2(1|x - 1| + 3) - 5) - 3| + 3) + 2)/(3(-1|(-3(1|x - 1| + 3)^2 - 2(1|x - 1| + 3) - 5) - 3| + 3) - 2))^2 - 2((-1(-1|(-3(1|x - 1| + 3)^2 - 2(1|x - 1| + 3) - 5) - 3| + 3) + 2)/(3(-1|(-3(1|x - 1| + 3)^2 - 2(1|x - 1| + 3) - 5) - 3| + 3) - 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": "3.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2|(-3|(2|(-5((2(4x - 1) - 1)/(3(4x - 1) - 2))^2 - 1((2(4x - 1) - 1)/(3(4x - 1) - 2)) + 1) + 2| - 1)| + 1) - 1| and g(x) = -1|(1|(2((-1((3x + 2)/(-3x + 4)) + 3)/(2((3x + 2)/(-3x + 4)) + 2)) - 3) + 2| + 2) - 2| - 3 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": "1.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -5(3|((-3(2cos(3\u03c0(2|(2x^2 + 5x - 3) + 3| + 1) - 1) - 1) + 2)/(2(2cos(3\u03c0(2|(2x^2 + 5x - 3) + 3| + 1) - 1) - 1))) - 2|) + 1 and g(x) = -1|(2|(3|(-3(-2cos(1\u03c0x - 3) - 3)^2 - 3(-2cos(1\u03c0x - 3) - 3) - 5) - 3| - 3) - 2| + 1) - 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": "4.9", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2|(2(-1cos(2\u03c0(-4(5(-1|x + 3| + 3) - 5) - 4)) - 3)^2 + 3) - 2| + 2 and g(x) = 2e^(2(-2(-1(-4(-1|x + 1| + 2) - 5)^2 - 5(-4(-1|x + 1| + 2) - 5) - 1)^2 - 4(-1(-4(-1|x + 1| + 2) - 5)^2 - 5(-4(-1|x + 1| + 2) - 5) - 1))) - 1 between the vertical lines x = -4.3 and x = -4.2. 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": "Calculate the area enclosed between the functions f(x) = 1|(3cos(2\u03c0(4(-4(3(1x + 1)^2 + 1(1x + 1) - 4) + 4) + 2)) - 1) - 2| + 2 and g(x) = (2(-1((1(2e^(-1(2x - 5)) - 1) - 2)/(-1(2e^(-1(2x - 5)) - 1) - 2))) + 1)/(-3(-1((1(2e^(-1(2x - 5)) - 1) - 2)/(-1(2e^(-1(2x - 5)) - 1) - 2))) + 1) 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": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (2(3((-1((-2(4((-2x - 2)/(1x + 2)) + 3) - 1)/(-2(4((-2x - 2)/(1x + 2)) + 3))) - 3)/(2((-2(4((-2x - 2)/(1x + 2)) + 3) - 1)/(-2(4((-2x - 2)/(1x + 2)) + 3))) - 1))^2 - 5((-1((-2(4((-2x - 2)/(1x + 2)) + 3) - 1)/(-2(4((-2x - 2)/(1x + 2)) + 3))) - 3)/(2((-2(4((-2x - 2)/(1x + 2)) + 3) - 1)/(-2(4((-2x - 2)/(1x + 2)) + 3))) - 1)) - 4) - 1)/(1(3((-1((-2(4((-2x - 2)/(1x + 2)) + 3) - 1)/(-2(4((-2x - 2)/(1x + 2)) + 3))) - 3)/(2((-2(4((-2x - 2)/(1x + 2)) + 3) - 1)/(-2(4((-2x - 2)/(1x + 2)) + 3))) - 1))^2 - 5((-1((-2(4((-2x - 2)/(1x + 2)) + 3) - 1)/(-2(4((-2x - 2)/(1x + 2)) + 3))) - 3)/(2((-2(4((-2x - 2)/(1x + 2)) + 3) - 1)/(-2(4((-2x - 2)/(1x + 2)) + 3))) - 1)) - 4) + 3) and g(x) = (3((1(-3|((3(4x^2 - 2x - 5) + 3)/(3(4x^2 - 2x - 5) - 2)) + 2| + 3) - 1)/(-2(-3|((3(4x^2 - 2x - 5) + 3)/(3(4x^2 - 2x - 5) - 2)) + 2| + 3) - 2)))/(-2((1(-3|((3(4x^2 - 2x - 5) + 3)/(3(4x^2 - 2x - 5) - 2)) + 2| + 3) - 1)/(-2(-3|((3(4x^2 - 2x - 5) + 3)/(3(4x^2 - 2x - 5) - 2)) + 2| + 3) - 2))) 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": "4.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1((-3(-2(3(2|(4x + 4) - 2|) - 2)^2 - 1(3(2|(4x + 4) - 2|) - 2) - 1) - 3)/(1(-2(3(2|(4x + 4) - 2|) - 2)^2 - 1(3(2|(4x + 4) - 2|) - 2) - 1) + 2)) - 3 and g(x) = -5((3(-4(-2(-2x^2 + 2x + 4)^2 - 3(-2x^2 + 2x + 4) - 3)^2 + 4(-2(-2x^2 + 2x + 4)^2 - 3(-2x^2 + 2x + 4) - 3) - 4) - 1)/(-2(-4(-2(-2x^2 + 2x + 4)^2 - 3(-2x^2 + 2x + 4) - 3)^2 + 4(-2(-2x^2 + 2x + 4)^2 - 3(-2x^2 + 2x + 4) - 3) - 4) + 1))^2 + 2((3(-4(-2(-2x^2 + 2x + 4)^2 - 3(-2x^2 + 2x + 4) - 3)^2 + 4(-2(-2x^2 + 2x + 4)^2 - 3(-2x^2 + 2x + 4) - 3) - 4) - 1)/(-2(-4(-2(-2x^2 + 2x + 4)^2 - 3(-2x^2 + 2x + 4) - 3)^2 + 4(-2(-2x^2 + 2x + 4)^2 - 3(-2x^2 + 2x + 4) - 3) - 4) + 1)) - 5 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": "3.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2(-1|(3e^(-2(-1(2(2x - 1) - 5) - 4)) - 3) - 2| + 1) + 5 and g(x) = (-1((2(3(1sin(2\u03c0(1|x| + 1) - 2) - 3)^2 + 4(1sin(2\u03c0(1|x| + 1) - 2) - 3) - 4) - 1)/(-2(3(1sin(2\u03c0(1|x| + 1) - 2) - 3)^2 + 4(1sin(2\u03c0(1|x| + 1) - 2) - 3) - 4) + 3)))/(1((2(3(1sin(2\u03c0(1|x| + 1) - 2) - 3)^2 + 4(1sin(2\u03c0(1|x| + 1) - 2) - 3) - 4) - 1)/(-2(3(1sin(2\u03c0(1|x| + 1) - 2) - 3)^2 + 4(1sin(2\u03c0(1|x| + 1) - 2) - 3) - 4) + 3)) + 2) between the vertical lines x = -4.7 and x = -4.4. 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": "Calculate the area enclosed between the functions f(x) = -4((2((-2(3|(-2cos(3\u03c0((1x)/(2x + 3)) + 1) + 1) + 2|))/(1(3|(-2cos(3\u03c0((1x)/(2x + 3)) + 1) + 1) + 2|) + 1)) + 2)/(-1((-2(3|(-2cos(3\u03c0((1x)/(2x + 3)) + 1) + 1) + 2|))/(1(3|(-2cos(3\u03c0((1x)/(2x + 3)) + 1) + 1) + 2|) + 1)) - 3)) + 5 and g(x) = (2(-5(2(1(1|x + 2| - 2)^2 + 1(1|x + 2| - 2) + 1)^2 + 3(1(1|x + 2| - 2)^2 + 1(1|x + 2| - 2) + 1) + 3) + 4) + 2)/(-2(-5(2(1(1|x + 2| - 2)^2 + 1(1|x + 2| - 2) + 1)^2 + 3(1(1|x + 2| - 2)^2 + 1(1|x + 2| - 2) + 1) + 3) + 4)) from x = -1.4 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": "Calculate the area enclosed between the functions f(x) = -3(2(1(-4(-2cos(2\u03c0(1|x - 1| + 1) + 1) + 1) - 3)^2 + 4(-4(-2cos(2\u03c0(1|x - 1| + 1) + 1) + 1) - 3) + 2) + 2) + 1 and g(x) = 2|(-1|(2|(-2(-3|x - 1| + 3)^2 + 3(-3|x - 1| + 3)) - 1| - 3) + 3| - 3) + 1| - 3 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": "6.6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3e^(1((-1(5(5(-1(-4x - 3) - 4)^2 + 3(-1(-4x - 3) - 4) + 1)^2 - 5(5(-1(-4x - 3) - 4)^2 + 3(-1(-4x - 3) - 4) + 1) + 2) - 2)/(1(5(5(-1(-4x - 3) - 4)^2 + 3(-1(-4x - 3) - 4) + 1)^2 - 5(5(-1(-4x - 3) - 4)^2 + 3(-1(-4x - 3) - 4) + 1) + 2) + 3))) + 2 and g(x) = 5(-3|((1((-2(-2x^2 + 1x + 4) + 3)/(-3(-2x^2 + 1x + 4) + 2)) - 3)/(-1((-2(-2x^2 + 1x + 4) + 3)/(-3(-2x^2 + 1x + 4) + 2)) - 3)) - 3|)^2 - 2(-3|((1((-2(-2x^2 + 1x + 4) + 3)/(-3(-2x^2 + 1x + 4) + 2)) - 3)/(-1((-2(-2x^2 + 1x + 4) + 3)/(-3(-2x^2 + 1x + 4) + 2)) - 3)) - 3|) - 5 from x = -1.0 to x = -0.9. 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) = 5((-1((-2((-3(2|(-1cos(1\u03c0x) + 3) - 2| - 1) + 2)/(3(2|(-1cos(1\u03c0x) + 3) - 2| - 1) - 1)) + 3)/(2((-3(2|(-1cos(1\u03c0x) + 3) - 2| - 1) + 2)/(3(2|(-1cos(1\u03c0x) + 3) - 2| - 1) - 1)) + 3)) - 1)/(1((-2((-3(2|(-1cos(1\u03c0x) + 3) - 2| - 1) + 2)/(3(2|(-1cos(1\u03c0x) + 3) - 2| - 1) - 1)) + 3)/(2((-3(2|(-1cos(1\u03c0x) + 3) - 2| - 1) + 2)/(3(2|(-1cos(1\u03c0x) + 3) - 2| - 1) - 1)) + 3)))) + 2 and g(x) = 2|(-4((-2(-1((3x - 2)/(-1x + 2))^2 - 1((3x - 2)/(-1x + 2))) - 1)/(-1(-1((3x - 2)/(-1x + 2))^2 - 1((3x - 2)/(-1x + 2))) + 2)) - 1) - 1| + 1 from x = 1.6 to x = 2.4. 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) = -2(3(2|(2(-1e^(1((2x - 1)/(2x + 1))) + 3) - 2) - 3| - 1)) - 3, g(x) = 5((1(5((-1(-3e^(2x) + 1) - 2)/(-2(-3e^(2x) + 1) + 3))^2 + 1((-1(-3e^(2x) + 1) - 2)/(-2(-3e^(2x) + 1) + 3)) + 4) - 2)/(2(5((-1(-3e^(2x) + 1) - 2)/(-2(-3e^(2x) + 1) + 3))^2 + 1((-1(-3e^(2x) + 1) - 2)/(-2(-3e^(2x) + 1) + 3)) + 4) + 3)) - 1, 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": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -3((-1(-3(-1|(1(-3|x| - 2) - 4) + 3| + 2)^2 + 5(-1|(1(-3|x| - 2) - 4) + 3| + 2) - 5) - 1)/(-3(-3(-1|(1(-3|x| - 2) - 4) + 3| + 2)^2 + 5(-1|(1(-3|x| - 2) - 4) + 3| + 2) - 5) + 2))^2 + 3((-1(-3(-1|(1(-3|x| - 2) - 4) + 3| + 2)^2 + 5(-1|(1(-3|x| - 2) - 4) + 3| + 2) - 5) - 1)/(-3(-3(-1|(1(-3|x| - 2) - 4) + 3| + 2)^2 + 5(-1|(1(-3|x| - 2) - 4) + 3| + 2) - 5) + 2)) - 4, g(x) = (1(-2|((2((-1(-2|x| + 1) + 3)/(2(-2|x| + 1) + 2)) + 2)/(-2((-1(-2|x| + 1) + 3)/(2(-2|x| + 1) + 2)) + 3)) - 3|) + 3)/(3(-2|((2((-1(-2|x| + 1) + 3)/(2(-2|x| + 1) + 2)) + 2)/(-2((-1(-2|x| + 1) + 3)/(2(-2|x| + 1) + 2)) + 3)) - 3|) + 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": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -5(-1(-1((1((3(-1|x - 3| - 2) + 3)/(1(-1|x - 3| - 2) + 1)) - 3)/(-1((3(-1|x - 3| - 2) + 3)/(1(-1|x - 3| - 2) + 1)) + 2)) + 5)^2 + 5(-1((1((3(-1|x - 3| - 2) + 3)/(1(-1|x - 3| - 2) + 1)) - 3)/(-1((3(-1|x - 3| - 2) + 3)/(1(-1|x - 3| - 2) + 1)) + 2)) + 5) - 3) - 3 and g(x) = 1|(-2(-2((2(-1|x + 3| + 3) - 2)/(1(-1|x + 3| + 3) - 2)) - 4)^2 - 1(-2((2(-1|x + 3| + 3) - 2)/(1(-1|x + 3| + 3) - 2)) - 4) - 3) - 3| - 1 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": "195.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1|((2(3(-1|(-5(-1x + 4)^2 - 1(-1x + 4) + 5) + 2| - 3) - 2) - 1)/(-2(3(-1|(-5(-1x + 4)^2 - 1(-1x + 4) + 5) + 2| - 3) - 2))) + 1| - 2, g(x) = 5(4(-3(-3sin(2\u03c0(5x + 5) - 3)) + 5) - 4) + 2, x = 2.7, 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": "19.7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (1(-1|((-3(-3|((-1((-1x + 3)/(-2x - 3)) - 1)/(-1((-1x + 3)/(-2x - 3)) - 3)) - 3| - 2) - 2)/(3(-3|((-1((-1x + 3)/(-2x - 3)) - 1)/(-1((-1x + 3)/(-2x - 3)) - 3)) - 3| - 2) + 2)) - 1|) + 1)/(-3(-1|((-3(-3|((-1((-1x + 3)/(-2x - 3)) - 1)/(-1((-1x + 3)/(-2x - 3)) - 3)) - 3| - 2) - 2)/(3(-3|((-1((-1x + 3)/(-2x - 3)) - 1)/(-1((-1x + 3)/(-2x - 3)) - 3)) - 3| - 2) + 2)) - 1|) - 2) and g(x) = 2|(-3|(3|(-2((1x)/(2x - 3)) + 5) + 3| - 1) - 1| + 3) - 3| - 2 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": "0.9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (2(-2|((-2(-4(2|((2x + 2)/(-3x + 4))| + 1)^2 + 5(2|((2x + 2)/(-3x + 4))| + 1) + 1))/(3(-4(2|((2x + 2)/(-3x + 4))| + 1)^2 + 5(2|((2x + 2)/(-3x + 4))| + 1) + 1) - 2)) - 1| + 1) + 2)/(2(-2|((-2(-4(2|((2x + 2)/(-3x + 4))| + 1)^2 + 5(2|((2x + 2)/(-3x + 4))| + 1) + 1))/(3(-4(2|((2x + 2)/(-3x + 4))| + 1)^2 + 5(2|((2x + 2)/(-3x + 4))| + 1) + 1) - 2)) - 1| + 1) - 3) and g(x) = (3(2|(-1((-2((1x + 2)/(2x)) - 3)/(-3((1x + 2)/(2x)) - 3))^2 - 4((-2((1x + 2)/(2x)) - 3)/(-3((1x + 2)/(2x)) - 3)) - 1) - 2| - 3) - 3)/(-2(2|(-1((-2((1x + 2)/(2x)) - 3)/(-3((1x + 2)/(2x)) - 3))^2 - 4((-2((1x + 2)/(2x)) - 3)/(-3((1x + 2)/(2x)) - 3)) - 1) - 2| - 3)) from x = -1.9 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": "Calculate the area enclosed between the functions f(x) = -4((1(-1|((-3(-1(1|x - 1| - 3) - 3))/(-3(-1(1|x - 1| - 3) - 3) - 3)) - 1| + 3))/(-1(-1|((-3(-1(1|x - 1| - 3) - 3))/(-3(-1(1|x - 1| - 3) - 3) - 3)) - 1| + 3) + 2))^2 + 3((1(-1|((-3(-1(1|x - 1| - 3) - 3))/(-3(-1(1|x - 1| - 3) - 3) - 3)) - 1| + 3))/(-1(-1|((-3(-1(1|x - 1| - 3) - 3))/(-3(-1(1|x - 1| - 3) - 3) - 3)) - 1| + 3) + 2)) + 4 and g(x) = -4(-3sin(2\u03c0(1(3|((2x + 3)/(2x + 3)) - 2| - 1) - 2) - 2) + 3) - 3 from x = 1.3 to x = 2.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34.9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (2((-1((1(-1|(2|(5x^2 + 4x + 1) - 2| - 1) - 3| + 1))/(-2(-1|(2|(5x^2 + 4x + 1) - 2| - 1) - 3| + 1) + 3)) + 2)/(-3((1(-1|(2|(5x^2 + 4x + 1) - 2| - 1) - 3| + 1))/(-2(-1|(2|(5x^2 + 4x + 1) - 2| - 1) - 3| + 1) + 3)) + 1)) + 1)/(1((-1((1(-1|(2|(5x^2 + 4x + 1) - 2| - 1) - 3| + 1))/(-2(-1|(2|(5x^2 + 4x + 1) - 2| - 1) - 3| + 1) + 3)) + 2)/(-3((1(-1|(2|(5x^2 + 4x + 1) - 2| - 1) - 3| + 1))/(-2(-1|(2|(5x^2 + 4x + 1) - 2| - 1) - 3| + 1) + 3)) + 1)) + 3) and g(x) = -2e^(1(-2(-3|(1(-1x + 1) + 3) + 3| - 2)^2 + 4(-3|(1(-1x + 1) + 3) + 3| - 2) + 2)) from x = -1.3 to x = 0.5. 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|((1(-1(1((1(2|x - 2| - 2) + 2)/(-2(2|x - 2| - 2) - 1))^2 - 2((1(2|x - 2| - 2) + 2)/(-2(2|x - 2| - 2) - 1)) - 2)^2 + 5(1((1(2|x - 2| - 2) + 2)/(-2(2|x - 2| - 2) - 1))^2 - 2((1(2|x - 2| - 2) + 2)/(-2(2|x - 2| - 2) - 1)) - 2) + 3) + 1)/(-2(-1(1((1(2|x - 2| - 2) + 2)/(-2(2|x - 2| - 2) - 1))^2 - 2((1(2|x - 2| - 2) + 2)/(-2(2|x - 2| - 2) - 1)) - 2)^2 + 5(1((1(2|x - 2| - 2) + 2)/(-2(2|x - 2| - 2) - 1))^2 - 2((1(2|x - 2| - 2) + 2)/(-2(2|x - 2| - 2) - 1)) - 2) + 3) - 2)) + 2| and g(x) = (-2(-2|(-1(1(-5x^2 + 3x + 1) - 3)^2 - 2(1(-5x^2 + 3x + 1) - 3) + 3)| + 1) + 1)/(-1(-2|(-1(1(-5x^2 + 3x + 1) - 3)^2 - 2(1(-5x^2 + 3x + 1) - 3) + 3)| + 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": "1.8", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1((1(1(2|(5((-1x + 2)/(2x + 1)) + 1)| + 1)^2 + 1(2|(5((-1x + 2)/(2x + 1)) + 1)| + 1) + 2) + 1)/(1(1(2|(5((-1x + 2)/(2x + 1)) + 1)| + 1)^2 + 1(2|(5((-1x + 2)/(2x + 1)) + 1)| + 1) + 2) + 1)) + 2 and g(x) = 3cos(1\u03c0(-2|(3|(-5(1x + 4) - 4) + 1| + 1) + 3| - 3) + 3) + 1 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2(2|(3(-1(-5(1x^2 + 1x) + 5) + 3)^2 + 1(-1(-5(1x^2 + 1x) + 5) + 3) - 5) + 3|) + 5 and g(x) = 3|((-1(4(5(-2x^2 + 4) + 1) + 3) - 3)/(-1(4(5(-2x^2 + 4) + 1) + 3) - 1)) + 3| + 2 from x = -1.1 to x = 0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "72.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -5((-1(-3|((1((1(2x + 1) - 3)/(-1(2x + 1) + 2)) - 2)/(-1((1(2x + 1) - 3)/(-1(2x + 1) + 2)) - 3)) + 1| + 3) + 2)/(3(-3|((1((1(2x + 1) - 3)/(-1(2x + 1) + 2)) - 2)/(-1((1(2x + 1) - 3)/(-1(2x + 1) + 2)) - 3)) + 1| + 3) - 2)) + 4 and g(x) = 1sin(2\u03c0((2((-2(1(3|x| - 1)^2 + 3) - 2)/(2(1(3|x| - 1)^2 + 3) - 1)) - 1)/(-1((-2(1(3|x| - 1)^2 + 3) - 2)/(2(1(3|x| - 1)^2 + 3) - 1)) - 2)) + 2) + 2 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": "0.7", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2((1(1(-3|(-4((-3x - 1)/(-3x - 1)) - 2) - 1|)^2 - 5(-3|(-4((-3x - 1)/(-3x - 1)) - 2) - 1|) - 1))/(3(1(-3|(-4((-3x - 1)/(-3x - 1)) - 2) - 1|)^2 - 5(-3|(-4((-3x - 1)/(-3x - 1)) - 2) - 1|) - 1) - 2)) + 3, g(x) = 5((-3(-1cos(3\u03c0(-3((1x + 3)/(-1x + 3))^2 - 5((1x + 3)/(-1x + 3)) - 2) - 1) - 1) - 3)/(2(-1cos(3\u03c0(-3((1x + 3)/(-1x + 3))^2 - 5((1x + 3)/(-1x + 3)) - 2) - 1) - 1) + 3)) - 3, x = 4.4, 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": "2.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3(-3(2|((-2((1((1x + 3)/(3x)) - 3)/(-2((1x + 3)/(3x)) - 3)) - 1)/(-3((1((1x + 3)/(3x)) - 3)/(-2((1x + 3)/(3x)) - 3)) + 1)) + 2| - 3)), g(x) = -1|(1|((-2(3cos(3\u03c0(-1x^2 + 4x + 3) - 1) + 2) + 2)/(-3(3cos(3\u03c0(-1x^2 + 4x + 3) - 1) + 2))) - 1| - 1) - 1| + 3, x = 0.7, 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": "5.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 5(-2|((3(2e^(1(1(3x + 3)^2 + 5(3x + 3) + 3)) + 3) - 1)/(-1(2e^(1(1(3x + 3)^2 + 5(3x + 3) + 3)) + 3) + 2)) + 1| + 3)^2 + 5(-2|((3(2e^(1(1(3x + 3)^2 + 5(3x + 3) + 3)) + 3) - 1)/(-1(2e^(1(1(3x + 3)^2 + 5(3x + 3) + 3)) + 3) + 2)) + 1| + 3) + 3 and g(x) = -1((1(-1(1sin(1\u03c0(3|x - 3| - 3) - 2) - 2) - 5))/(1(-1(1sin(1\u03c0(3|x - 3| - 3) - 2) - 2) - 5) + 2))^2 + 5((1(-1(1sin(1\u03c0(3|x - 3| - 3) - 2) - 2) - 5))/(1(-1(1sin(1\u03c0(3|x - 3| - 3) - 2) - 2) - 5) + 2)) + 1 from x = 1.4 to x = 1.8. 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": "Determine the area of the region enclosed by the graphs of f(x) = 2|((-2(1(-1(2(3x - 2) - 1) + 4)) - 3)/(-2(1(-1(2(3x - 2) - 1) + 4)) - 1)) + 2| - 3 and g(x) = -1(3(2(3(4x^2 + 5x - 3) + 4) - 1) + 2) - 4 between the vertical lines x = -1.5 and x = 0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "58.9", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (1((-2(5(2cos(2\u03c0((3(1x - 2) - 3)/(-3(1x - 2) + 4)) + 1))^2 + 5(2cos(2\u03c0((3(1x - 2) - 3)/(-3(1x - 2) + 4)) + 1)) - 3) - 1)/(-2(5(2cos(2\u03c0((3(1x - 2) - 3)/(-3(1x - 2) + 4)) + 1))^2 + 5(2cos(2\u03c0((3(1x - 2) - 3)/(-3(1x - 2) + 4)) + 1)) - 3) - 2)) - 1)/(3((-2(5(2cos(2\u03c0((3(1x - 2) - 3)/(-3(1x - 2) + 4)) + 1))^2 + 5(2cos(2\u03c0((3(1x - 2) - 3)/(-3(1x - 2) + 4)) + 1)) - 3) - 1)/(-2(5(2cos(2\u03c0((3(1x - 2) - 3)/(-3(1x - 2) + 4)) + 1))^2 + 5(2cos(2\u03c0((3(1x - 2) - 3)/(-3(1x - 2) + 4)) + 1)) - 3) - 2)) + 1), g(x) = 1|(3|(5(-1(-2cos(3\u03c0x + 2) + 1) + 1)^2 - 5(-1(-2cos(3\u03c0x + 2) + 1) + 1) - 4) - 2| + 3) + 3| - 1, x = -2.0, 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": "112.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3(-2cos(2\u03c0(-1((2(3|(2x^2 - 2x) - 1|) - 3)/(-1(3|(2x^2 - 2x) - 1|) - 1)) - 1) - 2) + 1) + 1 and g(x) = (1((2(-1(-2|(2e^(-1x)) + 3| + 2) + 1) + 3)/(3(-1(-2|(2e^(-1x)) + 3| + 2) + 1) - 1)) + 1)/(-3((2(-1(-2|(2e^(-1x)) + 3| + 2) + 1) + 3)/(3(-1(-2|(2e^(-1x)) + 3| + 2) + 1) - 1)) - 3) between the vertical lines x = -0.4 and x = -0.30000000000000004. 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) = 5(-2|((3((2(-4(-5x - 3)^2) + 3)/(3(-4(-5x - 3)^2) + 2)) + 2)/(-2((2(-4(-5x - 3)^2) + 3)/(3(-4(-5x - 3)^2) + 2)) + 1)) - 3| - 3) + 2 and g(x) = 5(1(-2(-2|(-4x^2 - 3x + 1)| - 1)^2 + 4(-2|(-4x^2 - 3x + 1)| - 1)) + 2) + 3 from x = -0.4 to x = -0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "192.7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1(3|((3(-1(1(-1x^2 + 2x - 5)^2 - 1(-1x^2 + 2x - 5) + 4) + 5) + 2)/(-2(-1(1(-1x^2 + 2x - 5)^2 - 1(-1x^2 + 2x - 5) + 4) + 5) + 3)) + 1| - 2)^2 + 3(3|((3(-1(1(-1x^2 + 2x - 5)^2 - 1(-1x^2 + 2x - 5) + 4) + 5) + 2)/(-2(-1(1(-1x^2 + 2x - 5)^2 - 1(-1x^2 + 2x - 5) + 4) + 5) + 3)) + 1| - 2) + 2 and g(x) = -2|(-4((-3((-1(-3x^2 - 5x + 4) + 3)/(1(-3x^2 - 5x + 4) + 3)))/(-1((-1(-3x^2 - 5x + 4) + 3)/(1(-3x^2 - 5x + 4) + 3)) - 1))) + 1| + 1 from x = -1.9 to x = 0.2. 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(2sin(1\u03c0(-1(-1(2(5x^2 - 1x + 2) - 2) + 4) - 2) + 3) + 2)^2 + 3(2sin(1\u03c0(-1(-1(2(5x^2 - 1x + 2) - 2) + 4) - 2) + 3) + 2) + 2, g(x) = 5(1(2(-1(1sin(1\u03c0x - 2) - 1)^2 + 5(1sin(1\u03c0x - 2) - 1) + 5)^2 - 1(-1(1sin(1\u03c0x - 2) - 1)^2 + 5(1sin(1\u03c0x - 2) - 1) + 5) - 4)^2 + 3(2(-1(1sin(1\u03c0x - 2) - 1)^2 + 5(1sin(1\u03c0x - 2) - 1) + 5)^2 - 1(-1(1sin(1\u03c0x - 2) - 1)^2 + 5(1sin(1\u03c0x - 2) - 1) + 5) - 4)), 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": "2.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (2(1(-3|(-2(2|(-1|x - 2|) - 1|) - 1) - 1| - 1)^2 - 5(-3|(-2(2|(-1|x - 2|) - 1|) - 1) - 1| - 1) + 3) - 2)/(1(1(-3|(-2(2|(-1|x - 2|) - 1|) - 1) - 1| - 1)^2 - 5(-3|(-2(2|(-1|x - 2|) - 1|) - 1) - 1| - 1) + 3)) and g(x) = 2|((1(-5(3|(-2x + 4)| - 3) - 4) + 1)/(2(-5(3|(-2x + 4)| - 3) - 4) - 3)) - 3| - 3 from x = 1.7 to x = 2.3. 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) = -4(-3(2cos(1\u03c0(2|(-3|(3|x - 3| + 1) - 1| + 2) - 3|) - 2) - 1)^2 + 5)^2 + 4(-3(2cos(1\u03c0(2|(-3|(3|x - 3| + 1) - 1| + 2) - 3|) - 2) - 1)^2 + 5) + 2 and g(x) = 1|(-3sin(2\u03c0((-2(-1|((1x + 1)/(-3x - 2)) - 1|))/(-1(-1|((1x + 1)/(-3x - 2)) - 1|) - 2)) - 2) - 3) + 2| + 2 between the vertical lines x = -0.8 and x = -0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "97.7", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2((1(3|(-3(1|((-1x - 3)/(-2x + 1))| - 2) + 5) + 3|) + 2)/(-2(3|(-3(1|((-1x - 3)/(-2x + 1))| - 2) + 5) + 3|) - 1)) - 3 and g(x) = -5(1sin(3\u03c0(-2|((-1(1|x - 1| - 2) - 1)/(-2(1|x - 1| - 2) + 3)) - 3| + 3) - 2) + 2)^2 + 1(1sin(3\u03c0(-2|((-1(1|x - 1| - 2) - 1)/(-2(1|x - 1| - 2) + 3)) - 3| + 3) - 2) + 2) + 4 between the vertical lines x = -0.7 and 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": "Calculate the area enclosed between the functions f(x) = 3|((3(-5(-2|(-3sin(1\u03c0(4x - 1) + 1) - 1)| + 2)^2 - 5(-2|(-3sin(1\u03c0(4x - 1) + 1) - 1)| + 2) + 1) - 1)/(-1(-5(-2|(-3sin(1\u03c0(4x - 1) + 1) - 1)| + 2)^2 - 5(-2|(-3sin(1\u03c0(4x - 1) + 1) - 1)| + 2) + 1) + 2)) - 1| - 1 and g(x) = -1|(-3((1(3|((-3x - 3)/(1x + 2)) - 3| + 3) + 3)/(-3(3|((-3x - 3)/(1x + 2)) - 3| + 3) - 1))^2) + 2| + 1 from x = -5.0 to x = -4.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1(1|(2(4(1(1|x + 1| + 3) - 3) - 4) + 5)| - 1)^2 - 4(1|(2(4(1(1|x + 1| + 3) - 3) - 4) + 5)| - 1) + 1, g(x) = (-3((-1(1|(-3sin(3\u03c0(-2|x + 3| - 1) - 3) - 2)| - 1) + 2)/(-3(1|(-3sin(3\u03c0(-2|x + 3| - 1) - 3) - 2)| - 1) - 2)) - 2)/(2((-1(1|(-3sin(3\u03c0(-2|x + 3| - 1) - 3) - 2)| - 1) + 2)/(-3(1|(-3sin(3\u03c0(-2|x + 3| - 1) - 3) - 2)| - 1) - 2)) - 1), x = -1.6, 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-1(3|(-2|(-2sin(1\u03c0(-3((-3x - 3)/(3x + 1))^2 + 3((-3x - 3)/(3x + 1))) - 2) + 2) - 1|) + 3| + 3) + 1)/(2(3|(-2|(-2sin(1\u03c0(-3((-3x - 3)/(3x + 1))^2 + 3((-3x - 3)/(3x + 1))) - 2) + 2) - 1|) + 3| + 3) + 3) and g(x) = 5(-1|(3|(1cos(3\u03c0(4x^2 - 4x) - 1) - 1) + 3| - 3) - 3| + 1)^2 + 2(-1|(3|(1cos(3\u03c0(4x^2 - 4x) - 1) - 1) + 3| - 3) - 3| + 1) - 4 between the vertical lines x = -2.1 and x = -2.0. 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": "Determine the area of the region enclosed by the graphs of f(x) = -2(-4(-2|((1(1sin(2\u03c0((3x - 1)/(-2x - 1)) + 3) - 2))/(-2(1sin(2\u03c0((3x - 1)/(-2x - 1)) + 3) - 2))) + 1| + 1)^2 + 3(-2|((1(1sin(2\u03c0((3x - 1)/(-2x - 1)) + 3) - 2))/(-2(1sin(2\u03c0((3x - 1)/(-2x - 1)) + 3) - 2))) + 1| + 1) + 3)^2 - 4(-4(-2|((1(1sin(2\u03c0((3x - 1)/(-2x - 1)) + 3) - 2))/(-2(1sin(2\u03c0((3x - 1)/(-2x - 1)) + 3) - 2))) + 1| + 1)^2 + 3(-2|((1(1sin(2\u03c0((3x - 1)/(-2x - 1)) + 3) - 2))/(-2(1sin(2\u03c0((3x - 1)/(-2x - 1)) + 3) - 2))) + 1| + 1) + 3) - 3 and g(x) = (-1(-1|(2(1(-2|x - 3| + 2) + 2)^2 - 3(1(-2|x - 3| + 2) + 2) - 1) + 2| + 2) - 2)/(2(-1|(2(1(-2|x - 3| + 2) + 2)^2 - 3(1(-2|x - 3| + 2) + 2) - 1) + 2| + 2) - 1) 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": "84.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-2(-2e^(1(-2|(-2(-2(-1x + 4) + 4) - 1) - 2| + 1)) + 3) + 2)/(3(-2e^(1(-2|(-2(-2(-1x + 4) + 4) - 1) - 2| + 1)) + 3) + 2) and g(x) = -2(3((-2(2(1e^(-1x) - 1) - 2) + 3)/(3(2(1e^(-1x) - 1) - 2) + 3)) - 4) - 2 from x = -0.7 to x = 1.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "103.4", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (2((1(-1(-2cos(2\u03c0(-3|(-2x^2 + 1x - 1) - 3| - 2) + 3))^2 - 5(-2cos(2\u03c0(-3|(-2x^2 + 1x - 1) - 3| - 2) + 3)) + 5) + 1)/(-1(-1(-2cos(2\u03c0(-3|(-2x^2 + 1x - 1) - 3| - 2) + 3))^2 - 5(-2cos(2\u03c0(-3|(-2x^2 + 1x - 1) - 3| - 2) + 3)) + 5) - 2)) + 3)/(-1((1(-1(-2cos(2\u03c0(-3|(-2x^2 + 1x - 1) - 3| - 2) + 3))^2 - 5(-2cos(2\u03c0(-3|(-2x^2 + 1x - 1) - 3| - 2) + 3)) + 5) + 1)/(-1(-1(-2cos(2\u03c0(-3|(-2x^2 + 1x - 1) - 3| - 2) + 3))^2 - 5(-2cos(2\u03c0(-3|(-2x^2 + 1x - 1) - 3| - 2) + 3)) + 5) - 2)) - 3) and g(x) = 1|(-2sin(2\u03c0(-3|((-2(1x^2 - 5x - 3) + 3)/(-2(1x^2 - 5x - 3) - 1)) - 3| - 3) - 1) - 1) - 3| between the vertical lines x = -4.0 and x = -3.8. 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": "Calculate the area enclosed between the functions f(x) = 3((2(-3cos(2\u03c0(-1|((-3((2x + 1)/(2x - 1)) + 1)/(3((2x + 1)/(2x - 1)) + 2))| + 1) + 2) - 3) + 1)/(1(-3cos(2\u03c0(-1|((-3((2x + 1)/(2x - 1)) + 1)/(3((2x + 1)/(2x - 1)) + 2))| + 1) + 2) - 3))) + 3 and g(x) = (3(-4((-3(2cos(2\u03c0(-3|x| - 2) - 2) + 3) + 2)/(2(2cos(2\u03c0(-3|x| - 2) - 2) + 3) + 1))^2 + 5((-3(2cos(2\u03c0(-3|x| - 2) - 2) + 3) + 2)/(2(2cos(2\u03c0(-3|x| - 2) - 2) + 3) + 1)) + 5) - 1)/(-1(-4((-3(2cos(2\u03c0(-3|x| - 2) - 2) + 3) + 2)/(2(2cos(2\u03c0(-3|x| - 2) - 2) + 3) + 1))^2 + 5((-3(2cos(2\u03c0(-3|x| - 2) - 2) + 3) + 2)/(2(2cos(2\u03c0(-3|x| - 2) - 2) + 3) + 1)) + 5) + 2) from x = -0.8 to x = -0.7. 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) = 3cos(2\u03c0(3(2(4(-4(2|x - 1| + 3)^2 - 3(2|x - 1| + 3) - 2) - 3) + 3) - 1)) + 2 and g(x) = -2|(-1|(1e^(1(2(-3|x + 1| - 2) + 1)) - 1) + 2| - 3) + 2| + 3 between the vertical lines x = 1.3 and x = 1.4. 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": "Determine the area of the region enclosed by the graphs of f(x) = 1((1(-4(-1cos(2\u03c0(-2(-2x + 2)^2 + 2(-2x + 2) - 4) - 3) - 2) - 4) - 3)/(2(-4(-1cos(2\u03c0(-2(-2x + 2)^2 + 2(-2x + 2) - 4) - 3) - 2) - 4) - 1))^2 + 5((1(-4(-1cos(2\u03c0(-2(-2x + 2)^2 + 2(-2x + 2) - 4) - 3) - 2) - 4) - 3)/(2(-4(-1cos(2\u03c0(-2(-2x + 2)^2 + 2(-2x + 2) - 4) - 3) - 2) - 4) - 1)) + 1 and g(x) = 1cos(3\u03c0(-4(-1|(-4(-5x + 1) - 5)| + 3) + 3) - 3) + 3 between the vertical lines x = -3.6 and x = -3.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "25.4", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 5(-1cos(1\u03c0(-1(-1(-5(1|x + 2| - 3)^2 - 2(1|x + 2| - 3) - 4)^2 + 1))) - 1) + 2, g(x) = 2(1|(4((-2(-5x - 2) + 3)/(1(-5x - 2))) + 5) - 1| + 1)^2 - 5(1|(4((-2(-5x - 2) + 3)/(1(-5x - 2))) + 5) - 1| + 1) + 4, 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": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (2(2|(4(2(2|(-1|x - 2| + 2) + 1| - 1)^2 - 5(2|(-1|x - 2| + 2) + 1| - 1) - 2)^2 - 2(2(2|(-1|x - 2| + 2) + 1| - 1)^2 - 5(2|(-1|x - 2| + 2) + 1| - 1) - 2) - 1) + 2|) + 3)/(-3(2|(4(2(2|(-1|x - 2| + 2) + 1| - 1)^2 - 5(2|(-1|x - 2| + 2) + 1| - 1) - 2)^2 - 2(2(2|(-1|x - 2| + 2) + 1| - 1)^2 - 5(2|(-1|x - 2| + 2) + 1| - 1) - 2) - 1) + 2|) + 2), g(x) = -3|(1((-1(5((-2x + 1)/(3x + 3)) - 5) - 3)/(1(5((-2x + 1)/(3x + 3)) - 5) - 2)) - 5) + 3| + 2, 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) = 1(-2|(-1|(-1(2|(4x - 4) + 2| - 3)^2 + 1(2|(4x - 4) + 2| - 3) - 2) + 3|) - 2|) - 5 and g(x) = (2(4((-1(-3(-3sin(3\u03c0x + 3) - 3) + 4) - 1)/(2(-3(-3sin(3\u03c0x + 3) - 3) + 4) + 1)) + 4) + 3)/(-2(4((-1(-3(-3sin(3\u03c0x + 3) - 3) + 4) - 1)/(2(-3(-3sin(3\u03c0x + 3) - 3) + 4) + 1)) + 4) + 3) between the vertical lines x = 0.2 and x = 0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.9", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2|(5(-1(-1|((-2((-2x)/(1x + 1)) - 3)/(2((-2x)/(1x + 1)) + 1)) + 1| + 3)^2 - 4(-1|((-2((-2x)/(1x + 1)) - 3)/(2((-2x)/(1x + 1)) + 1)) + 1| + 3)) - 4) + 1| - 2, g(x) = 4(4(3|(-1(-1|x + 3| - 3)) + 3| + 2) + 1) + 4, 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": "-1295.8", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (2(-1(1|((3((-3((2x + 1)/(1x + 3)) - 3)/(2((2x + 1)/(1x + 3)) - 1)))/(1((-3((2x + 1)/(1x + 3)) - 3)/(2((2x + 1)/(1x + 3)) - 1)) + 3)) + 2| - 3)) - 2)/(1(-1(1|((3((-3((2x + 1)/(1x + 3)) - 3)/(2((2x + 1)/(1x + 3)) - 1)))/(1((-3((2x + 1)/(1x + 3)) - 3)/(2((2x + 1)/(1x + 3)) - 1)) + 3)) + 2| - 3))), g(x) = (2(-3sin(1\u03c0(-1((-3(1|x - 1|) + 3)/(3(1|x - 1|) - 2)) - 3) - 2)) + 1)/(1(-3sin(1\u03c0(-1((-3(1|x - 1|) + 3)/(3(1|x - 1|) - 2)) - 3) - 2)) + 3), x = -3.0, 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (2(3(-2(1|(-1(-3|x - 3| + 2)^2 - 2(-3|x - 3| + 2)) - 2| + 1) + 4)) + 2)/(2(3(-2(1|(-1(-3|x - 3| + 2)^2 - 2(-3|x - 3| + 2)) - 2| + 1) + 4)) + 3) and g(x) = (-1(-1|(3(-2|(-1cos(3\u03c0x) - 1)|)^2 - 1(-2|(-1cos(3\u03c0x) - 1)|) - 2) - 2| - 3) - 3)/(-2(-1|(3(-2|(-1cos(3\u03c0x) - 1)|)^2 - 1(-2|(-1cos(3\u03c0x) - 1)|) - 2) - 2| - 3) + 3) 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) = -3|(-1|(2(-1((2(-1|x - 2| + 2) - 1)/(3(-1|x - 2| + 2) - 2)) + 4) - 3) - 1| + 2) + 2| - 2 and g(x) = -5(1((1(3sin(3\u03c0(-1x + 1) - 1) - 3) - 2)/(2(3sin(3\u03c0(-1x + 1) - 1) - 3) - 1))^2 + 2)^2 - 3(1((1(3sin(3\u03c0(-1x + 1) - 1) - 3) - 2)/(2(3sin(3\u03c0(-1x + 1) - 1) - 3) - 1))^2 + 2) - 5 from x = 0.7 to x = 0.7999999999999999. 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|(1cos(1\u03c0((3(3|(-1(-1x^2 + 4) + 2)| - 3) - 2)/(-3(3|(-1(-1x^2 + 4) + 2)| - 3) + 1)) + 2) + 1) - 2| - 2 and g(x) = -1|(2|((1((-2(2x^2 + 1x - 4) - 2)/(3(2x^2 + 1x - 4) - 2)) + 2)/(-2((-2(2x^2 + 1x - 4) - 2)/(3(2x^2 + 1x - 4) - 2)) + 3)) - 2| - 3)| - 1 from x = -1.8 to x = -1.7. 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": "Determine the area of the region enclosed by the graphs of f(x) = (1(2(-5((-1(-5(1x^2 + 4x) - 3) + 2)/(-1(-5(1x^2 + 4x) - 3)))^2 + 2((-1(-5(1x^2 + 4x) - 3) + 2)/(-1(-5(1x^2 + 4x) - 3))) + 2) + 3) + 3)/(2(2(-5((-1(-5(1x^2 + 4x) - 3) + 2)/(-1(-5(1x^2 + 4x) - 3)))^2 + 2((-1(-5(1x^2 + 4x) - 3) + 2)/(-1(-5(1x^2 + 4x) - 3))) + 2) + 3) - 1) and g(x) = -2|((-2(-5(-1sin(3\u03c0(4x^2 + 4x - 5) + 3))^2 - 5(-1sin(3\u03c0(4x^2 + 4x - 5) + 3)) + 3) + 2)/(2(-5(-1sin(3\u03c0(4x^2 + 4x - 5) + 3))^2 - 5(-1sin(3\u03c0(4x^2 + 4x - 5) + 3)) + 3) + 3))| + 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": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -5(-3cos(2\u03c0(-5(1(4(-3x - 5) + 2) + 5) + 1) + 3) + 1) + 1, g(x) = (1(-3|(-1(-2(-2|x + 3| - 3)^2 + 4(-2|x + 3| - 3) - 2)^2 - 1(-2(-2|x + 3| - 3)^2 + 4(-2|x + 3| - 3) - 2) + 4)|))/(-2(-3|(-1(-2(-2|x + 3| - 3)^2 + 4(-2|x + 3| - 3) - 2)^2 - 1(-2(-2|x + 3| - 3)^2 + 4(-2|x + 3| - 3) - 2) + 4)|) - 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": "1.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (1(-2|(-5(-3((-3(3cos(1\u03c0x + 1) - 2))/(-2(3cos(1\u03c0x + 1) - 2) - 2))^2 + 5((-3(3cos(1\u03c0x + 1) - 2))/(-2(3cos(1\u03c0x + 1) - 2) - 2)) + 3) - 4)| + 1) - 3)/(-1(-2|(-5(-3((-3(3cos(1\u03c0x + 1) - 2))/(-2(3cos(1\u03c0x + 1) - 2) - 2))^2 + 5((-3(3cos(1\u03c0x + 1) - 2))/(-2(3cos(1\u03c0x + 1) - 2) - 2)) + 3) - 4)| + 1) - 1), g(x) = -1(-3((-2(-2|(-3x^2 - 1x + 2) - 3| + 1) + 2)/(1(-2|(-3x^2 - 1x + 2) - 3| + 1)))^2 + 5((-2(-2|(-3x^2 - 1x + 2) - 3| + 1) + 2)/(1(-2|(-3x^2 - 1x + 2) - 3| + 1))) - 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": "2.7", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1((2((-1(2(-1(3x + 3) - 5)^2 - 5(-1(3x + 3) - 5) + 4))/(-1(2(-1(3x + 3) - 5)^2 - 5(-1(3x + 3) - 5) + 4))) + 3)/(3((-1(2(-1(3x + 3) - 5)^2 - 5(-1(3x + 3) - 5) + 4))/(-1(2(-1(3x + 3) - 5)^2 - 5(-1(3x + 3) - 5) + 4))) - 2)) - 4, g(x) = -4(-2|(-2e^(2((1(-3x + 1) - 3)/(3(-3x + 1) + 1))) + 3)| + 2)^2 + 5(-2|(-2e^(2((1(-3x + 1) - 3)/(3(-3x + 1) + 1))) + 3)| + 2) + 1, 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": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2|((-2(2sin(2\u03c0(-1(-5(3x)^2 - 3(3x) - 5)^2 - 3(-5(3x)^2 - 3(3x) - 5)) + 1)) + 2)/(3(2sin(2\u03c0(-1(-5(3x)^2 - 3(3x) - 5)^2 - 3(-5(3x)^2 - 3(3x) - 5)) + 1)) + 2)) - 2| + 2 and g(x) = 2sin(2\u03c0(2(-1(4((1x)/(-1x + 2)) + 2) + 5)^2 + 5(-1(4((1x)/(-1x + 2)) + 2) + 5) + 5) + 2) - 2 from x = 0.9 to x = 1.0. 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": "Determine the area of the region enclosed by the graphs of f(x) = (1(1cos(3\u03c0(2(4((-1((-1x + 1)/(-3x + 4)) - 1)/(3((-1x + 1)/(-3x + 4)) - 2))^2 - 3((-1((-1x + 1)/(-3x + 4)) - 1)/(3((-1x + 1)/(-3x + 4)) - 2)) + 1) + 1) + 1) + 2))/(1(1cos(3\u03c0(2(4((-1((-1x + 1)/(-3x + 4)) - 1)/(3((-1x + 1)/(-3x + 4)) - 2))^2 - 3((-1((-1x + 1)/(-3x + 4)) - 1)/(3((-1x + 1)/(-3x + 4)) - 2)) + 1) + 1) + 1) + 2) + 1) and g(x) = (1((-3(-1(-4(1x^2 + 2x - 1) - 2) - 5) + 1)/(-2(-1(-4(1x^2 + 2x - 1) - 2) - 5) + 3)) + 2)/(-2((-3(-1(-4(1x^2 + 2x - 1) - 2) - 5) + 1)/(-2(-1(-4(1x^2 + 2x - 1) - 2) - 5) + 3))) between the vertical lines x = -2.7 and x = 0.7. 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) = -3(-5(-2sin(1\u03c0(-1(2(-4x^2 - 1x) - 1)) + 3) - 2) + 5)^2 + 2(-5(-2sin(1\u03c0(-1(2(-4x^2 - 1x) - 1)) + 3) - 2) + 5) + 5 and g(x) = -3(-1(-1|(3|(-3|x - 1| + 2) - 1| - 2) + 3| - 2)^2 - 3(-1|(3|(-3|x - 1| + 2) - 1| - 2) + 3| - 2) - 4)^2 - 1(-1(-1|(3|(-3|x - 1| + 2) - 1| - 2) + 3| - 2)^2 - 3(-1|(3|(-3|x - 1| + 2) - 1| - 2) + 3| - 2) - 4) - 1 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": "84.7", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 4(4(-1(3(-2e^(-2(1|x + 1| - 3)) + 3) - 5)^2 + 2)) + 4, g(x) = 1e^(2(-5(1(5(-3|x + 2| + 3)^2 - 2(-3|x + 2| + 3) - 3) + 1) - 4)) - 3, x = -4.4, 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": "10.6", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-3((3(-3|((1((-3(-3e^(-2x)) + 2)/(2(-3e^(-2x)) - 1)) + 3)/(-3((-3(-3e^(-2x)) + 2)/(2(-3e^(-2x)) - 1)) + 4)) - 1|) - 3)/(-1(-3|((1((-3(-3e^(-2x)) + 2)/(2(-3e^(-2x)) - 1)) + 3)/(-3((-3(-3e^(-2x)) + 2)/(2(-3e^(-2x)) - 1)) + 4)) - 1|) + 2)) + 1)/(-1((3(-3|((1((-3(-3e^(-2x)) + 2)/(2(-3e^(-2x)) - 1)) + 3)/(-3((-3(-3e^(-2x)) + 2)/(2(-3e^(-2x)) - 1)) + 4)) - 1|) - 3)/(-1(-3|((1((-3(-3e^(-2x)) + 2)/(2(-3e^(-2x)) - 1)) + 3)/(-3((-3(-3e^(-2x)) + 2)/(2(-3e^(-2x)) - 1)) + 4)) - 1|) + 2)) - 2), g(x) = 4(-2|(-2sin(3\u03c0(3(1x^2 - 1x - 1)^2 + 3(1x^2 - 1x - 1) + 3) + 2) - 2)| - 1)^2 - 5(-2|(-2sin(3\u03c0(3(1x^2 - 1x - 1)^2 + 3(1x^2 - 1x - 1) + 3) + 2) - 2)| - 1) + 4, 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": "14.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (1(-5(-5(3cos(3\u03c0((2((3x - 3)/(-2x + 3)))/(-3((3x - 3)/(-2x + 3)) + 4)) + 1) + 3) + 2)^2 - 2(-5(3cos(3\u03c0((2((3x - 3)/(-2x + 3)))/(-3((3x - 3)/(-2x + 3)) + 4)) + 1) + 3) + 2) + 2) + 3)/(-3(-5(-5(3cos(3\u03c0((2((3x - 3)/(-2x + 3)))/(-3((3x - 3)/(-2x + 3)) + 4)) + 1) + 3) + 2)^2 - 2(-5(3cos(3\u03c0((2((3x - 3)/(-2x + 3)))/(-3((3x - 3)/(-2x + 3)) + 4)) + 1) + 3) + 2) + 2) + 1) and g(x) = 1((-2(1|(3(2x^2 - 5x + 4)^2 - 2(2x^2 - 5x + 4) - 1) + 1| + 1) + 2)/(2(1|(3(2x^2 - 5x + 4)^2 - 2(2x^2 - 5x + 4) - 1) + 1| + 1) + 2)) + 2 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": "2.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-3((2(-1(3e^(-2((-2(2x - 2) - 3)/(1(2x - 2) + 2)))) - 5))/(-2(-1(3e^(-2((-2(2x - 2) - 3)/(1(2x - 2) + 2)))) - 5) - 1)))/(1((2(-1(3e^(-2((-2(2x - 2) - 3)/(1(2x - 2) + 2)))) - 5))/(-2(-1(3e^(-2((-2(2x - 2) - 3)/(1(2x - 2) + 2)))) - 5) - 1))), g(x) = -3|(4(-1(-4(2e^(1x) - 1) - 3)^2 + 2(-4(2e^(1x) - 1) - 3) + 5)^2 + 4(-1(-4(2e^(1x) - 1) - 3)^2 + 2(-4(2e^(1x) - 1) - 3) + 5) - 5) - 2| + 3, x = -1.2, 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": "1.6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3(1(-1|((2(-3(-2|x + 3| - 3)^2 - 4(-2|x + 3| - 3) - 5) - 2)/(2(-3(-2|x + 3| - 3)^2 - 4(-2|x + 3| - 3) - 5) + 3))| + 2)^2 - 2(-1|((2(-3(-2|x + 3| - 3)^2 - 4(-2|x + 3| - 3) - 5) - 2)/(2(-3(-2|x + 3| - 3)^2 - 4(-2|x + 3| - 3) - 5) + 3))| + 2) + 5)^2 + 1 and g(x) = (-3((3((1(1|(-1x + 3) - 1| - 2) - 3)/(2(1|(-1x + 3) - 1| - 2) - 3)) - 3)/(1((1(1|(-1x + 3) - 1| - 2) - 3)/(2(1|(-1x + 3) - 1| - 2) - 3)) - 3)) + 1)/(-3((3((1(1|(-1x + 3) - 1| - 2) - 3)/(2(1|(-1x + 3) - 1| - 2) - 3)) - 3)/(1((1(1|(-1x + 3) - 1| - 2) - 3)/(2(1|(-1x + 3) - 1| - 2) - 3)) - 3)) - 1) from x = -0.4 to x = 4.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "222.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1((1(4(-2(-5(1x^2 - 3x) - 3)^2 - 5(-5(1x^2 - 3x) - 3) + 3) + 5) + 3)/(2(4(-2(-5(1x^2 - 3x) - 3)^2 - 5(-5(1x^2 - 3x) - 3) + 3) + 5))) + 1, g(x) = -5(2|(-3cos(1\u03c0(1|(-1|x - 1|) + 1| - 2) + 3) - 3) + 1|)^2 - 2(2|(-3cos(1\u03c0(1|(-1|x - 1|) + 1| - 2) + 3) - 3) + 1|) + 3, x = 1.7, 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": "7.8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2(-3(-4((2((-3(-3x - 4) + 1)/(-2(-3x - 4) + 3)) - 3)/(1((-3(-3x - 4) + 1)/(-2(-3x - 4) + 3)) - 3)) + 5)^2 + 5(-4((2((-3(-3x - 4) + 1)/(-2(-3x - 4) + 3)) - 3)/(1((-3(-3x - 4) + 1)/(-2(-3x - 4) + 3)) - 3)) + 5) + 5) + 5 and g(x) = -2sin(1\u03c0(1(-3(3|((1x + 3)/(2x + 1))| + 1) - 5) - 3) + 3) - 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (2((-2(-3((-3((1(3cos(2\u03c0x + 1) - 3) + 3)/(-1(3cos(2\u03c0x + 1) - 3) - 2)) - 3)/(1((1(3cos(2\u03c0x + 1) - 3) + 3)/(-1(3cos(2\u03c0x + 1) - 3) - 2))))^2 + 3((-3((1(3cos(2\u03c0x + 1) - 3) + 3)/(-1(3cos(2\u03c0x + 1) - 3) - 2)) - 3)/(1((1(3cos(2\u03c0x + 1) - 3) + 3)/(-1(3cos(2\u03c0x + 1) - 3) - 2)))) + 5))/(-1(-3((-3((1(3cos(2\u03c0x + 1) - 3) + 3)/(-1(3cos(2\u03c0x + 1) - 3) - 2)) - 3)/(1((1(3cos(2\u03c0x + 1) - 3) + 3)/(-1(3cos(2\u03c0x + 1) - 3) - 2))))^2 + 3((-3((1(3cos(2\u03c0x + 1) - 3) + 3)/(-1(3cos(2\u03c0x + 1) - 3) - 2)) - 3)/(1((1(3cos(2\u03c0x + 1) - 3) + 3)/(-1(3cos(2\u03c0x + 1) - 3) - 2)))) + 5) + 2)))/(1((-2(-3((-3((1(3cos(2\u03c0x + 1) - 3) + 3)/(-1(3cos(2\u03c0x + 1) - 3) - 2)) - 3)/(1((1(3cos(2\u03c0x + 1) - 3) + 3)/(-1(3cos(2\u03c0x + 1) - 3) - 2))))^2 + 3((-3((1(3cos(2\u03c0x + 1) - 3) + 3)/(-1(3cos(2\u03c0x + 1) - 3) - 2)) - 3)/(1((1(3cos(2\u03c0x + 1) - 3) + 3)/(-1(3cos(2\u03c0x + 1) - 3) - 2)))) + 5))/(-1(-3((-3((1(3cos(2\u03c0x + 1) - 3) + 3)/(-1(3cos(2\u03c0x + 1) - 3) - 2)) - 3)/(1((1(3cos(2\u03c0x + 1) - 3) + 3)/(-1(3cos(2\u03c0x + 1) - 3) - 2))))^2 + 3((-3((1(3cos(2\u03c0x + 1) - 3) + 3)/(-1(3cos(2\u03c0x + 1) - 3) - 2)) - 3)/(1((1(3cos(2\u03c0x + 1) - 3) + 3)/(-1(3cos(2\u03c0x + 1) - 3) - 2)))) + 5) + 2))) and g(x) = (-2(-1|((2(1(-2sin(1\u03c0x + 3))^2 - 3(-2sin(1\u03c0x + 3)) + 3) - 3)/(3(1(-2sin(1\u03c0x + 3))^2 - 3(-2sin(1\u03c0x + 3)) + 3) - 2)) - 1| + 1) - 1)/(3(-1|((2(1(-2sin(1\u03c0x + 3))^2 - 3(-2sin(1\u03c0x + 3)) + 3) - 3)/(3(1(-2sin(1\u03c0x + 3))^2 - 3(-2sin(1\u03c0x + 3)) + 3) - 2)) - 1| + 1)) between the vertical lines x = 4.2 and x = 4.9. 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) = -2(3|(-2|((-1(5(1x^2 + 3)^2 + 4) - 2)/(-3(5(1x^2 + 3)^2 + 4) + 1))| + 1) + 2| - 3) + 1 and g(x) = -1((-2(-1((2(-2e^(1x)) + 1)/(2(-2e^(1x))))^2 + 3) - 2)/(3(-1((2(-2e^(1x)) + 1)/(2(-2e^(1x))))^2 + 3) + 3))^2 - 4((-2(-1((2(-2e^(1x)) + 1)/(2(-2e^(1x))))^2 + 3) - 2)/(3(-1((2(-2e^(1x)) + 1)/(2(-2e^(1x))))^2 + 3) + 3)) + 2 from x = -3 to x = 3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "66.8", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-1(1(2e^(1((-2(-3(-3x^2 + 1x + 2) - 2) + 1)/(1(-3(-3x^2 + 1x + 2) - 2) - 3))) + 3) - 4) + 3)/(-3(1(2e^(1((-2(-3(-3x^2 + 1x + 2) - 2) + 1)/(1(-3(-3x^2 + 1x + 2) - 2) - 3))) + 3) - 4) - 3) and g(x) = 1sin(1\u03c0(1(-3(-3|(1x + 3) + 1| - 1) - 2)^2 - 1(-3(-3|(1x + 3) + 1| - 1) - 2) + 2) + 3) - 3 between the vertical lines x = 0.2 and x = 0.30000000000000004. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1|(-1(5(-1|((-1(4x + 5))/(2(4x + 5) - 3)) + 1| + 3) - 2) + 2) - 3| - 1, g(x) = 4(-1(-3e^(2(-3(-2x^2 + 2x + 2)^2 + 4(-2x^2 + 2x + 2) + 5)) + 2)^2 + 5(-3e^(2(-3(-2x^2 + 2x + 2)^2 + 4(-2x^2 + 2x + 2) + 5)) + 2) + 3) + 1, x = 0.1, 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": "39.7", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-2((-1((-2(-1(2(-1x^2 + 3x - 5)^2 + 3(-1x^2 + 3x - 5) - 5) + 3) - 2)/(2(-1(2(-1x^2 + 3x - 5)^2 + 3(-1x^2 + 3x - 5) - 5) + 3) + 1)))/(1((-2(-1(2(-1x^2 + 3x - 5)^2 + 3(-1x^2 + 3x - 5) - 5) + 3) - 2)/(2(-1(2(-1x^2 + 3x - 5)^2 + 3(-1x^2 + 3x - 5) - 5) + 3) + 1)) - 2)) + 2)/(1((-1((-2(-1(2(-1x^2 + 3x - 5)^2 + 3(-1x^2 + 3x - 5) - 5) + 3) - 2)/(2(-1(2(-1x^2 + 3x - 5)^2 + 3(-1x^2 + 3x - 5) - 5) + 3) + 1)))/(1((-2(-1(2(-1x^2 + 3x - 5)^2 + 3(-1x^2 + 3x - 5) - 5) + 3) - 2)/(2(-1(2(-1x^2 + 3x - 5)^2 + 3(-1x^2 + 3x - 5) - 5) + 3) + 1)) - 2)) - 3), g(x) = -3|((3(2(3cos(1\u03c0(2|x + 1| + 3)) - 2)^2 - 2(3cos(1\u03c0(2|x + 1| + 3)) - 2) - 5) - 1)/(-3(2(3cos(1\u03c0(2|x + 1| + 3)) - 2)^2 - 2(3cos(1\u03c0(2|x + 1| + 3)) - 2) - 5) - 1)) - 2|, x = -3.7, 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": "36.8", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2((1(1|(-2|(1(5x + 2) - 5) - 2| + 3) + 1| - 3) + 1)/(-1(1|(-2|(1(5x + 2) - 5) - 2| + 3) + 1| - 3) + 2)) + 2 and g(x) = (3(1|(1((-1((-2x - 1)/(-1x - 2)))/(3((-2x - 1)/(-1x - 2)) + 2)) + 2) - 1| - 2) - 1)/(-3(1|(1((-1((-2x - 1)/(-1x - 2)))/(3((-2x - 1)/(-1x - 2)) + 2)) + 2) - 1| - 2) + 4) 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": "25.7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (1(-2(-3|(1|(-2((3x + 2)/(1x)) - 4) + 1| - 3) + 1| - 2)^2 - 4(-3|(1|(-2((3x + 2)/(1x)) - 4) + 1| - 3) + 1| - 2) + 5) - 2)/(2(-2(-3|(1|(-2((3x + 2)/(1x)) - 4) + 1| - 3) + 1| - 2)^2 - 4(-3|(1|(-2((3x + 2)/(1x)) - 4) + 1| - 3) + 1| - 2) + 5) - 3) and g(x) = (2(1(1|(3|(3x - 4) - 2| - 3) + 2| - 3)^2 + 3(1|(3|(3x - 4) - 2| - 3) + 2| - 3) - 1))/(-2(1(1|(3|(3x - 4) - 2| - 3) + 2| - 3)^2 + 3(1|(3|(3x - 4) - 2| - 3) + 2| - 3) - 1) + 1) from x = 1.5 to x = 2.5. 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((-2(-4((1((2((-1x + 3)/(2x - 1)) + 2)/(-1((-1x + 3)/(2x - 1)) - 2)) + 3)/(-3((2((-1x + 3)/(2x - 1)) + 2)/(-1((-1x + 3)/(2x - 1)) - 2)) - 1)) + 3))/(-2(-4((1((2((-1x + 3)/(2x - 1)) + 2)/(-1((-1x + 3)/(2x - 1)) - 2)) + 3)/(-3((2((-1x + 3)/(2x - 1)) + 2)/(-1((-1x + 3)/(2x - 1)) - 2)) - 1)) + 3) + 3)) - 2)/(3((-2(-4((1((2((-1x + 3)/(2x - 1)) + 2)/(-1((-1x + 3)/(2x - 1)) - 2)) + 3)/(-3((2((-1x + 3)/(2x - 1)) + 2)/(-1((-1x + 3)/(2x - 1)) - 2)) - 1)) + 3))/(-2(-4((1((2((-1x + 3)/(2x - 1)) + 2)/(-1((-1x + 3)/(2x - 1)) - 2)) + 3)/(-3((2((-1x + 3)/(2x - 1)) + 2)/(-1((-1x + 3)/(2x - 1)) - 2)) - 1)) + 3) + 3)) + 1) and g(x) = 3(5(-1|(-3(3cos(1\u03c0x + 1) - 1)) - 2|) + 1) + 3 from x = -3.9 to x = -3.8. 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": "Find the area of the region bounded by the curves f(x) = 1|(1((2(-1|(-3cos(3\u03c0(-4x^2 - 1x) + 2) - 2) + 3|) + 3)/(-3(-1|(-3cos(3\u03c0(-4x^2 - 1x) + 2) - 2) + 3|) - 3))^2) + 2| + 3, g(x) = (-2(1(5(1(1x^2 - 3x - 4) + 3)^2 - 2(1(1x^2 - 3x - 4) + 3) - 2) + 1) + 1)/(3(1(5(1(1x^2 - 3x - 4) + 3)^2 - 2(1(1x^2 - 3x - 4) + 3) - 2) + 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": "6.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-3(3(-1|(-4((-1(3|x - 2| - 3) - 2)/(-3(3|x - 2| - 3)))) - 2|)^2 - 3) + 2)/(2(3(-1|(-4((-1(3|x - 2| - 3) - 2)/(-3(3|x - 2| - 3)))) - 2|)^2 - 3) + 1) and g(x) = 3(5(-4(4(3x^2 + 1x - 5)^2 + 5(3x^2 + 1x - 5) - 2) + 5)^2 + 1(-4(4(3x^2 + 1x - 5)^2 + 5(3x^2 + 1x - 5) - 2) + 5) - 5) + 4 between the vertical lines x = 0.9 and x = 1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "196.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-1(3|(-2cos(3\u03c0(-2|((1(1x - 5) - 3)/(2(1x - 5) - 1)) + 2| + 3) + 1) + 1)|) - 2)/(3(3|(-2cos(3\u03c0(-2|((1(1x - 5) - 3)/(2(1x - 5) - 1)) + 2| + 3) + 1) + 1)|)) and g(x) = (-1(-5(-3cos(3\u03c0(3(-5x^2 + 1x - 5) + 4) + 3)) - 5) - 2)/(-2(-5(-3cos(3\u03c0(3(-5x^2 + 1x - 5) + 4) + 3)) - 5) + 1) 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 3|(-4((-1(-2|(-1|((-1x + 1)/(1x - 3)) - 3| - 2) - 2| - 2) + 1)/(1(-2|(-1|((-1x + 1)/(1x - 3)) - 3| - 2) - 2| - 2))) - 4) + 1| - 2 and g(x) = -4(4((-3(1|(-5x^2 + 5x + 2) + 3| - 2))/(-3(1|(-5x^2 + 5x + 2) + 3| - 2) - 3))^2 - 3((-3(1|(-5x^2 + 5x + 2) + 3| - 2))/(-3(1|(-5x^2 + 5x + 2) + 3| - 2) - 3)) - 3)^2 + 1(4((-3(1|(-5x^2 + 5x + 2) + 3| - 2))/(-3(1|(-5x^2 + 5x + 2) + 3| - 2) - 3))^2 - 3((-3(1|(-5x^2 + 5x + 2) + 3| - 2))/(-3(1|(-5x^2 + 5x + 2) + 3| - 2) - 3)) - 3) + 3 from x = 1.8 to x = 1.9000000000000001. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -4(-1|(-3|(-1|(-4(2sin(3\u03c0x + 2) - 1) + 1)| + 3)| + 1) + 2| - 2)^2 + 3(-1|(-3|(-1|(-4(2sin(3\u03c0x + 2) - 1) + 1)| + 3)| + 1) + 2| - 2) - 2 and g(x) = -1|(-4(-3((2(1sin(3\u03c0x + 2) - 1) - 3)/(1(1sin(3\u03c0x + 2) - 1) - 3))^2 - 5((2(1sin(3\u03c0x + 2) - 1) - 3)/(1(1sin(3\u03c0x + 2) - 1) - 3)) - 1)^2 + 5(-3((2(1sin(3\u03c0x + 2) - 1) - 3)/(1(1sin(3\u03c0x + 2) - 1) - 3))^2 - 5((2(1sin(3\u03c0x + 2) - 1) - 3)/(1(1sin(3\u03c0x + 2) - 1) - 3)) - 1) - 4) - 2| - 1 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": "412.7", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1|(2|(2|(-3|(5(-1|x| - 1) + 2) - 1| + 1) - 3| - 1) + 1| - 3) - 2| + 2 and g(x) = 1(-3|(2(1(4x - 2)^2 - 5(4x - 2) + 5)^2 + 1(1(4x - 2)^2 - 5(4x - 2) + 5)) - 1| - 1)^2 - 3(-3|(2(1(4x - 2)^2 - 5(4x - 2) + 5)^2 + 1(1(4x - 2)^2 - 5(4x - 2) + 5)) - 1| - 1) - 5 between the vertical lines x = 0.7 and x = 1.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "84.7", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1sin(1\u03c0(-1((3(-1(4((-1x + 3)/(2x + 3))^2 + 5((-1x + 3)/(2x + 3)) + 2) + 3) + 2)/(1(-1(4((-1x + 3)/(2x + 3))^2 + 5((-1x + 3)/(2x + 3)) + 2) + 3) - 2)) - 5)) and g(x) = (1(2(-3|((-3(-2|x + 1| + 1) + 1)/(-2(-2|x + 1| + 1) + 3))| + 2) - 1))/(-1(2(-3|((-3(-2|x + 1| + 1) + 1)/(-2(-2|x + 1| + 1) + 3))| + 2) - 1)) 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) = (-1(-5(4(-1((2(-2cos(3\u03c0x - 2) - 1) + 3)/(-3(-2cos(3\u03c0x - 2) - 1) - 2))^2 - 5((2(-2cos(3\u03c0x - 2) - 1) + 3)/(-3(-2cos(3\u03c0x - 2) - 1) - 2)) - 4) - 2) + 1))/(2(-5(4(-1((2(-2cos(3\u03c0x - 2) - 1) + 3)/(-3(-2cos(3\u03c0x - 2) - 1) - 2))^2 - 5((2(-2cos(3\u03c0x - 2) - 1) + 3)/(-3(-2cos(3\u03c0x - 2) - 1) - 2)) - 4) - 2) + 1) + 1), g(x) = 3((2(-2sin(3\u03c0((1(4x^2 + 1x + 4) - 2)/(-2(4x^2 + 1x + 4) - 1)) - 3) - 2) - 3)/(-2(-2sin(3\u03c0((1(4x^2 + 1x + 4) - 2)/(-2(4x^2 + 1x + 4) - 1)) - 3) - 2) + 3))^2 + 2((2(-2sin(3\u03c0((1(4x^2 + 1x + 4) - 2)/(-2(4x^2 + 1x + 4) - 1)) - 3) - 2) - 3)/(-2(-2sin(3\u03c0((1(4x^2 + 1x + 4) - 2)/(-2(4x^2 + 1x + 4) - 1)) - 3) - 2) + 3)) + 3, x = 1.1, 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": "13.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2((-1((1(2|(-1(-5x + 4)^2 + 3(-5x + 4) - 5) - 3| - 2))/(2(2|(-1(-5x + 4)^2 + 3(-5x + 4) - 5) - 3| - 2) - 1)) + 1)/(-1((1(2|(-1(-5x + 4)^2 + 3(-5x + 4) - 5) - 3| - 2))/(2(2|(-1(-5x + 4)^2 + 3(-5x + 4) - 5) - 3| - 2) - 1)) - 2))^2 + 4((-1((1(2|(-1(-5x + 4)^2 + 3(-5x + 4) - 5) - 3| - 2))/(2(2|(-1(-5x + 4)^2 + 3(-5x + 4) - 5) - 3| - 2) - 1)) + 1)/(-1((1(2|(-1(-5x + 4)^2 + 3(-5x + 4) - 5) - 3| - 2))/(2(2|(-1(-5x + 4)^2 + 3(-5x + 4) - 5) - 3| - 2) - 1)) - 2)) - 4, g(x) = -1(-2(1|(-1|((3x + 1)/(1x)) + 3|) - 3| - 1)^2 + 4(1|(-1|((3x + 1)/(1x)) + 3|) - 3| - 1) + 5) - 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": "1.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2|((3(-3|(-2|(-1|(-1sin(3\u03c0x - 2) - 1) - 3| + 1) + 3| - 3) - 3| + 1) - 3)/(1(-3|(-2|(-1|(-1sin(3\u03c0x - 2) - 1) - 3| + 1) + 3| - 3) - 3| + 1) + 1)) - 1| and g(x) = -2((2((-3(3(-1sin(1\u03c0x + 1) - 1) + 5) - 3)/(-3(3(-1sin(1\u03c0x + 1) - 1) + 5) - 1)))/(-3((-3(3(-1sin(1\u03c0x + 1) - 1) + 5) - 3)/(-3(3(-1sin(1\u03c0x + 1) - 1) + 5) - 1)) + 4)) - 1 from x = 2.5 to x = 3.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39.6", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1|((2(3|((-1(1(1x^2 - 3x - 1) - 1) - 3)/(-2(1(1x^2 - 3x - 1) - 1) - 3)) + 2| - 1) - 1)/(3(3|((-1(1(1x^2 - 3x - 1) - 1) - 3)/(-2(1(1x^2 - 3x - 1) - 1) - 3)) + 2| - 1))) - 2| + 2 and g(x) = 1(1(-1sin(1\u03c0((3(3|x - 3| - 3))/(-2(3|x - 3| - 3) + 3)) - 1))^2 - 5(-1sin(1\u03c0((3(3|x - 3| - 3))/(-2(3|x - 3| - 3) + 3)) - 1)) + 4) + 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": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3cos(1\u03c0(-3|(2|(-1(-3|(1|x - 3| - 1)| - 2)^2 - 4(-3|(1|x - 3| - 1)| - 2) - 1) - 3| + 2) - 2| - 2) - 2) - 1 and g(x) = -2|(-1|(2cos(1\u03c0(1((1x - 3)/(1x)) - 1) + 1) + 2) + 1| - 3) + 2| + 2 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -4(-2sin(2\u03c0(-1|(-2|(4(2|x - 2| + 3) + 2) + 1| + 3) + 1| - 1) - 1) - 1)^2 + 1(-2sin(2\u03c0(-1|(-2|(4(2|x - 2| + 3) + 2) + 1| + 3) + 1| - 1) - 1) - 1) + 5 and g(x) = (1((3(3(-1e^(-1(4x + 3)) - 2)^2 + 5(-1e^(-1(4x + 3)) - 2) - 4) + 1)/(-2(3(-1e^(-1(4x + 3)) - 2)^2 + 5(-1e^(-1(4x + 3)) - 2) - 4) + 3)) + 1)/(-2((3(3(-1e^(-1(4x + 3)) - 2)^2 + 5(-1e^(-1(4x + 3)) - 2) - 4) + 1)/(-2(3(-1e^(-1(4x + 3)) - 2)^2 + 5(-1e^(-1(4x + 3)) - 2) - 4) + 3))) between the vertical lines x = -1.9 and x = -1.7999999999999998. 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) = 4(1|(-3|(-4(2|(2|x - 1|)| - 2)^2 - 2(2|(2|x - 1|)| - 2) + 3) - 3| - 1) + 1| - 3) - 1 and g(x) = (-3(-5((3((-1(-2|x + 1| + 1) - 1)/(-3(-2|x + 1| + 1) - 2)) + 3)/(3((-1(-2|x + 1| + 1) - 1)/(-3(-2|x + 1| + 1) - 2)) - 2))^2 + 4) - 1)/(-1(-5((3((-1(-2|x + 1| + 1) - 1)/(-3(-2|x + 1| + 1) - 2)) + 3)/(3((-1(-2|x + 1| + 1) - 1)/(-3(-2|x + 1| + 1) - 2)) - 2))^2 + 4) - 3) from x = 1.3 to x = 1.6. 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": "Find the area of the region bounded by the curves f(x) = 2(1sin(3\u03c0(-4(-2|(2(1x + 5)^2 + 5(1x + 5)) - 3| - 3) - 3)) - 2)^2 - 2(1sin(3\u03c0(-4(-2|(2(1x + 5)^2 + 5(1x + 5)) - 3| - 3) - 3)) - 2) - 4, g(x) = 2|((-1(-3cos(2\u03c0(1(-3|x - 1| + 1)^2 - 3(-3|x - 1| + 1) - 2) + 2) + 3) + 3)/(1(-3cos(2\u03c0(1(-3|x - 1| + 1)^2 - 3(-3|x - 1| + 1) - 2) + 2) + 3))) - 3| - 3, x = -4.7, and x = -4.6000000000000005. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "259.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (3(1(-1sin(1\u03c0(2|(2(2|x + 1| + 2)^2 - 1(2|x + 1| + 2) - 2) + 2| - 1) - 3) - 3)^2 - 4) - 3)/(3(1(-1sin(1\u03c0(2|(2(2|x + 1| + 2)^2 - 1(2|x + 1| + 2) - 2) + 2| - 1) - 3) - 3)^2 - 4) - 2) and g(x) = -5(4((-1(-3|((2x - 1)/(-3x - 2)) + 2| - 1) - 1)/(2(-3|((2x - 1)/(-3x - 2)) + 2| - 1)))^2 - 1((-1(-3|((2x - 1)/(-3x - 2)) + 2| - 1) - 1)/(2(-3|((2x - 1)/(-3x - 2)) + 2| - 1))) - 3)^2 + 2(4((-1(-3|((2x - 1)/(-3x - 2)) + 2| - 1) - 1)/(2(-3|((2x - 1)/(-3x - 2)) + 2| - 1)))^2 - 1((-1(-3|((2x - 1)/(-3x - 2)) + 2| - 1) - 1)/(2(-3|((2x - 1)/(-3x - 2)) + 2| - 1))) - 3) - 3 between the vertical lines x = 0.7 and x = 1.2. 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": "Calculate the area enclosed between the functions f(x) = -3(-1(-4(1(3(-3|x - 2| - 1) + 1) + 2)^2 + 3(1(3(-3|x - 2| - 1) + 1) + 2) + 1) - 1) + 1 and g(x) = -2(-5(-3cos(3\u03c0((-2(1|x - 1|) - 3)/(3(1|x - 1|) - 2)))) - 2) - 3 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": "1.9", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -3(-1(3|(5((-3(3|x| - 1) + 3)/(-2(3|x| - 1) + 1))^2 + 5((-3(3|x| - 1) + 3)/(-2(3|x| - 1) + 1)) + 2) + 2| - 1) - 1), g(x) = 3|(-1(4(1|(-1cos(2\u03c0x + 3) - 1)| - 1)^2 - 2(1|(-1cos(2\u03c0x + 3) - 1)| - 1) - 5)^2 + 1(4(1|(-1cos(2\u03c0x + 3) - 1)| - 1)^2 - 2(1|(-1cos(2\u03c0x + 3) - 1)| - 1) - 5) - 1) + 3| - 3, x = -0.6, 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": "274.8", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1(-1((-1(-1sin(1\u03c0(-2((-3x)/(1x - 2)) + 2) - 2) + 1) - 1)/(-3(-1sin(1\u03c0(-2((-3x)/(1x - 2)) + 2) - 2) + 1) + 2)) + 3) - 3, g(x) = 2|(3(-3(-3|(-2|x + 3| + 1)| - 2) - 5) + 5)| - 3, x = -2.9, 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": "68.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1(-1(5((2((2(3x^2 + 5x + 3) + 2)/(-1(3x^2 + 5x + 3) + 2)) + 3)/(1((2(3x^2 + 5x + 3) + 2)/(-1(3x^2 + 5x + 3) + 2)))) + 3) + 4)^2 - 1(-1(5((2((2(3x^2 + 5x + 3) + 2)/(-1(3x^2 + 5x + 3) + 2)) + 3)/(1((2(3x^2 + 5x + 3) + 2)/(-1(3x^2 + 5x + 3) + 2)))) + 3) + 4) and g(x) = -3((-3(-2cos(3\u03c0((-1(1x^2 + 1x + 4) + 2)/(-1(1x^2 + 1x + 4)))) - 1) + 1)/(-3(-2cos(3\u03c0((-1(1x^2 + 1x + 4) + 2)/(-1(1x^2 + 1x + 4)))) - 1) - 1))^2 - 5((-3(-2cos(3\u03c0((-1(1x^2 + 1x + 4) + 2)/(-1(1x^2 + 1x + 4)))) - 1) + 1)/(-3(-2cos(3\u03c0((-1(1x^2 + 1x + 4) + 2)/(-1(1x^2 + 1x + 4)))) - 1) - 1)) - 1 between the vertical lines x = -2.4 and x = -0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "92.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2(-4((1(1(2|(3e^(-1x) - 3) + 2| - 1)^2 + 1(2|(3e^(-1x) - 3) + 2| - 1) - 2) - 3)/(-2(1(2|(3e^(-1x) - 3) + 2| - 1)^2 + 1(2|(3e^(-1x) - 3) + 2| - 1) - 2) - 2)) - 1) - 5 and g(x) = -1|(-3|(1|(-3sin(1\u03c0(-2x^2 - 5x - 4) + 3) + 3) + 1| + 2)| - 1) - 1| + 1 from x = 1.3 to x = 1.4. 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) = 3sin(2\u03c0((-2(5(-2(5(5x^2 + 4x)^2 - 3(5x^2 + 4x) - 5) + 3) + 2) - 3)/(-2(5(-2(5(5x^2 + 4x)^2 - 3(5x^2 + 4x) - 5) + 3) + 2) - 3)) + 2) - 3 and g(x) = -2|(1(-5(-3(-2e^(1x)) - 3)^2 - 4(-3(-2e^(1x)) - 3) + 1) + 1) - 2| + 3 between the vertical lines x = -1.2 and x = -0.6. 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(1e^(1(-2|(-1((-2((2x - 2)/(-1x - 1)) + 2)/(1((2x - 2)/(-1x - 1)) - 3)) - 5) + 3| + 2)) - 3) - 1)/(-2(1e^(1(-2|(-1((-2((2x - 2)/(-1x - 1)) + 2)/(1((2x - 2)/(-1x - 1)) - 3)) - 5) + 3| + 2)) - 3) - 3) and g(x) = 5(-3|(2cos(1\u03c0(-1(-5x^2 + 2x - 1)^2 + 4(-5x^2 + 2x - 1) - 2) - 2) + 1) - 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": "2.4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1|(-2(2sin(2\u03c0(3((-3(-4x^2 - 5x + 4))/(-2(-4x^2 - 5x + 4) + 3))^2 - 3((-3(-4x^2 - 5x + 4))/(-2(-4x^2 - 5x + 4) + 3)) - 2) + 2) + 2)^2 - 3(2sin(2\u03c0(3((-3(-4x^2 - 5x + 4))/(-2(-4x^2 - 5x + 4) + 3))^2 - 3((-3(-4x^2 - 5x + 4))/(-2(-4x^2 - 5x + 4) + 3)) - 2) + 2) + 2) + 2)| and g(x) = (-3(-1|(1(-3(-4x + 2) + 2)^2 - 2(-3(-4x + 2) + 2)) + 1| + 1) - 1)/(-2(-1|(1(-3(-4x + 2) + 2)^2 - 2(-3(-4x + 2) + 2)) + 1| + 1) - 2) from x = 0.3 to x = 0.5. 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) = (-3(-2sin(1\u03c0((2(1(1|(-1|x - 1| - 2) - 2| + 3) + 2) - 3)/(-1(1(1|(-1|x - 1| - 2) - 2| + 3) + 2) + 3)) + 3) + 2))/(2(-2sin(1\u03c0((2(1(1|(-1|x - 1| - 2) - 2| + 3) + 2) - 3)/(-1(1(1|(-1|x - 1| - 2) - 2| + 3) + 2) + 3)) + 3) + 2) - 1) and g(x) = (3(-1((-1(3sin(2\u03c0(-5x^2 - 5x - 1) - 2)) - 2)/(1(3sin(2\u03c0(-5x^2 - 5x - 1) - 2)))) - 2) - 2)/(2(-1((-1(3sin(2\u03c0(-5x^2 - 5x - 1) - 2)) - 2)/(1(3sin(2\u03c0(-5x^2 - 5x - 1) - 2)))) - 2) + 3) from x = 2.5 to 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": "Find the area of the region bounded by the curves f(x) = 2(3(3|(-2sin(1\u03c0(-2|(-4x - 1)| - 1) - 2) + 1)| - 3)^2 - 4(3|(-2sin(1\u03c0(-2|(-4x - 1)| - 1) - 2) + 1)| - 3) - 2)^2 - 3(3(3|(-2sin(1\u03c0(-2|(-4x - 1)| - 1) - 2) + 1)| - 3)^2 - 4(3|(-2sin(1\u03c0(-2|(-4x - 1)| - 1) - 2) + 1)| - 3) - 2) - 3, g(x) = 2sin(3\u03c0((-1(4(4(-1|x - 2| - 2)^2 - 3(-1|x - 2| - 2) - 3) + 5) - 3)/(-3(4(4(-1|x - 2| - 2)^2 - 3(-1|x - 2| - 2) - 3) + 5) + 2)) - 1) + 1, x = 0.7, and x = 0.7999999999999999. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-3(4((3(5((-3(-2x + 4) + 1)/(-1(-2x + 4) + 2)) - 1))/(2(5((-3(-2x + 4) + 1)/(-1(-2x + 4) + 2)) - 1) + 2)) - 5))/(1(4((3(5((-3(-2x + 4) + 1)/(-1(-2x + 4) + 2)) - 1))/(2(5((-3(-2x + 4) + 1)/(-1(-2x + 4) + 2)) - 1) + 2)) - 5) - 2) and g(x) = 2|(5(5((2(1x^2 + 4x - 1) + 1)/(-2(1x^2 + 4x - 1))) - 5) + 4) + 1| - 2 between the vertical lines x = 0.2 and x = 1.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "212.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (2(-2|((2(-4(-2(3|x + 3| + 1)^2 + 3(3|x + 3| + 1) - 5)^2 + 1(-2(3|x + 3| + 1)^2 + 3(3|x + 3| + 1) - 5) + 4) - 2)/(-1(-4(-2(3|x + 3| + 1)^2 + 3(3|x + 3| + 1) - 5)^2 + 1(-2(3|x + 3| + 1)^2 + 3(3|x + 3| + 1) - 5) + 4))) - 3| - 2) + 3)/(3(-2|((2(-4(-2(3|x + 3| + 1)^2 + 3(3|x + 3| + 1) - 5)^2 + 1(-2(3|x + 3| + 1)^2 + 3(3|x + 3| + 1) - 5) + 4) - 2)/(-1(-4(-2(3|x + 3| + 1)^2 + 3(3|x + 3| + 1) - 5)^2 + 1(-2(3|x + 3| + 1)^2 + 3(3|x + 3| + 1) - 5) + 4))) - 3| - 2) - 2), g(x) = 3|(-2|(-3|(-2|(-3|x - 3| + 2) + 2| + 3) + 3|) + 3| + 1) + 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": "Find the area of the region bounded by the curves f(x) = -1|(-1(-1|(2|(-2(3x + 5)^2 - 5(3x + 5) + 5) + 1| + 2) - 3| - 3)) - 2| - 3, g(x) = -2|((3(-2cos(3\u03c0((-2(2|x - 1|) + 2)/(-2(2|x - 1|) + 1)) - 3) - 3) + 2)/(1(-2cos(3\u03c0((-2(2|x - 1|) + 2)/(-2(2|x - 1|) + 1)) - 3) - 3) - 2)) + 3| - 1, 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": "1.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -4(-5(-1sin(1\u03c0(4(-5(1x + 3) - 4)^2 + 4(-5(1x + 3) - 4) - 5) - 2) - 1)^2 + 1(-1sin(1\u03c0(4(-5(1x + 3) - 4)^2 + 4(-5(1x + 3) - 4) - 5) - 2) - 1)) - 4 and g(x) = 5((1(4((-1((-2x + 2)/(1x + 1)) + 3)/(3((-2x + 2)/(1x + 1)))) + 1) + 1)/(-1(4((-1((-2x + 2)/(1x + 1)) + 3)/(3((-2x + 2)/(1x + 1)))) + 1) + 2)) - 4 from x = -1.0 to x = -0.9. 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": "Find the area of the region bounded by the curves f(x) = 2(3((-1(-3|(5(-3x - 3)^2 - 2(-3x - 3) + 3) + 1| + 2) - 2)/(-1(-3|(5(-3x - 3)^2 - 2(-3x - 3) + 3) + 1| + 2)))^2 - 3((-1(-3|(5(-3x - 3)^2 - 2(-3x - 3) + 3) + 1| + 2) - 2)/(-1(-3|(5(-3x - 3)^2 - 2(-3x - 3) + 3) + 1| + 2))) + 2) + 5, g(x) = 3(2(-1cos(3\u03c0(-3(5x^2 + 4x + 5) + 3) + 1) + 1)^2 - 2(-1cos(3\u03c0(-3(5x^2 + 4x + 5) + 3) + 1) + 1))^2 + 2(2(-1cos(3\u03c0(-3(5x^2 + 4x + 5) + 3) + 1) + 1)^2 - 2(-1cos(3\u03c0(-3(5x^2 + 4x + 5) + 3) + 1) + 1)) - 3, 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": "1.6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1(3|(-2((1(-3sin(3\u03c0(-2|x - 2| - 1) - 2) + 1))/(2(-3sin(3\u03c0(-2|x - 2| - 1) - 2) + 1))) + 4) - 1| - 1) - 1 and g(x) = (1(-3(1(-2|(-2|x - 1| + 1) + 1| + 2)^2 + 5(-2|(-2|x - 1| + 1) + 1| + 2)) - 2) - 3)/(1(-3(1(-2|(-2|x - 1| + 1) + 1| + 2)^2 + 5(-2|(-2|x - 1| + 1) + 1| + 2)) - 2) + 2) from x = 2.5 to x = 3.8. Round 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) = (2((2((-2(-3(2((1x + 2)/(2x - 1))^2 + 4((1x + 2)/(2x - 1)) + 3) + 4) - 3)/(-1(-3(2((1x + 2)/(2x - 1))^2 + 4((1x + 2)/(2x - 1)) + 3) + 4) - 1)) + 1)/(-1((-2(-3(2((1x + 2)/(2x - 1))^2 + 4((1x + 2)/(2x - 1)) + 3) + 4) - 3)/(-1(-3(2((1x + 2)/(2x - 1))^2 + 4((1x + 2)/(2x - 1)) + 3) + 4) - 1)))) - 3)/(1((2((-2(-3(2((1x + 2)/(2x - 1))^2 + 4((1x + 2)/(2x - 1)) + 3) + 4) - 3)/(-1(-3(2((1x + 2)/(2x - 1))^2 + 4((1x + 2)/(2x - 1)) + 3) + 4) - 1)) + 1)/(-1((-2(-3(2((1x + 2)/(2x - 1))^2 + 4((1x + 2)/(2x - 1)) + 3) + 4) - 3)/(-1(-3(2((1x + 2)/(2x - 1))^2 + 4((1x + 2)/(2x - 1)) + 3) + 4) - 1)))) + 2) and g(x) = 1(-3|(-1(-1|(2sin(3\u03c0x + 1) - 3) + 3| + 3)^2 - 2(-1|(2sin(3\u03c0x + 1) - 3) + 3| + 3) + 4) + 2| - 1)^2 - 5(-3|(-1(-1|(2sin(3\u03c0x + 1) - 3) + 3| + 3)^2 - 2(-1|(2sin(3\u03c0x + 1) - 3) + 3| + 3) + 4) + 2| - 1) - 3 from x = 0.8 to x = 0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "26.9", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (3(4((3(5(-3(-1e^(-1x) - 1) - 1)^2 - 2(-3(-1e^(-1x) - 1) - 1) + 2))/(3(5(-3(-1e^(-1x) - 1) - 1)^2 - 2(-3(-1e^(-1x) - 1) - 1) + 2) + 2))^2 - 5))/(2(4((3(5(-3(-1e^(-1x) - 1) - 1)^2 - 2(-3(-1e^(-1x) - 1) - 1) + 2))/(3(5(-3(-1e^(-1x) - 1) - 1)^2 - 2(-3(-1e^(-1x) - 1) - 1) + 2) + 2))^2 - 5)), g(x) = 2(1((-1(2|(-1x^2 + 3x) - 2| - 2) - 3)/(-2(2|(-1x^2 + 3x) - 2| - 2) - 2)) + 1) + 4, x = 0.8, 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": "3.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2|(-1(-1|((-1((2(-3|x - 2| - 2) + 1)/(3(-3|x - 2| - 2))) - 1)/(-2((2(-3|x - 2| - 2) + 1)/(3(-3|x - 2| - 2))) + 1))| - 3) - 3)| + 2 and g(x) = (1(2sin(1\u03c0(3((-1((-2x - 3)/(-1x - 2)))/(-3((-2x - 3)/(-1x - 2)) - 3)) + 4)) - 2) - 2)/(2(2sin(1\u03c0(3((-1((-2x - 3)/(-1x - 2)))/(-3((-2x - 3)/(-1x - 2)) - 3)) + 4)) - 2)) between the vertical lines x = -1.7 and x = -1.5999999999999999. 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": "Determine the area of the region enclosed by the graphs of f(x) = -1((1(2e^(-1(-2|(-4((2x + 1)/(-3x))^2 + 1((2x + 1)/(-3x)) - 5) + 2| + 3)) - 3) + 3)/(-1(2e^(-1(-2|(-4((2x + 1)/(-3x))^2 + 1((2x + 1)/(-3x)) - 5) + 2| + 3)) - 3) - 1))^2 - 4((1(2e^(-1(-2|(-4((2x + 1)/(-3x))^2 + 1((2x + 1)/(-3x)) - 5) + 2| + 3)) - 3) + 3)/(-1(2e^(-1(-2|(-4((2x + 1)/(-3x))^2 + 1((2x + 1)/(-3x)) - 5) + 2| + 3)) - 3) - 1)) + 3 and g(x) = -2(-2(-5(-3(-5x + 5) + 5)^2 + 5(-3(-5x + 5) + 5) + 4) - 4) + 2 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": "3.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1|(-3(2(-1(-3((-1x - 2)/(2x - 3)) - 2) + 2) - 4)) + 2| + 1 and g(x) = 1(4(1|(1(4x^2 - 4)^2 + 5(4x^2 - 4)) - 1| - 3)^2 - 1(1|(1(4x^2 - 4)^2 + 5(4x^2 - 4)) - 1| - 3))^2 + 5(4(1|(1(4x^2 - 4)^2 + 5(4x^2 - 4)) - 1| - 3)^2 - 1(1|(1(4x^2 - 4)^2 + 5(4x^2 - 4)) - 1| - 3)) - 1 from x = -1.0 to x = -0.9. 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(-3|(2sin(1\u03c0(-1(2(-5x + 5) - 2)^2 + 1(2(-5x + 5) - 2) - 5) - 3)) + 2| + 2)^2 - 5(-3|(2sin(1\u03c0(-1(2(-5x + 5) - 2)^2 + 1(2(-5x + 5) - 2) - 5) - 3)) + 2| + 2) + 2 and g(x) = 3e^(-1(3(-1(-3(2x)^2 + 2(2x))^2 + 5(-3(2x)^2 + 2(2x)) - 3) + 5)) + 3 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": "1.8", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1(-2|((-2(-2e^(1(-4(-1x) + 3)) + 1) + 1)/(-2(-2e^(1(-4(-1x) + 3)) + 1) - 3)) - 2| + 2) + 4, g(x) = 2|((-1((-3(2|(3x^2 - 1x + 3) - 2| - 2) + 1)/(-1(2|(3x^2 - 1x + 3) - 2| - 2) - 3)) - 2)/(-2((-3(2|(3x^2 - 1x + 3) - 2| - 2) + 1)/(-1(2|(3x^2 - 1x + 3) - 2| - 2) - 3)) - 1)) + 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": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2|(-3cos(1\u03c0(2|(1|((-1((-2x + 3)/(-1x + 2)) + 3)/(2((-2x + 3)/(-1x + 2)) - 3)) + 1| - 2) - 1| - 1) - 1) + 1) - 2| + 2 and g(x) = -1|(-2|(4((-1(2sin(2\u03c0x - 3) + 2) + 3)/(2(2sin(2\u03c0x - 3) + 2) + 1))^2 - 4) - 3| + 3) + 3| + 2 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": "1.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3|((2(4((1(-5(5x^2 + 5x - 2)^2 + 3(5x^2 + 5x - 2) - 4) - 2)/(-1(-5(5x^2 + 5x - 2)^2 + 3(5x^2 + 5x - 2) - 4) - 2))^2 + 5((1(-5(5x^2 + 5x - 2)^2 + 3(5x^2 + 5x - 2) - 4) - 2)/(-1(-5(5x^2 + 5x - 2)^2 + 3(5x^2 + 5x - 2) - 4) - 2)) - 2) + 1)/(3(4((1(-5(5x^2 + 5x - 2)^2 + 3(5x^2 + 5x - 2) - 4) - 2)/(-1(-5(5x^2 + 5x - 2)^2 + 3(5x^2 + 5x - 2) - 4) - 2))^2 + 5((1(-5(5x^2 + 5x - 2)^2 + 3(5x^2 + 5x - 2) - 4) - 2)/(-1(-5(5x^2 + 5x - 2)^2 + 3(5x^2 + 5x - 2) - 4) - 2)) - 2) + 2))| + 2, g(x) = -4(-2|(-3sin(3\u03c0(1(-3|x| - 3) + 3) - 1) - 3) + 2| + 3)^2 - 4(-2|(-3sin(3\u03c0(1(-3|x| - 3) + 3) - 1) - 3) + 2| + 3) + 2, x = -1.2, and x = -1.0999999999999999. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1(-2e^(-1((2(-1((-2(2|x|) + 3)/(-2(2|x|) + 1))) - 1)/(2(-1((-2(2|x|) + 3)/(-2(2|x|) + 1)))))) + 2)^2 + 3(-2e^(-1((2(-1((-2(2|x|) + 3)/(-2(2|x|) + 1))) - 1)/(2(-1((-2(2|x|) + 3)/(-2(2|x|) + 1)))))) + 2) - 5 and g(x) = -1(-2e^(-1((3(2|(-1|x| - 1) + 3| - 2))/(-1(2|(-1|x| - 1) + 3| - 2) + 2))) + 2)^2 + 1 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(-3(1(-3sin(2\u03c0(-1(1|x + 1| - 2)^2 + 2) - 3) - 1)^2 + 3(-3sin(2\u03c0(-1(1|x + 1| - 2)^2 + 2) - 3) - 1) + 5) + 1) + 3 and g(x) = 1|(5(-3(1e^(1((-2x)/(-3x + 2))) + 3) + 3) + 1)| + 2 from x = 0.0 to x = 0.2. 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": "Determine the area of the region enclosed by the graphs of f(x) = (-3(2cos(2\u03c0((3((-1(1(-5x^2 + 3x - 1)^2 - 5(-5x^2 + 3x - 1) - 4) + 2)/(-1(1(-5x^2 + 3x - 1)^2 - 5(-5x^2 + 3x - 1) - 4) + 2)) - 3)/(-2((-1(1(-5x^2 + 3x - 1)^2 - 5(-5x^2 + 3x - 1) - 4) + 2)/(-1(1(-5x^2 + 3x - 1)^2 - 5(-5x^2 + 3x - 1) - 4) + 2)) - 2)) - 1) + 1) + 1)/(3(2cos(2\u03c0((3((-1(1(-5x^2 + 3x - 1)^2 - 5(-5x^2 + 3x - 1) - 4) + 2)/(-1(1(-5x^2 + 3x - 1)^2 - 5(-5x^2 + 3x - 1) - 4) + 2)) - 3)/(-2((-1(1(-5x^2 + 3x - 1)^2 - 5(-5x^2 + 3x - 1) - 4) + 2)/(-1(1(-5x^2 + 3x - 1)^2 - 5(-5x^2 + 3x - 1) - 4) + 2)) - 2)) - 1) + 1) + 3) and g(x) = -4(5(5(-1|(5x - 4) + 1| + 3) - 2)^2 - 5(5(-1|(5x - 4) + 1| + 3) - 2) - 2) - 5 between the vertical lines x = 1.1 and x = 1.2000000000000002. 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) = 5(-3|((-1((1(-1(1|x - 1| + 2)^2 + 3(1|x - 1| + 2) + 5) - 3)/(3(-1(1|x - 1| + 2)^2 + 3(1|x - 1| + 2) + 5) + 2)) - 1)/(-1((1(-1(1|x - 1| + 2)^2 + 3(1|x - 1| + 2) + 5) - 3)/(3(-1(1|x - 1| + 2)^2 + 3(1|x - 1| + 2) + 5) + 2)) - 3))|) + 2, g(x) = -1(1|(-3(-3((-3x)/(-1x - 3))^2 + 5((-3x)/(-1x - 3)) - 1)^2 - 2(-3((-3x)/(-1x - 3))^2 + 5((-3x)/(-1x - 3)) - 1) + 3) + 2| - 1)^2 - 1(1|(-3(-3((-3x)/(-1x - 3))^2 + 5((-3x)/(-1x - 3)) - 1)^2 - 2(-3((-3x)/(-1x - 3))^2 + 5((-3x)/(-1x - 3)) - 1) + 3) + 2| - 1) - 5, x = 3.2, 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": "9.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1e^(2(1((2(-3|(5(-5x^2 - 3x - 2) + 5) + 1| + 2) - 3)/(3(-3|(5(-5x^2 - 3x - 2) + 5) + 1| + 2)))^2 + 2((2(-3|(5(-5x^2 - 3x - 2) + 5) + 1| + 2) - 3)/(3(-3|(5(-5x^2 - 3x - 2) + 5) + 1| + 2))) - 4)) - 1, g(x) = (-1(3sin(3\u03c0(-3(1(-1x^2 + 2x + 4)^2 - 1(-1x^2 + 2x + 4) - 4) + 4) + 2) - 2) + 3)/(3(3sin(3\u03c0(-3(1(-1x^2 + 2x + 4)^2 - 1(-1x^2 + 2x + 4) - 4) + 4) + 2) - 2) + 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": "Find the area of the region bounded by the curves f(x) = 2((3(-2|(1(3|(-2x^2 + 4x - 2) + 1| - 3) - 5)| + 1) + 2)/(-1(-2|(1(3|(-2x^2 + 4x - 2) + 1| - 3) - 5)| + 1)))^2 - 3, g(x) = -1((1(-2(2|(-2x + 5) + 3|)^2 + 1(2|(-2x + 5) + 3|) + 2) - 3)/(1(-2(2|(-2x + 5) + 3|)^2 + 1(2|(-2x + 5) + 3|) + 2) - 2))^2 + 5((1(-2(2|(-2x + 5) + 3|)^2 + 1(2|(-2x + 5) + 3|) + 2) - 3)/(1(-2(2|(-2x + 5) + 3|)^2 + 1(2|(-2x + 5) + 3|) + 2) - 2)) + 3, 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": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -5(-3(-1(-3|((-2(4x + 3) + 3)/(1(4x + 3) - 2)) + 2| + 1)^2 + 4(-3|((-2(4x + 3) + 3)/(1(4x + 3) - 2)) + 2| + 1)) + 1) + 3 and g(x) = (-1((1((-3(3|(-2|x + 1| + 2) + 3| - 3) - 1)/(1(3|(-2|x + 1| + 2) + 3| - 3) + 3)))/(3((-3(3|(-2|x + 1| + 2) + 3| - 3) - 1)/(1(3|(-2|x + 1| + 2) + 3| - 3) + 3)) + 2)))/(-1((1((-3(3|(-2|x + 1| + 2) + 3| - 3) - 1)/(1(3|(-2|x + 1| + 2) + 3| - 3) + 3)))/(3((-3(3|(-2|x + 1| + 2) + 3| - 3) - 1)/(1(3|(-2|x + 1| + 2) + 3| - 3) + 3)) + 2)) - 1) from x = 0.5 to x = 2.0. 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": "Determine the area of the region enclosed by the graphs of f(x) = -3((2(-3cos(2\u03c0(-5((-1(2x^2 - 4x + 3) - 2)/(2(2x^2 - 4x + 3))) + 5) - 1) - 2) - 3)/(-1(-3cos(2\u03c0(-5((-1(2x^2 - 4x + 3) - 2)/(2(2x^2 - 4x + 3))) + 5) - 1) - 2) - 3)) and g(x) = -4(3|(-1|(2((-2x - 3)/(2x + 3)) + 2) + 2|) + 3|)^2 - 3(3|(-1|(2((-2x - 3)/(2x + 3)) + 2) + 2|) + 3|) + 2 between the vertical lines x = 2.5 and x = 3.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "132.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2|(5(-5(1(1(1|x + 2| + 3)^2 - 2(1|x + 2| + 3)) - 5) + 1)^2 - 3(-5(1(1(1|x + 2| + 3)^2 - 2(1|x + 2| + 3)) - 5) + 1)) + 1| - 3 and g(x) = (-1(-4((-1(-2(-1x + 4)^2 + 2(-1x + 4) + 3) + 1)/(-1(-2(-1x + 4)^2 + 2(-1x + 4) + 3) - 2)) - 3) - 1)/(3(-4((-1(-2(-1x + 4)^2 + 2(-1x + 4) + 3) + 1)/(-1(-2(-1x + 4)^2 + 2(-1x + 4) + 3) - 2)) - 3) + 3) from x = -2.5 to x = -1.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "383.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1(3(-3cos(2\u03c0(-3((1(-2|x - 2| + 2) - 1)/(-2(-2|x - 2| + 2) + 3))^2 - 3((1(-2|x - 2| + 2) - 1)/(-2(-2|x - 2| + 2) + 3)) - 2) - 2) - 1) + 2)^2 - 1(3(-3cos(2\u03c0(-3((1(-2|x - 2| + 2) - 1)/(-2(-2|x - 2| + 2) + 3))^2 - 3((1(-2|x - 2| + 2) - 1)/(-2(-2|x - 2| + 2) + 3)) - 2) - 2) - 1) + 2) - 4 and g(x) = 2cos(2\u03c0(3(3(1(3|x - 3| + 3)^2 - 1(3|x - 3| + 3))^2 + 1(1(3|x - 3| + 3)^2 - 1(3|x - 3| + 3)) - 4) - 5) + 3) + 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": "3.7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1((-3((-2(1(-5(-2x - 5) + 5)^2 - 2(-5(-2x - 5) + 5) + 1) + 2)/(-3(1(-5(-2x - 5) + 5)^2 - 2(-5(-2x - 5) + 5) + 1) + 4)) - 1)/(2((-2(1(-5(-2x - 5) + 5)^2 - 2(-5(-2x - 5) + 5) + 1) + 2)/(-3(1(-5(-2x - 5) + 5)^2 - 2(-5(-2x - 5) + 5) + 1) + 4)) - 3))^2 - 1((-3((-2(1(-5(-2x - 5) + 5)^2 - 2(-5(-2x - 5) + 5) + 1) + 2)/(-3(1(-5(-2x - 5) + 5)^2 - 2(-5(-2x - 5) + 5) + 1) + 4)) - 1)/(2((-2(1(-5(-2x - 5) + 5)^2 - 2(-5(-2x - 5) + 5) + 1) + 2)/(-3(1(-5(-2x - 5) + 5)^2 - 2(-5(-2x - 5) + 5) + 1) + 4)) - 3)) - 5 and g(x) = (1((2(-1((-3(-1x^2 + 3x - 4) - 2)/(2(-1x^2 + 3x - 4) + 2))^2 + 2((-3(-1x^2 + 3x - 4) - 2)/(2(-1x^2 + 3x - 4) + 2)) + 5) + 2)/(-2(-1((-3(-1x^2 + 3x - 4) - 2)/(2(-1x^2 + 3x - 4) + 2))^2 + 2((-3(-1x^2 + 3x - 4) - 2)/(2(-1x^2 + 3x - 4) + 2)) + 5) + 1)) - 2)/(-1((2(-1((-3(-1x^2 + 3x - 4) - 2)/(2(-1x^2 + 3x - 4) + 2))^2 + 2((-3(-1x^2 + 3x - 4) - 2)/(2(-1x^2 + 3x - 4) + 2)) + 5) + 2)/(-2(-1((-3(-1x^2 + 3x - 4) - 2)/(2(-1x^2 + 3x - 4) + 2))^2 + 2((-3(-1x^2 + 3x - 4) - 2)/(2(-1x^2 + 3x - 4) + 2)) + 5) + 1)) + 3) from x = -2.8 to x = -2.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "46.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-1(3|(-2(-1((3(1x^2 - 2x + 1) + 2)/(-1(1x^2 - 2x + 1))) - 2) - 1)|) + 2)/(1(3|(-2(-1((3(1x^2 - 2x + 1) + 2)/(-1(1x^2 - 2x + 1))) - 2) - 1)|)), g(x) = (2(-1(-3sin(1\u03c0((-3(-3x + 3) + 1)/(-3(-3x + 3) - 1)) - 2))^2 - 2(-3sin(1\u03c0((-3(-3x + 3) + 1)/(-3(-3x + 3) - 1)) - 2)) + 3))/(-2(-1(-3sin(1\u03c0((-3(-3x + 3) + 1)/(-3(-3x + 3) - 1)) - 2))^2 - 2(-3sin(1\u03c0((-3(-3x + 3) + 1)/(-3(-3x + 3) - 1)) - 2)) + 3) - 1), x = -2.0, 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": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1|(-2|((-2(1(-2(-2|x - 1| - 2) - 5)) - 2)/(-1(1(-2(-2|x - 1| - 2) - 5)) + 3)) - 2| - 1)| - 1 and g(x) = 5(5(3(-2e^(2(-4x + 4))) + 2)) + 2 between the vertical lines x = 1.1 and x = 1.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "25.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 5((-1(-5(-5(5((-3x + 2)/(-1x))^2 + 5((-3x + 2)/(-1x))) - 5) - 1) + 1)/(-1(-5(-5(5((-3x + 2)/(-1x))^2 + 5((-3x + 2)/(-1x))) - 5) - 1) - 3)) + 3, g(x) = (2(-1sin(2\u03c0(4(4(2|x| - 1) - 1) - 2) + 2) - 1) + 2)/(3(-1sin(2\u03c0(4(4(2|x| - 1) - 1) - 2) + 2) - 1) + 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": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1(-2(-2|(1|(-1|(-1e^(-1x) - 1) + 1| + 3) - 2| - 3) - 1| + 2) - 2)^2 - 1(-2(-2|(1|(-1|(-1e^(-1x) - 1) + 1| + 3) - 2| - 3) - 1| + 2) - 2) + 5 and g(x) = -3|(-2(-1(3cos(1\u03c0(2|x - 1| - 3) + 2) - 3))^2 + 4(-1(3cos(1\u03c0(2|x - 1| - 3) + 2) - 3)) + 3) + 1| + 2 from x = 3.5 to x = 3.9. 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) = -1|((-1(-2(-3(-1(-1x^2 + 1x - 1) - 5)^2 + 1(-1(-1x^2 + 1x - 1) - 5) - 4)^2 - 2) - 2)/(-1(-2(-3(-1(-1x^2 + 1x - 1) - 5)^2 + 1(-1(-1x^2 + 1x - 1) - 5) - 4)^2 - 2) - 1))| - 3 and g(x) = -3(-3(1sin(3\u03c0(1((1x - 1)/(-3x + 4))^2 - 4((1x - 1)/(-3x + 4)) - 5) - 1) - 1)^2 + 5(1sin(3\u03c0(1((1x - 1)/(-3x + 4))^2 - 4((1x - 1)/(-3x + 4)) - 5) - 1) - 1))^2 + 2(-3(1sin(3\u03c0(1((1x - 1)/(-3x + 4))^2 - 4((1x - 1)/(-3x + 4)) - 5) - 1) - 1)^2 + 5(1sin(3\u03c0(1((1x - 1)/(-3x + 4))^2 - 4((1x - 1)/(-3x + 4)) - 5) - 1) - 1)) from x = -3.3 to x = -0.9. 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": "Determine the area of the region enclosed by the graphs of f(x) = 3|(-2(-3|(-2sin(3\u03c0(-1|(-4x) - 3| + 2)) + 1) + 1|)^2 - 1(-3|(-2sin(3\u03c0(-1|(-4x) - 3| + 2)) + 1) + 1|) - 4) + 1| + 1 and g(x) = (-2(-2|(-3sin(2\u03c0(1((3x - 2)/(-2x + 3)))) - 3)| + 2) + 3)/(-2(-2|(-3sin(2\u03c0(1((3x - 2)/(-2x + 3)))) - 3)| + 2) - 1) between the vertical lines x = 1.7 and x = 2.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "368.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (1(3sin(2\u03c0(-5((-3(-3|(-2x)| - 2) - 3)/(1(-3|(-2x)| - 2)))^2 - 4((-3(-3|(-2x)| - 2) - 3)/(1(-3|(-2x)| - 2)))) + 3) + 1))/(2(3sin(2\u03c0(-5((-3(-3|(-2x)| - 2) - 3)/(1(-3|(-2x)| - 2)))^2 - 4((-3(-3|(-2x)| - 2) - 3)/(1(-3|(-2x)| - 2)))) + 3) + 1) - 3) and g(x) = -2|(-5(1((3(5x^2 - 3))/(1(5x^2 - 3)))) + 3)| + 1 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": "10.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1(-1(-1|((-3(2(-5x - 4)^2 - 4(-5x - 4) + 2) + 1)/(3(2(-5x - 4)^2 - 4(-5x - 4) + 2) + 1)) + 1|) - 5)^2 + 4(-1(-1|((-3(2(-5x - 4)^2 - 4(-5x - 4) + 2) + 1)/(3(2(-5x - 4)^2 - 4(-5x - 4) + 2) + 1)) + 1|) - 5) + 5, g(x) = (1((-2(-2((3((-3x + 3)/(3x + 3)) - 1)/(2((-3x + 3)/(3x + 3)) + 3))^2 + 5((3((-3x + 3)/(3x + 3)) - 1)/(2((-3x + 3)/(3x + 3)) + 3))) + 3)/(-1(-2((3((-3x + 3)/(3x + 3)) - 1)/(2((-3x + 3)/(3x + 3)) + 3))^2 + 5((3((-3x + 3)/(3x + 3)) - 1)/(2((-3x + 3)/(3x + 3)) + 3))) - 1)) - 1)/(-3((-2(-2((3((-3x + 3)/(3x + 3)) - 1)/(2((-3x + 3)/(3x + 3)) + 3))^2 + 5((3((-3x + 3)/(3x + 3)) - 1)/(2((-3x + 3)/(3x + 3)) + 3))) + 3)/(-1(-2((3((-3x + 3)/(3x + 3)) - 1)/(2((-3x + 3)/(3x + 3)) + 3))^2 + 5((3((-3x + 3)/(3x + 3)) - 1)/(2((-3x + 3)/(3x + 3)) + 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": "56.9", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (1(1((-1(5((-3(-1sin(2\u03c0x - 1) - 3) - 3)/(1(-1sin(2\u03c0x - 1) - 3) - 3))^2 + 5((-3(-1sin(2\u03c0x - 1) - 3) - 3)/(1(-1sin(2\u03c0x - 1) - 3) - 3))) + 3)/(-2(5((-3(-1sin(2\u03c0x - 1) - 3) - 3)/(1(-1sin(2\u03c0x - 1) - 3) - 3))^2 + 5((-3(-1sin(2\u03c0x - 1) - 3) - 3)/(1(-1sin(2\u03c0x - 1) - 3) - 3))) + 3))^2 - 5((-1(5((-3(-1sin(2\u03c0x - 1) - 3) - 3)/(1(-1sin(2\u03c0x - 1) - 3) - 3))^2 + 5((-3(-1sin(2\u03c0x - 1) - 3) - 3)/(1(-1sin(2\u03c0x - 1) - 3) - 3))) + 3)/(-2(5((-3(-1sin(2\u03c0x - 1) - 3) - 3)/(1(-1sin(2\u03c0x - 1) - 3) - 3))^2 + 5((-3(-1sin(2\u03c0x - 1) - 3) - 3)/(1(-1sin(2\u03c0x - 1) - 3) - 3))) + 3)) + 2) + 3)/(-2(1((-1(5((-3(-1sin(2\u03c0x - 1) - 3) - 3)/(1(-1sin(2\u03c0x - 1) - 3) - 3))^2 + 5((-3(-1sin(2\u03c0x - 1) - 3) - 3)/(1(-1sin(2\u03c0x - 1) - 3) - 3))) + 3)/(-2(5((-3(-1sin(2\u03c0x - 1) - 3) - 3)/(1(-1sin(2\u03c0x - 1) - 3) - 3))^2 + 5((-3(-1sin(2\u03c0x - 1) - 3) - 3)/(1(-1sin(2\u03c0x - 1) - 3) - 3))) + 3))^2 - 5((-1(5((-3(-1sin(2\u03c0x - 1) - 3) - 3)/(1(-1sin(2\u03c0x - 1) - 3) - 3))^2 + 5((-3(-1sin(2\u03c0x - 1) - 3) - 3)/(1(-1sin(2\u03c0x - 1) - 3) - 3))) + 3)/(-2(5((-3(-1sin(2\u03c0x - 1) - 3) - 3)/(1(-1sin(2\u03c0x - 1) - 3) - 3))^2 + 5((-3(-1sin(2\u03c0x - 1) - 3) - 3)/(1(-1sin(2\u03c0x - 1) - 3) - 3))) + 3)) + 2) + 3) and g(x) = 2(-4(5(-3((-2x - 1)/(3x + 2)) - 1) - 4) - 1) 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": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2((-1(3(-3(1e^(1(1x - 5)) + 1)^2 + 3(1e^(1(1x - 5)) + 1) - 4) - 1))/(-2(3(-3(1e^(1(1x - 5)) + 1)^2 + 3(1e^(1(1x - 5)) + 1) - 4) - 1))) + 4 and g(x) = -3cos(3\u03c0(1|(1(1(-4x + 4)^2 - 5(-4x + 4) + 5)^2 - 3(1(-4x + 4)^2 - 5(-4x + 4) + 5) + 2) - 2| + 1) + 1) + 2 from x = -2.7 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": "Calculate the area enclosed between the functions f(x) = 2((-3(-1((2(-4(3cos(2\u03c0x - 2) + 3)^2 + 5(3cos(2\u03c0x - 2) + 3) - 1) - 2)/(-3(-4(3cos(2\u03c0x - 2) + 3)^2 + 5(3cos(2\u03c0x - 2) + 3) - 1) + 1)) - 3))/(1(-1((2(-4(3cos(2\u03c0x - 2) + 3)^2 + 5(3cos(2\u03c0x - 2) + 3) - 1) - 2)/(-3(-4(3cos(2\u03c0x - 2) + 3)^2 + 5(3cos(2\u03c0x - 2) + 3) - 1) + 1)) - 3) - 2))^2 - 1((-3(-1((2(-4(3cos(2\u03c0x - 2) + 3)^2 + 5(3cos(2\u03c0x - 2) + 3) - 1) - 2)/(-3(-4(3cos(2\u03c0x - 2) + 3)^2 + 5(3cos(2\u03c0x - 2) + 3) - 1) + 1)) - 3))/(1(-1((2(-4(3cos(2\u03c0x - 2) + 3)^2 + 5(3cos(2\u03c0x - 2) + 3) - 1) - 2)/(-3(-4(3cos(2\u03c0x - 2) + 3)^2 + 5(3cos(2\u03c0x - 2) + 3) - 1) + 1)) - 3) - 2)) - 4 and g(x) = 3|(-1(1|(5((-2x - 1)/(-3x + 4))) + 2| + 2) + 5) + 3| + 3 from x = 1.7 to x = 1.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3(2|((2(-1|((-2(5x^2 - 3x + 2))/(1(5x^2 - 3x + 2))) + 2| + 1) + 2)/(-3(-1|((-2(5x^2 - 3x + 2))/(1(5x^2 - 3x + 2))) + 2| + 1))) - 3| - 3)^2 + 4(2|((2(-1|((-2(5x^2 - 3x + 2))/(1(5x^2 - 3x + 2))) + 2| + 1) + 2)/(-3(-1|((-2(5x^2 - 3x + 2))/(1(5x^2 - 3x + 2))) + 2| + 1))) - 3| - 3) - 3 and g(x) = -5(-2sin(2\u03c0(2((-2(-2x + 5) - 3)/(-3(-2x + 5) - 3))) + 3) + 2)^2 - 3(-2sin(2\u03c0(2((-2(-2x + 5) - 3)/(-3(-2x + 5) - 3))) + 3) + 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": "4.6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 3(-1cos(3\u03c0(3(-4(-4(2x^2 - 4x)^2 + 4(2x^2 - 4x) - 2) + 2) - 1) + 1) + 1) - 2 and g(x) = (1(-5(-2(-3|(2sin(1\u03c0x + 1) - 3) + 2| + 3) + 2)^2 + 5(-2(-3|(2sin(1\u03c0x + 1) - 3) + 2| + 3) + 2) - 1) - 1)/(-1(-5(-2(-3|(2sin(1\u03c0x + 1) - 3) + 2| + 3) + 2)^2 + 5(-2(-3|(2sin(1\u03c0x + 1) - 3) + 2| + 3) + 2) - 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": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -4(-4(-2(3(5((-1x - 2)/(-1x - 1)) + 3) - 3)^2 - 1(3(5((-1x - 2)/(-1x - 1)) + 3) - 3) + 3) + 5) + 3 and g(x) = -3(2|(3(3e^(-1(3x^2 - 5)) + 2) - 1) - 1| + 1) between the vertical lines x = -1.8 and x = -1.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2(1(-1|(-1|(-1(-5x - 5) + 1) - 3| - 1) - 1|) + 3)^2 - 1(1(-1|(-1|(-1(-5x - 5) + 1) - 3| - 1) - 1|) + 3) + 3 and g(x) = (-3((-1(-3(4(-5x^2 - 1x + 3) + 4)^2 - 1(4(-5x^2 - 1x + 3) + 4) + 1) - 1)/(2(-3(4(-5x^2 - 1x + 3) + 4)^2 - 1(4(-5x^2 - 1x + 3) + 4) + 1) - 3)) - 2)/(1((-1(-3(4(-5x^2 - 1x + 3) + 4)^2 - 1(4(-5x^2 - 1x + 3) + 4) + 1) - 1)/(2(-3(4(-5x^2 - 1x + 3) + 4)^2 - 1(4(-5x^2 - 1x + 3) + 4) + 1) - 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) = (-3(5((3(1((1(1x^2 + 2x) - 3)/(-3(1x^2 + 2x) + 2)) - 2) + 2)/(1(1((1(1x^2 + 2x) - 3)/(-3(1x^2 + 2x) + 2)) - 2) + 2))^2 + 1((3(1((1(1x^2 + 2x) - 3)/(-3(1x^2 + 2x) + 2)) - 2) + 2)/(1(1((1(1x^2 + 2x) - 3)/(-3(1x^2 + 2x) + 2)) - 2) + 2)) + 2) + 2)/(-1(5((3(1((1(1x^2 + 2x) - 3)/(-3(1x^2 + 2x) + 2)) - 2) + 2)/(1(1((1(1x^2 + 2x) - 3)/(-3(1x^2 + 2x) + 2)) - 2) + 2))^2 + 1((3(1((1(1x^2 + 2x) - 3)/(-3(1x^2 + 2x) + 2)) - 2) + 2)/(1(1((1(1x^2 + 2x) - 3)/(-3(1x^2 + 2x) + 2)) - 2) + 2)) + 2) + 3) and g(x) = (1(1(-5((2((-1x - 3)/(-1x + 3)) - 3)/(-2((-1x - 3)/(-1x + 3)) - 1)) - 4)^2 - 1(-5((2((-1x - 3)/(-1x + 3)) - 3)/(-2((-1x - 3)/(-1x + 3)) - 1)) - 4) - 1) - 1)/(-3(1(-5((2((-1x - 3)/(-1x + 3)) - 3)/(-2((-1x - 3)/(-1x + 3)) - 1)) - 4)^2 - 1(-5((2((-1x - 3)/(-1x + 3)) - 3)/(-2((-1x - 3)/(-1x + 3)) - 1)) - 4) - 1) + 2) from x = 2.5 to x = 4.6. 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": "Calculate the area enclosed between the functions f(x) = (-1(1(2|(2|((1(1|x + 1| + 2) - 1)/(-1(1|x + 1| + 2) - 1)) + 1| + 2) - 2|) + 5) - 2)/(3(1(2|(2|((1(1|x + 1| + 2) - 1)/(-1(1|x + 1| + 2) - 1)) + 1| + 2) - 2|) + 5) - 1) and g(x) = 3(2(-1|((-2(-5x^2 + 4x) + 3)/(-3(-5x^2 + 4x) + 2))| + 2) - 3) + 5 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": "103.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3(-2|(-2(1(5((3x + 3)/(-2x + 3)) + 1) - 5) + 1) - 3| + 2)^2 + 2(-2|(-2(1(5((3x + 3)/(-2x + 3)) + 1) - 5) + 1) - 3| + 2) + 1 and g(x) = (-1(-4(1|(-5(-2x)^2 - 5(-2x) + 2) - 3|) + 1) - 2)/(2(-4(1|(-5(-2x)^2 - 5(-2x) + 2) - 3|) + 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3|(-4(3sin(2\u03c0(4((-2(2x - 1) - 2)/(3(2x - 1))) - 3) + 1) - 1) + 3) + 3| + 2 and g(x) = (-2(-4(-1((1(-4x^2 + 5x - 3) + 3)/(-1(-4x^2 + 5x - 3)))^2 - 5((1(-4x^2 + 5x - 3) + 3)/(-1(-4x^2 + 5x - 3))) - 2)^2 - 4(-1((1(-4x^2 + 5x - 3) + 3)/(-1(-4x^2 + 5x - 3)))^2 - 5((1(-4x^2 + 5x - 3) + 3)/(-1(-4x^2 + 5x - 3))) - 2) + 3) + 1)/(-2(-4(-1((1(-4x^2 + 5x - 3) + 3)/(-1(-4x^2 + 5x - 3)))^2 - 5((1(-4x^2 + 5x - 3) + 3)/(-1(-4x^2 + 5x - 3))) - 2)^2 - 4(-1((1(-4x^2 + 5x - 3) + 3)/(-1(-4x^2 + 5x - 3)))^2 - 5((1(-4x^2 + 5x - 3) + 3)/(-1(-4x^2 + 5x - 3))) - 2) + 3) - 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": "3.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 5((1(-3(-3e^(1(1(-1|x - 3| - 3)^2 - 3(-1|x - 3| - 3))) - 2)^2 + 1(-3e^(1(1(-1|x - 3| - 3)^2 - 3(-1|x - 3| - 3))) - 2) + 2) + 1)/(-2(-3(-3e^(1(1(-1|x - 3| - 3)^2 - 3(-1|x - 3| - 3))) - 2)^2 + 1(-3e^(1(1(-1|x - 3| - 3)^2 - 3(-1|x - 3| - 3))) - 2) + 2) - 1))^2 + 5((1(-3(-3e^(1(1(-1|x - 3| - 3)^2 - 3(-1|x - 3| - 3))) - 2)^2 + 1(-3e^(1(1(-1|x - 3| - 3)^2 - 3(-1|x - 3| - 3))) - 2) + 2) + 1)/(-2(-3(-3e^(1(1(-1|x - 3| - 3)^2 - 3(-1|x - 3| - 3))) - 2)^2 + 1(-3e^(1(1(-1|x - 3| - 3)^2 - 3(-1|x - 3| - 3))) - 2) + 2) - 1)) - 1, g(x) = -3((3((1(-2(3e^(1x) + 1)^2 + 3(3e^(1x) + 1) + 5) + 1)/(3(-2(3e^(1x) + 1)^2 + 3(3e^(1x) + 1) + 5) - 1)) + 1)/(-3((1(-2(3e^(1x) + 1)^2 + 3(3e^(1x) + 1) + 5) + 1)/(3(-2(3e^(1x) + 1)^2 + 3(3e^(1x) + 1) + 5) - 1)) + 4))^2 + 3((3((1(-2(3e^(1x) + 1)^2 + 3(3e^(1x) + 1) + 5) + 1)/(3(-2(3e^(1x) + 1)^2 + 3(3e^(1x) + 1) + 5) - 1)) + 1)/(-3((1(-2(3e^(1x) + 1)^2 + 3(3e^(1x) + 1) + 5) + 1)/(3(-2(3e^(1x) + 1)^2 + 3(3e^(1x) + 1) + 5) - 1)) + 4)) + 1, x = -0.9, 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": "88.4", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1|((2((2(-3((-1(1|x + 3| - 3) - 3)/(2(1|x + 3| - 3) + 2)) + 4) - 1)/(-2(-3((-1(1|x + 3| - 3) - 3)/(2(1|x + 3| - 3) + 2)) + 4) + 3)) - 1)/(-3((2(-3((-1(1|x + 3| - 3) - 3)/(2(1|x + 3| - 3) + 2)) + 4) - 1)/(-2(-3((-1(1|x + 3| - 3) - 3)/(2(1|x + 3| - 3) + 2)) + 4) + 3)) + 2))| - 2, g(x) = -1(-3e^(-1(3|(2|((-1x - 3)/(-1x - 3)) + 3|) + 3| + 1)) + 1) - 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -4((-3(-2|(-5((-1((1x - 3)/(-1x + 2)) + 3)/(-1((1x - 3)/(-1x + 2)) - 1))^2 - 4((-1((1x - 3)/(-1x + 2)) + 3)/(-1((1x - 3)/(-1x + 2)) - 1)) + 4) + 1| - 2) + 2)/(-3(-2|(-5((-1((1x - 3)/(-1x + 2)) + 3)/(-1((1x - 3)/(-1x + 2)) - 1))^2 - 4((-1((1x - 3)/(-1x + 2)) + 3)/(-1((1x - 3)/(-1x + 2)) - 1)) + 4) + 1| - 2) - 3))^2 + 3 and g(x) = -2((2(-4((-3(-4x^2 - 2x + 2) + 2)/(-3(-4x^2 - 2x + 2) + 2)) + 5))/(-1(-4((-3(-4x^2 - 2x + 2) + 2)/(-3(-4x^2 - 2x + 2) + 2)) + 5) + 2))^2 - 4((2(-4((-3(-4x^2 - 2x + 2) + 2)/(-3(-4x^2 - 2x + 2) + 2)) + 5))/(-1(-4((-3(-4x^2 - 2x + 2) + 2)/(-3(-4x^2 - 2x + 2) + 2)) + 5) + 2)) + 2 from x = 2.1 to x = 2.6. Round 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) = 4(-3|(2cos(1\u03c0((-1(-5((-3x - 3)/(3x + 1))^2 - 5((-3x - 3)/(3x + 1)) - 1) - 3)/(-3(-5((-3x - 3)/(3x + 1))^2 - 5((-3x - 3)/(3x + 1)) - 1) - 1)) - 3) + 2) - 1| - 1) + 5 and g(x) = (3((3(2|(3|(4x^2 - 2x - 1) - 3|)| - 3) - 1)/(-1(2|(3|(4x^2 - 2x - 1) - 3|)| - 3) + 2)) - 1)/(-1((3(2|(3|(4x^2 - 2x - 1) - 3|)| - 3) - 1)/(-1(2|(3|(4x^2 - 2x - 1) - 3|)| - 3) + 2)) - 1) from x = -4.1 to x = -3.9999999999999996. 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) = -1|(3|(4(-5(-3sin(1\u03c0(3x^2 + 5x + 4) + 2) + 3)) + 4) + 1| + 3) - 2| and g(x) = 1|((-3(1|((-1(5x - 3) + 3)/(-1(5x - 3) - 3)) + 2|) + 2)/(-3(1|((-1(5x - 3) + 3)/(-1(5x - 3) - 3)) + 2|) + 4)) - 1| - 3 from x = -2.6 to x = -2.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "26.9", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2(-1|(1(-3|(1(-5x + 5)^2 - 2(-5x + 5) + 2) + 2| - 1)^2 + 4(-3|(1(-5x + 5)^2 - 2(-5x + 5) + 2) + 2| - 1) - 4) + 3|)^2 + 1(-1|(1(-3|(1(-5x + 5)^2 - 2(-5x + 5) + 2) + 2| - 1)^2 + 4(-3|(1(-5x + 5)^2 - 2(-5x + 5) + 2) + 2| - 1) - 4) + 3|) - 4, g(x) = 1|(-2(-5(1(3|x + 1| + 1)^2 - 2(3|x + 1| + 1) + 1)^2 - 3(1(3|x + 1| + 1)^2 - 2(3|x + 1| + 1) + 1)) + 1)| - 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": "175.9", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (3(5((3(2sin(3\u03c0((2(1|x + 3| + 1) + 3)/(-2(1|x + 3| + 1) + 3))) - 3) + 3)/(1(2sin(3\u03c0((2(1|x + 3| + 1) + 3)/(-2(1|x + 3| + 1) + 3))) - 3) - 2))^2 - 1((3(2sin(3\u03c0((2(1|x + 3| + 1) + 3)/(-2(1|x + 3| + 1) + 3))) - 3) + 3)/(1(2sin(3\u03c0((2(1|x + 3| + 1) + 3)/(-2(1|x + 3| + 1) + 3))) - 3) - 2)) - 4) - 3)/(-3(5((3(2sin(3\u03c0((2(1|x + 3| + 1) + 3)/(-2(1|x + 3| + 1) + 3))) - 3) + 3)/(1(2sin(3\u03c0((2(1|x + 3| + 1) + 3)/(-2(1|x + 3| + 1) + 3))) - 3) - 2))^2 - 1((3(2sin(3\u03c0((2(1|x + 3| + 1) + 3)/(-2(1|x + 3| + 1) + 3))) - 3) + 3)/(1(2sin(3\u03c0((2(1|x + 3| + 1) + 3)/(-2(1|x + 3| + 1) + 3))) - 3) - 2)) - 4) + 2), g(x) = 1(-3|((3(4(1cos(2\u03c0x - 2) + 3)^2 - 2(1cos(2\u03c0x - 2) + 3) - 5) - 3)/(-1(4(1cos(2\u03c0x - 2) + 3)^2 - 2(1cos(2\u03c0x - 2) + 3) - 5))) + 2| + 2) - 5, x = 0.6, 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": "5.8", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1(-3((-2((-2(-1e^(-2((-1x + 1)/(-2x + 1)))) - 1)/(-1(-1e^(-2((-1x + 1)/(-2x + 1)))) - 2)) - 3)/(-1((-2(-1e^(-2((-1x + 1)/(-2x + 1)))) - 1)/(-1(-1e^(-2((-1x + 1)/(-2x + 1)))) - 2)) + 2)) + 3), g(x) = -1(2(2(-3|(-2|x + 1|) + 3| + 3)^2 + 3(-3|(-2|x + 1|) + 3| + 3) + 3) + 5), 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": "Determine the area of the region enclosed by the graphs of f(x) = -2(-2(3|((-3(3|(1x^2 - 2x + 1) + 3|) - 2)/(-1(3|(1x^2 - 2x + 1) + 3|) + 3)) - 3| - 3) + 2) + 4 and g(x) = -2((1(4(-2|(3x^2 - 4x + 4)|)^2 - 1(-2|(3x^2 - 4x + 4)|) - 2) - 2)/(1(4(-2|(3x^2 - 4x + 4)|)^2 - 1(-2|(3x^2 - 4x + 4)|) - 2) + 2)) - 4 between the vertical lines x = -1.3 and x = 3.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35.7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1(-1sin(1\u03c0(2|(2(-2|((1x + 3)/(1x + 1)) + 1|) - 5) - 2|) + 1) + 2) - 3 and g(x) = 1(3(2sin(3\u03c0(5(2x + 3)^2 - 3(2x + 3) + 3) - 3)) + 4)^2 - 5(3(2sin(3\u03c0(5(2x + 3)^2 - 3(2x + 3) + 3) - 3)) + 4) - 5 from x = -0.6 to x = -0.5. 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((1((-1(4((-2(1x + 2) + 1)/(-2(1x + 2) + 1)) - 5) - 2)/(2(4((-2(1x + 2) + 1)/(-2(1x + 2) + 1)) - 5))) - 3)/(-2((-1(4((-2(1x + 2) + 1)/(-2(1x + 2) + 1)) - 5) - 2)/(2(4((-2(1x + 2) + 1)/(-2(1x + 2) + 1)) - 5))) - 3))^2 - 4((1((-1(4((-2(1x + 2) + 1)/(-2(1x + 2) + 1)) - 5) - 2)/(2(4((-2(1x + 2) + 1)/(-2(1x + 2) + 1)) - 5))) - 3)/(-2((-1(4((-2(1x + 2) + 1)/(-2(1x + 2) + 1)) - 5) - 2)/(2(4((-2(1x + 2) + 1)/(-2(1x + 2) + 1)) - 5))) - 3)) - 2 and g(x) = -1((-1(5(-2cos(1\u03c0(-2x + 4) + 3) + 1)^2 + 4(-2cos(1\u03c0(-2x + 4) + 3) + 1) + 3) - 2)/(-1(5(-2cos(1\u03c0(-2x + 4) + 3) + 1)^2 + 4(-2cos(1\u03c0(-2x + 4) + 3) + 1) + 3) + 2)) + 1 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": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1((-3(1((1((2((-3x - 3)/(1x - 3)) - 1)/(3((-3x - 3)/(1x - 3)) + 2)) + 3)/(-1((2((-3x - 3)/(1x - 3)) - 1)/(3((-3x - 3)/(1x - 3)) + 2)) - 1))^2 - 2((1((2((-3x - 3)/(1x - 3)) - 1)/(3((-3x - 3)/(1x - 3)) + 2)) + 3)/(-1((2((-3x - 3)/(1x - 3)) - 1)/(3((-3x - 3)/(1x - 3)) + 2)) - 1)) - 5) - 3)/(1(1((1((2((-3x - 3)/(1x - 3)) - 1)/(3((-3x - 3)/(1x - 3)) + 2)) + 3)/(-1((2((-3x - 3)/(1x - 3)) - 1)/(3((-3x - 3)/(1x - 3)) + 2)) - 1))^2 - 2((1((2((-3x - 3)/(1x - 3)) - 1)/(3((-3x - 3)/(1x - 3)) + 2)) + 3)/(-1((2((-3x - 3)/(1x - 3)) - 1)/(3((-3x - 3)/(1x - 3)) + 2)) - 1)) - 5) + 3)) - 3 and g(x) = -2|(2(-2(1((-2x + 3)/(2x - 1)) + 5) - 5) - 2) + 3| from x = -1.5 to x = 0.3. 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": "Calculate the area enclosed between the functions f(x) = (-1(-4(-4(1(1|(-5x + 5) - 2| + 2) - 4) + 2)^2 - 2(-4(1(1|(-5x + 5) - 2| + 2) - 4) + 2) + 5) - 3)/(2(-4(-4(1(1|(-5x + 5) - 2| + 2) - 4) + 2)^2 - 2(-4(1(1|(-5x + 5) - 2| + 2) - 4) + 2) + 5) - 1) and g(x) = 1(-1|(4((1(-2|x + 2|) - 2)/(-1(-2|x + 2|) + 3)) + 5) - 3| + 2) from x = 0.0 to 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": "Determine the area of the region enclosed by the graphs of f(x) = -1((-1(2|((-3(-3|(-2x^2 + 1x + 2) + 1| + 1) - 1)/(-3(-3|(-2x^2 + 1x + 2) + 1| + 1) - 3))| + 1) - 3)/(1(2|((-3(-3|(-2x^2 + 1x + 2) + 1| + 1) - 1)/(-3(-3|(-2x^2 + 1x + 2) + 1| + 1) - 3))| + 1) + 1)) + 1 and g(x) = (-2((-2(-4(-1(3x + 2)^2 + 4(3x + 2) + 1) - 3) + 1)/(3(-4(-1(3x + 2)^2 + 4(3x + 2) + 1) - 3) + 1)) - 3)/(1((-2(-4(-1(3x + 2)^2 + 4(3x + 2) + 1) - 3) + 1)/(3(-4(-1(3x + 2)^2 + 4(3x + 2) + 1) - 3) + 1)) + 2) 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": "6.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3|(-1(5(2((3(1x^2 + 5x + 1) + 2)/(-2(1x^2 + 5x + 1) - 3)) + 2)^2 - 3(2((3(1x^2 + 5x + 1) + 2)/(-2(1x^2 + 5x + 1) - 3)) + 2) + 4) - 3)| + 3 and g(x) = 5(2(-1(5(3x^2 - 3x - 1) - 5)^2 + 4(5(3x^2 - 3x - 1) - 5) + 5) + 2) + 4 from x = 1.4 to x = 1.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20.7", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1|(4(-2|(3|(-1|(-3|x + 2| - 3) + 3| + 2) - 1| + 3)| - 1) + 3)| - 2, g(x) = 4(-3(3|(-1(1e^(-2x) + 1)^2 + 4(1e^(-2x) + 1)) - 1| - 2)^2 - 4)^2 + 4(-3(3|(-1(1e^(-2x) + 1)^2 + 4(1e^(-2x) + 1)) - 1| - 2)^2 - 4) - 5, 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": "345.9", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2|(3((-2(-2e^(-1((-2(-4x - 5) - 1)/(1(-4x - 5) + 2))) + 2) - 2)/(3(-2e^(-1((-2(-4x - 5) - 1)/(1(-4x - 5) + 2))) + 2)))^2 - 5((-2(-2e^(-1((-2(-4x - 5) - 1)/(1(-4x - 5) + 2))) + 2) - 2)/(3(-2e^(-1((-2(-4x - 5) - 1)/(1(-4x - 5) + 2))) + 2))) + 3) + 1| + 1, g(x) = 3|(3(2(-3(-3x^2 - 4x - 2)^2 + 1(-3x^2 - 4x - 2) + 2)^2 + 1(-3(-3x^2 - 4x - 2)^2 + 1(-3x^2 - 4x - 2) + 2) - 2) - 2) + 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": "3.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2cos(3\u03c0(2((-1(-3|(-2(1x^2 + 1x)^2 - 2(1x^2 + 1x) + 4) + 2| + 3) + 2)/(1(-3|(-2(1x^2 + 1x)^2 - 2(1x^2 + 1x) + 4) + 2| + 3)))^2 - 1((-1(-3|(-2(1x^2 + 1x)^2 - 2(1x^2 + 1x) + 4) + 2| + 3) + 2)/(1(-3|(-2(1x^2 + 1x)^2 - 2(1x^2 + 1x) + 4) + 2| + 3))) - 2) - 3) + 1 and g(x) = -1(1(-3(-1(-5x + 3)^2 - 4(-5x + 3) + 1) + 5) + 2)^2 - 4(1(-3(-1(-5x + 3)^2 - 4(-5x + 3) + 1) + 5) + 2) - 1 between the vertical lines x = 0.8 and x = 1.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9.9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2|(2|(1((1(1(4x - 3) + 2) + 3)/(-3(1(4x - 3) + 2) - 1))^2 - 4((1(1(4x - 3) + 2) + 3)/(-3(1(4x - 3) + 2) - 1)) + 1) + 2| + 2) - 2| + 2 and g(x) = -2|((-3((3(3(3x + 5)^2 + 5(3x + 5) + 2) - 2)/(-3(3(3x + 5)^2 + 5(3x + 5) + 2) - 2)) - 1)/(3((3(3(3x + 5)^2 + 5(3x + 5) + 2) - 2)/(-3(3(3x + 5)^2 + 5(3x + 5) + 2) - 2)) + 1)) + 3| + 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2(-4((-1((-2(1|(1x^2 - 5x + 4) + 2| + 1) - 3)/(-2(1|(1x^2 - 5x + 4) + 2| + 1) + 1)) + 2)/(-1((-2(1|(1x^2 - 5x + 4) + 2| + 1) - 3)/(-2(1|(1x^2 - 5x + 4) + 2| + 1) + 1)) + 3)) - 1) + 3 and g(x) = 3|(3|(1cos(3\u03c0(2|(-2|x - 2| + 3) - 1| + 3) - 3) + 1) + 3| + 3) - 1| + 3 from x = 1.7 to x = 3.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35.8", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1e^(2((-3(-2(3((1(-2|x - 3| - 2) - 1)/(-3(-2|x - 3| - 2) - 2))^2 - 5((1(-2|x - 3| - 2) - 1)/(-3(-2|x - 3| - 2) - 2)) - 1)^2 + 2(3((1(-2|x - 3| - 2) - 1)/(-3(-2|x - 3| - 2) - 2))^2 - 5((1(-2|x - 3| - 2) - 1)/(-3(-2|x - 3| - 2) - 2)) - 1) - 1) + 2)/(-2(-2(3((1(-2|x - 3| - 2) - 1)/(-3(-2|x - 3| - 2) - 2))^2 - 5((1(-2|x - 3| - 2) - 1)/(-3(-2|x - 3| - 2) - 2)) - 1)^2 + 2(3((1(-2|x - 3| - 2) - 1)/(-3(-2|x - 3| - 2) - 2))^2 - 5((1(-2|x - 3| - 2) - 1)/(-3(-2|x - 3| - 2) - 2)) - 1) - 1)))) - 3, g(x) = 4(2(2((-3((1x)/(3x + 3)) + 1)/(3((1x)/(3x + 3)) + 1)) - 5)^2 + 3(2((-3((1x)/(3x + 3)) + 1)/(3((1x)/(3x + 3)) + 1)) - 5) - 2)^2 - 2(2(2((-3((1x)/(3x + 3)) + 1)/(3((1x)/(3x + 3)) + 1)) - 5)^2 + 3(2((-3((1x)/(3x + 3)) + 1)/(3((1x)/(3x + 3)) + 1)) - 5) - 2) + 5, 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": "0.9", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-3(4(1(3sin(1\u03c0(-3((-1x - 2)/(-3x + 2)) - 4) - 1) + 3) + 2)^2 + 4(1(3sin(1\u03c0(-3((-1x - 2)/(-3x + 2)) - 4) - 1) + 3) + 2) + 4) - 3)/(-1(4(1(3sin(1\u03c0(-3((-1x - 2)/(-3x + 2)) - 4) - 1) + 3) + 2)^2 + 4(1(3sin(1\u03c0(-3((-1x - 2)/(-3x + 2)) - 4) - 1) + 3) + 2) + 4) - 1), g(x) = (-3(5((-2((1((-3x)/(2x - 1)))/(3((-3x)/(2x - 1)) + 1)))/(2((1((-3x)/(2x - 1)))/(3((-3x)/(2x - 1)) + 1)) - 3))^2 + 5((-2((1((-3x)/(2x - 1)))/(3((-3x)/(2x - 1)) + 1)))/(2((1((-3x)/(2x - 1)))/(3((-3x)/(2x - 1)) + 1)) - 3))) + 3)/(-3(5((-2((1((-3x)/(2x - 1)))/(3((-3x)/(2x - 1)) + 1)))/(2((1((-3x)/(2x - 1)))/(3((-3x)/(2x - 1)) + 1)) - 3))^2 + 5((-2((1((-3x)/(2x - 1)))/(3((-3x)/(2x - 1)) + 1)))/(2((1((-3x)/(2x - 1)))/(3((-3x)/(2x - 1)) + 1)) - 3))) - 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": "4.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -4(2|(-3(-2(5((1x - 1)/(3x + 1)) + 5) - 3)^2 - 1(-2(5((1x - 1)/(3x + 1)) + 5) - 3) + 4) + 2|)^2 + 4(2|(-3(-2(5((1x - 1)/(3x + 1)) + 5) - 3)^2 - 1(-2(5((1x - 1)/(3x + 1)) + 5) - 3) + 4) + 2|) + 1 and g(x) = -1((-2(-1|((3(-3x - 5) + 1)/(-1(-3x - 5) - 1)) - 2| - 3) + 1)/(2(-1|((3(-3x - 5) + 1)/(-1(-3x - 5) - 1)) - 2| - 3) + 1)) - 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": "88.9", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1(1|(1|((-3(3|(-2|x + 1| - 2) + 3| - 2) - 1)/(1(3|(-2|x + 1| - 2) + 3| - 2))) + 2| + 3) - 3| - 1) - 3 and g(x) = -3|(1|((1(2e^(-1((-3x + 1)/(-2x + 3))) - 3) - 1)/(-3(2e^(-1((-3x + 1)/(-2x + 3))) - 3)))| - 2) - 3| - 1 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": "9.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2(1|(1(2sin(2\u03c0(-5(1x - 3)) + 3) + 2)^2 + 1(2sin(2\u03c0(-5(1x - 3)) + 3) + 2) - 3) + 1| + 1) and g(x) = 5(-4(4(-2(-2x + 4) + 4)^2 - 1(-2(-2x + 4) + 4) - 2)^2 - 5(4(-2(-2x + 4) + 4)^2 - 1(-2(-2x + 4) + 4) - 2) + 4) between the vertical lines x = 0.9 and x = 1.0. 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) = -5(-3e^(-1(-2(-4(-4(-3|x - 2| - 3) + 1)^2 + 5(-4(-3|x - 2| - 3) + 1) + 3) - 3)) + 1)^2 - 5(-3e^(-1(-2(-4(-4(-3|x - 2| - 3) + 1)^2 + 5(-4(-3|x - 2| - 3) + 1) + 3) - 3)) + 1) + 2, g(x) = -3|(3|(-1(1(-2x^2 - 5x + 3) - 5)^2 - 3(1(-2x^2 - 5x + 3) - 5) + 3) - 2| - 2)|, x = -2.6, 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": "5.7", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -4(3sin(2\u03c0(4(2(1(1x + 2) - 1)^2 - 2) + 1) + 3) + 2) + 1 and g(x) = 2(-1(-3e^(-1(5(2x - 3) - 2)) + 3) - 4)^2 - 3(-1(-3e^(-1(5(2x - 3) - 2)) + 3) - 4) + 1 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": "2.5", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1(-1sin(3\u03c0(-1(-3|(1(1|x - 2| + 1) - 4) + 2| + 3) - 1) - 2) - 3)^2 + 5, g(x) = 5((1(3(-3|(-3x + 2) - 2|)^2 - 4(-3|(-3x + 2) - 2|) - 5) + 1)/(-3(3(-3|(-3x + 2) - 2|)^2 - 4(-3|(-3x + 2) - 2|) - 5) + 4))^2 + 2((1(3(-3|(-3x + 2) - 2|)^2 - 4(-3|(-3x + 2) - 2|) - 5) + 1)/(-3(3(-3|(-3x + 2) - 2|)^2 - 4(-3|(-3x + 2) - 2|) - 5) + 4)) + 1, x = -0.1, 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": "2.8", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2(2sin(3\u03c0(4(5((-2(-3x^2 + 4) + 2)/(-3(-3x^2 + 4) - 1)) + 5)^2 + 5) + 3) - 2) + 3 and g(x) = 5(1(-1|(3((-1x + 1)/(2x + 3)) - 4) - 2| + 2)^2 + 1(-1|(3((-1x + 1)/(2x + 3)) - 4) - 2| + 2) - 5)^2 - 2(1(-1|(3((-1x + 1)/(2x + 3)) - 4) - 2| + 2)^2 + 1(-1|(3((-1x + 1)/(2x + 3)) - 4) - 2| + 2) - 5) - 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": "2.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2cos(2\u03c0(-1|(2|(1(-2|(-1|x - 3| + 1)| - 2)^2 + 3(-2|(-1|x - 3| + 1)| - 2) - 5) - 1|) + 1|) + 2) - 1, g(x) = -2|((1(4(1e^(-1(-3|x - 3| + 1)) - 3)^2 + 1(1e^(-1(-3|x - 3| + 1)) - 3) - 1) - 2)/(1(4(1e^(-1(-3|x - 3| + 1)) - 3)^2 + 1(1e^(-1(-3|x - 3| + 1)) - 3) - 1) + 2)) + 2|, 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": "Calculate the area enclosed between the functions f(x) = -1(1|(2|(-3(1(4x^2 - 4) + 5) + 3) - 1| - 3) + 1| - 1)^2 + 3(1|(2|(-3(1(4x^2 - 4) + 5) + 3) - 1| - 3) + 1| - 1) - 3 and g(x) = -5((2(5(-1(-2x^2 - 4x - 3) - 3) + 3))/(-2(5(-1(-2x^2 - 4x - 3) - 3) + 3) - 1))^2 - 1((2(5(-1(-2x^2 - 4x - 3) - 3) + 3))/(-2(5(-1(-2x^2 - 4x - 3) - 3) + 3) - 1)) - 4 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": "1.8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-2(-4(1|(3|(-1(3|x - 3| - 2) + 1) - 1|) - 3| - 1)^2 + 1(1|(3|(-1(3|x - 3| - 2) + 1) - 1|) - 3| - 1) + 4) - 3)/(1(-4(1|(3|(-1(3|x - 3| - 2) + 1) - 1|) - 3| - 1)^2 + 1(1|(3|(-1(3|x - 3| - 2) + 1) - 1|) - 3| - 1) + 4) - 3) and g(x) = 1(-1((-2(-1|(2|x - 1| - 1) + 1| + 2) + 2)/(2(-1|(2|x - 1| - 1) + 1| + 2) + 3))^2 + 5((-2(-1|(2|x - 1| - 1) + 1| + 2) + 2)/(2(-1|(2|x - 1| - 1) + 1| + 2) + 3)) - 5) - 1 from x = 4.1 to x = 4.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 3|(2(1(-3|(3(1cos(2\u03c0x - 3) - 2)^2 + 5(1cos(2\u03c0x - 3) - 2) - 2) + 2|) - 5) + 3) + 2| - 2 and g(x) = -4(3((-2(-1((2x + 3)/(3x - 2))) - 1)/(3(-1((2x + 3)/(3x - 2))) + 3)) + 3) + 1 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": "2.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1(-3|(3cos(3\u03c0(-4(-3|(1x + 1) - 3| - 1)^2 - 4(-3|(1x + 1) - 3| - 1) + 5) + 2) - 3) - 2| - 3) + 5 and g(x) = 2|((-1(3(5((3x + 1)/(1x + 3))^2 - 2((3x + 1)/(1x + 3))) - 1) + 1)/(2(3(5((3x + 1)/(1x + 3))^2 - 2((3x + 1)/(1x + 3))) - 1) - 3)) + 3| - 2 from x = -0.5 to x = 0.4. 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": "Determine the area of the region enclosed by the graphs of f(x) = 4(-1(-3sin(3\u03c0(-5(-2(5x^2 + 3x) + 4) + 4)) - 1) + 2) - 1 and g(x) = 2e^(-1((1(-4((-3(-3x^2 + 4x + 5) + 3)/(1(-3x^2 + 4x + 5) + 3)) + 4) + 3)/(1(-4((-3(-3x^2 + 4x + 5) + 3)/(1(-3x^2 + 4x + 5) + 3)) + 4) + 1))) - 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": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1|((-1(-2(4(-4(1e^(1x) + 1) - 5) - 3)^2 - 2(4(-4(1e^(1x) + 1) - 5) - 3)) + 3)/(1(-2(4(-4(1e^(1x) + 1) - 5) - 3)^2 - 2(4(-4(1e^(1x) + 1) - 5) - 3)) + 1))| + 3 and g(x) = 1|((-3(5(-3e^(1(5x^2 + 3x + 4)) - 3) + 4) - 1)/(-1(5(-3e^(1(5x^2 + 3x + 4)) - 3) + 4) + 2)) + 2| - 3 between the vertical lines x = -1.0 and 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) = -4(1((-3(-1(2(-4x + 1) + 4) + 5) - 2)/(-2(-1(2(-4x + 1) + 4) + 5) - 1)) + 3)^2 - 4(1((-3(-1(2(-4x + 1) + 4) + 5) - 2)/(-2(-1(2(-4x + 1) + 4) + 5) - 1)) + 3) + 3 and g(x) = (1(-1|(-5(1|(1cos(3\u03c0x) - 1) + 1| - 3)^2 + 4(1|(1cos(3\u03c0x) - 1) + 1| - 3) - 3) - 1| + 3))/(-1(-1|(-5(1|(1cos(3\u03c0x) - 1) + 1| - 3)^2 + 4(1|(1cos(3\u03c0x) - 1) + 1| - 3) - 3) - 1| + 3) + 2) 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": "2.9", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2|((-2(3((-1((3(-5x + 1))/(-1(-5x + 1) + 2)) + 2)/(1((3(-5x + 1))/(-1(-5x + 1) + 2)) + 3))^2 + 2((-1((3(-5x + 1))/(-1(-5x + 1) + 2)) + 2)/(1((3(-5x + 1))/(-1(-5x + 1) + 2)) + 3)) - 4) - 3)/(-3(3((-1((3(-5x + 1))/(-1(-5x + 1) + 2)) + 2)/(1((3(-5x + 1))/(-1(-5x + 1) + 2)) + 3))^2 + 2((-1((3(-5x + 1))/(-1(-5x + 1) + 2)) + 2)/(1((3(-5x + 1))/(-1(-5x + 1) + 2)) + 3)) - 4) - 3)) + 1| - 1, g(x) = -1|(2|((-2(4(-2x^2 - 1x + 2)^2 + 3(-2x^2 - 1x + 2)) + 1)/(-1(4(-2x^2 - 1x + 2)^2 + 3(-2x^2 - 1x + 2)) + 2)) - 1| - 1)| - 3, 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": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (1(3((1((-2((3(-1|x - 1| + 3) - 3)/(2(-1|x - 1| + 3) - 1)) - 2)/(-3((3(-1|x - 1| + 3) - 3)/(2(-1|x - 1| + 3) - 1)))) - 2)/(-1((-2((3(-1|x - 1| + 3) - 3)/(2(-1|x - 1| + 3) - 1)) - 2)/(-3((3(-1|x - 1| + 3) - 3)/(2(-1|x - 1| + 3) - 1)))) - 3))^2 - 2((1((-2((3(-1|x - 1| + 3) - 3)/(2(-1|x - 1| + 3) - 1)) - 2)/(-3((3(-1|x - 1| + 3) - 3)/(2(-1|x - 1| + 3) - 1)))) - 2)/(-1((-2((3(-1|x - 1| + 3) - 3)/(2(-1|x - 1| + 3) - 1)) - 2)/(-3((3(-1|x - 1| + 3) - 3)/(2(-1|x - 1| + 3) - 1)))) - 3))) - 1)/(-3(3((1((-2((3(-1|x - 1| + 3) - 3)/(2(-1|x - 1| + 3) - 1)) - 2)/(-3((3(-1|x - 1| + 3) - 3)/(2(-1|x - 1| + 3) - 1)))) - 2)/(-1((-2((3(-1|x - 1| + 3) - 3)/(2(-1|x - 1| + 3) - 1)) - 2)/(-3((3(-1|x - 1| + 3) - 3)/(2(-1|x - 1| + 3) - 1)))) - 3))^2 - 2((1((-2((3(-1|x - 1| + 3) - 3)/(2(-1|x - 1| + 3) - 1)) - 2)/(-3((3(-1|x - 1| + 3) - 3)/(2(-1|x - 1| + 3) - 1)))) - 2)/(-1((-2((3(-1|x - 1| + 3) - 3)/(2(-1|x - 1| + 3) - 1)) - 2)/(-3((3(-1|x - 1| + 3) - 3)/(2(-1|x - 1| + 3) - 1)))) - 3))) - 2) and g(x) = 3|((-1((2(2e^(2(-2x^2 - 3x)) - 3) - 2)/(-1(2e^(2(-2x^2 - 3x)) - 3) - 1)) + 3)/(-2((2(2e^(2(-2x^2 - 3x)) - 3) - 2)/(-1(2e^(2(-2x^2 - 3x)) - 3) - 1)) - 3))| - 2 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": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2|(2(-2(2|(-2|(3x + 1) + 2|) + 3| - 2) - 4) - 1) + 3| - 2 and g(x) = 1(-3sin(1\u03c0(-1(-1(1x^2 - 2x - 1)^2 - 2(1x^2 - 2x - 1) - 2)^2 + 5(-1(1x^2 - 2x - 1)^2 - 2(1x^2 - 2x - 1) - 2) + 1) + 2) + 2) - 2 between the vertical lines x = -1.5 and x = -1.4. 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) = -2|((-2(-1sin(2\u03c0(-3((-2(-2|x + 2| + 1) - 1)/(-3(-2|x + 2| + 1) + 2)) + 5) - 1) - 2) - 1)/(2(-1sin(2\u03c0(-3((-2(-2|x + 2| + 1) - 1)/(-3(-2|x + 2| + 1) + 2)) + 5) - 1) - 2) + 1)) + 2| - 1, g(x) = 5(5(-1|(-3sin(1\u03c0((3x + 2)/(-3x - 3)) - 2) - 2) - 1| + 2)^2 - 3(-1|(-3sin(1\u03c0((3x + 2)/(-3x - 3)) - 2) - 2) - 1| + 2) - 1) - 2, 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": "15.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -3(-3(-2(-2cos(2\u03c0(2|((-1x - 3)/(2x - 1)) - 3| + 2) - 3)) + 1) + 4)^2 - 1(-3(-2(-2cos(2\u03c0(2|((-1x - 3)/(2x - 1)) - 3| + 2) - 3)) + 1) + 4), g(x) = -3(-3(-3|(3(-1x - 2) - 3) + 1|)^2 + 4(-3|(3(-1x - 2) - 3) + 1|) - 3)^2 - 3(-3(-3|(3(-1x - 2) - 3) + 1|)^2 + 4(-3|(3(-1x - 2) - 3) + 1|) - 3) - 3, x = -2.8, 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": "62.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 4((2(-2(3|((1(-2x + 5) - 3)/(-1(-2x + 5) - 2)) + 1| + 1) - 2) + 1)/(1(-2(3|((1(-2x + 5) - 3)/(-1(-2x + 5) - 2)) + 1| + 1) - 2) + 3))^2 - 4((2(-2(3|((1(-2x + 5) - 3)/(-1(-2x + 5) - 2)) + 1| + 1) - 2) + 1)/(1(-2(3|((1(-2x + 5) - 3)/(-1(-2x + 5) - 2)) + 1| + 1) - 2) + 3)) + 4, g(x) = 5(-2cos(1\u03c0(-1|(-1((-1x + 1)/(1x + 1))^2 + 3((-1x + 1)/(1x + 1)) - 3) - 3|) - 2) + 2) - 2, x = 3.6, 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": "1.9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -4(-3((2((2(3|(4x^2 - 1x + 3) + 1|))/(-1(3|(4x^2 - 1x + 3) + 1|))) + 2)/(3((2(3|(4x^2 - 1x + 3) + 1|))/(-1(3|(4x^2 - 1x + 3) + 1|))) - 1)) + 4) - 1 and g(x) = 5(-3(-2|(3e^(1(3x + 5)) + 1) - 2| + 3) + 2) - 5 from x = -2.7 to x = -1.8. 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) = (-1((3(-5(5((-2((2x - 2)/(3x)) + 3)/(2((2x - 2)/(3x)))) - 3)^2 - 4(5((-2((2x - 2)/(3x)) + 3)/(2((2x - 2)/(3x)))) - 3) + 2) - 2)/(1(-5(5((-2((2x - 2)/(3x)) + 3)/(2((2x - 2)/(3x)))) - 3)^2 - 4(5((-2((2x - 2)/(3x)) + 3)/(2((2x - 2)/(3x)))) - 3) + 2) + 3)) + 2)/(-3((3(-5(5((-2((2x - 2)/(3x)) + 3)/(2((2x - 2)/(3x)))) - 3)^2 - 4(5((-2((2x - 2)/(3x)) + 3)/(2((2x - 2)/(3x)))) - 3) + 2) - 2)/(1(-5(5((-2((2x - 2)/(3x)) + 3)/(2((2x - 2)/(3x)))) - 3)^2 - 4(5((-2((2x - 2)/(3x)) + 3)/(2((2x - 2)/(3x)))) - 3) + 2) + 3)) + 2) and g(x) = -3(1cos(1\u03c0((-1((-3(4x^2 + 1x - 4) + 3)/(-3(4x^2 + 1x - 4) + 1)) - 3)/(2((-3(4x^2 + 1x - 4) + 3)/(-3(4x^2 + 1x - 4) + 1)) - 1)) + 2) + 1) + 5 between the vertical lines x = 1.1 and x = 1.2000000000000002. 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(-1(-1(-1(3|x + 2| + 3)^2 - 2)^2 + 5(-1(3|x + 2| + 3)^2 - 2) + 2) - 2)^2 - 3(-1(-1(-1(3|x + 2| + 3)^2 - 2)^2 + 5(-1(3|x + 2| + 3)^2 - 2) + 2) - 2) + 2) + 1)/(-3(4(-1(-1(-1(3|x + 2| + 3)^2 - 2)^2 + 5(-1(3|x + 2| + 3)^2 - 2) + 2) - 2)^2 - 3(-1(-1(-1(3|x + 2| + 3)^2 - 2)^2 + 5(-1(3|x + 2| + 3)^2 - 2) + 2) - 2) + 2) - 2) and g(x) = 3|(-2cos(1\u03c0(-5((-3(-2|x| + 1) + 3)/(-3(-2|x| + 1) - 3))^2 - 2((-3(-2|x| + 1) + 3)/(-3(-2|x| + 1) - 3)) + 5) + 1) - 2) + 2| - 1 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": "Find the area of the region bounded by the curves f(x) = (1(-2|((-2(1((3(-1x^2 - 4x) + 3)/(-3(-1x^2 - 4x) + 4)) - 2) + 1)/(-1(1((3(-1x^2 - 4x) + 3)/(-3(-1x^2 - 4x) + 4)) - 2))) - 2| - 1) + 3)/(3(-2|((-2(1((3(-1x^2 - 4x) + 3)/(-3(-1x^2 - 4x) + 4)) - 2) + 1)/(-1(1((3(-1x^2 - 4x) + 3)/(-3(-1x^2 - 4x) + 4)) - 2))) - 2| - 1) + 3), g(x) = -2|(2|(2(3(1e^(-1x)) - 3)^2 + 5(3(1e^(-1x)) - 3))|) + 3| + 3, 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": "6.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 4(3cos(2\u03c0(1(2|(3|(5x - 5) + 2| + 1) - 3| - 2)^2 + 5) - 1) - 2) - 2 and g(x) = 4(3((3(1(1|x - 3| - 1)^2 - 5(1|x - 3| - 1) - 2) - 1)/(1(1(1|x - 3| - 1)^2 - 5(1|x - 3| - 1) - 2) + 2))^2 + 4((3(1(1|x - 3| - 1)^2 - 5(1|x - 3| - 1) - 2) - 1)/(1(1(1|x - 3| - 1)^2 - 5(1|x - 3| - 1) - 2) + 2)) - 2) + 2 between the vertical lines x = 2.4 and x = 2.5. 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(-1((1((-2(5x - 3) + 2)/(-3(5x - 3) + 4)) - 1)/(-2((-2(5x - 3) + 2)/(-3(5x - 3) + 4)) - 1))^2 - 1((1((-2(5x - 3) + 2)/(-3(5x - 3) + 4)) - 1)/(-2((-2(5x - 3) + 2)/(-3(5x - 3) + 4)) - 1)) + 2))/(-1(-1((1((-2(5x - 3) + 2)/(-3(5x - 3) + 4)) - 1)/(-2((-2(5x - 3) + 2)/(-3(5x - 3) + 4)) - 1))^2 - 1((1((-2(5x - 3) + 2)/(-3(5x - 3) + 4)) - 1)/(-2((-2(5x - 3) + 2)/(-3(5x - 3) + 4)) - 1)) + 2) + 2)) + 2)/(-2((3(-1((1((-2(5x - 3) + 2)/(-3(5x - 3) + 4)) - 1)/(-2((-2(5x - 3) + 2)/(-3(5x - 3) + 4)) - 1))^2 - 1((1((-2(5x - 3) + 2)/(-3(5x - 3) + 4)) - 1)/(-2((-2(5x - 3) + 2)/(-3(5x - 3) + 4)) - 1)) + 2))/(-1(-1((1((-2(5x - 3) + 2)/(-3(5x - 3) + 4)) - 1)/(-2((-2(5x - 3) + 2)/(-3(5x - 3) + 4)) - 1))^2 - 1((1((-2(5x - 3) + 2)/(-3(5x - 3) + 4)) - 1)/(-2((-2(5x - 3) + 2)/(-3(5x - 3) + 4)) - 1)) + 2) + 2)) + 1) and g(x) = (3(2(-1(-1sin(1\u03c0(2x - 5) + 1) + 1) + 3)^2 - 4(-1(-1sin(1\u03c0(2x - 5) + 1) + 1) + 3)) + 2)/(1(2(-1(-1sin(1\u03c0(2x - 5) + 1) + 1) + 3)^2 - 4(-1(-1sin(1\u03c0(2x - 5) + 1) + 1) + 3)) - 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": "15.8", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 5(2|(-2|((1(-1(3x^2 - 3x - 3) + 2) + 2)/(2(-1(3x^2 - 3x - 3) + 2) - 1)) + 1|)| - 3) + 2, g(x) = (-1(1cos(3\u03c0(1|(4(3x + 5)^2 + 2) + 2| - 1) - 2) - 2) - 2)/(1(1cos(3\u03c0(1|(4(3x + 5)^2 + 2) + 2| - 1) - 2) - 2) + 1), 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": "5.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 3cos(3\u03c0(-3|(-1(-4(-1(-1|x + 1| - 2)^2 + 2(-1|x + 1| - 2) - 4)) - 3) - 1| - 3) - 1) - 3 and g(x) = (-3(-4(1|(2|(1x^2 + 2x + 2)| + 2) + 2| + 3) - 2) + 3)/(3(-4(1|(2|(1x^2 + 2x + 2)| + 2) + 2| + 3) - 2)) from x = 4.7 to 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) = -1(4(3|(4(1cos(2\u03c0((-2x - 1)/(-2x + 3)) - 2) + 1) - 3) + 3| - 3) - 3)^2 + 2(4(3|(4(1cos(2\u03c0((-2x - 1)/(-2x + 3)) - 2) + 1) - 3) + 3| - 3) - 3) - 1, g(x) = -2|(-2e^(-2(3(1|((1x - 2)/(-3x + 1)) - 2| - 2) + 2)) - 3) + 3| - 2, x = 2.2, and x = 2.3000000000000003. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "56.5", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3e^(-1((1(-1(-5(5((-3x + 3)/(-3x - 1))^2 - 2((-3x + 3)/(-3x - 1)) + 1)^2 + 4(5((-3x + 3)/(-3x - 1))^2 - 2((-3x + 3)/(-3x - 1)) + 1) + 1) - 2) - 1)/(-1(-1(-5(5((-3x + 3)/(-3x - 1))^2 - 2((-3x + 3)/(-3x - 1)) + 1)^2 + 4(5((-3x + 3)/(-3x - 1))^2 - 2((-3x + 3)/(-3x - 1)) + 1) + 1) - 2) + 2))) + 2, g(x) = 2|(-1|((-3(3|(-5x - 5) - 1|) - 3)/(-1(3|(-5x - 5) - 1|) - 2)) + 2| + 3) - 3| - 3, x = 0.9, 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": "2.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (3(-2|(1cos(3\u03c0((-3(-3(-1|x + 1|)^2 - 3(-1|x + 1|) + 3) + 2)/(1(-3(-1|x + 1|)^2 - 3(-1|x + 1|) + 3) + 2)) - 3) - 1) - 1| + 2) + 2)/(1(-2|(1cos(3\u03c0((-3(-3(-1|x + 1|)^2 - 3(-1|x + 1|) + 3) + 2)/(1(-3(-1|x + 1|)^2 - 3(-1|x + 1|) + 3) + 2)) - 3) - 1) - 1| + 2) + 3), g(x) = -3|(-3(-1cos(2\u03c0(1((-2x + 1)/(2x - 3))^2 + 3((-2x + 1)/(2x - 3)) - 2))) - 4) - 2| + 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": "3.7", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1|(1(-1((-1(3(1x + 4)^2 - 4(1x + 4)) - 1)/(-3(3(1x + 4)^2 - 4(1x + 4)) + 1)) + 4) - 3)| - 1, g(x) = 1|(2|(3e^(2(-3((-1x - 2)/(1x)) - 1))) - 2| - 2) - 1| - 3, x = -4.1, and x = -3.9999999999999996. 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) = -1(2|((-2((-3(1(-3cos(2\u03c0x - 1) + 1)^2 + 2(-3cos(2\u03c0x - 1) + 1) - 4) + 1)/(1(1(-3cos(2\u03c0x - 1) + 1)^2 + 2(-3cos(2\u03c0x - 1) + 1) - 4) - 3)) + 1)/(-2((-3(1(-3cos(2\u03c0x - 1) + 1)^2 + 2(-3cos(2\u03c0x - 1) + 1) - 4) + 1)/(1(1(-3cos(2\u03c0x - 1) + 1)^2 + 2(-3cos(2\u03c0x - 1) + 1) - 4) - 3)) + 3)) - 2| - 2) + 2 and g(x) = (1(-4(2|(-2|(-1x + 2) - 2| - 2) - 2| + 2) + 5) + 3)/(3(-4(2|(-2|(-1x + 2) - 2| - 2) - 2| + 2) + 5) + 1) 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) = -3|(2((-2((-2(1(1x^2 - 4x + 1)^2 + 5(1x^2 - 4x + 1) - 1))/(1(1(1x^2 - 4x + 1)^2 + 5(1x^2 - 4x + 1) - 1) - 2)) + 2)/(1((-2(1(1x^2 - 4x + 1)^2 + 5(1x^2 - 4x + 1) - 1))/(1(1(1x^2 - 4x + 1)^2 + 5(1x^2 - 4x + 1) - 1) - 2)) + 1))^2 - 5((-2((-2(1(1x^2 - 4x + 1)^2 + 5(1x^2 - 4x + 1) - 1))/(1(1(1x^2 - 4x + 1)^2 + 5(1x^2 - 4x + 1) - 1) - 2)) + 2)/(1((-2(1(1x^2 - 4x + 1)^2 + 5(1x^2 - 4x + 1) - 1))/(1(1(1x^2 - 4x + 1)^2 + 5(1x^2 - 4x + 1) - 1) - 2)) + 1)) - 3) + 1| + 2 and g(x) = (-1(2|(1((-2(-1x^2 + 2x + 5) - 3)/(-2(-1x^2 + 2x + 5) + 1))^2 + 5((-2(-1x^2 + 2x + 5) - 3)/(-2(-1x^2 + 2x + 5) + 1)) + 5) + 1| - 1) - 3)/(1(2|(1((-2(-1x^2 + 2x + 5) - 3)/(-2(-1x^2 + 2x + 5) + 1))^2 + 5((-2(-1x^2 + 2x + 5) - 3)/(-2(-1x^2 + 2x + 5) + 1)) + 5) + 1| - 1) + 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": "58.6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -5(1|((1(3|(4((2x + 3)/(-1x - 1)) + 4) - 1| - 3))/(3(3|(4((2x + 3)/(-1x - 1)) + 4) - 1| - 3)))|)^2 - 3(1|((1(3|(4((2x + 3)/(-1x - 1)) + 4) - 1| - 3))/(3(3|(4((2x + 3)/(-1x - 1)) + 4) - 1| - 3)))|) - 3 and g(x) = -1(5((-3(-2(2cos(1\u03c0x + 3) - 1)^2 + 2(2cos(1\u03c0x + 3) - 1) + 5) + 2)/(-1(-2(2cos(1\u03c0x + 3) - 1)^2 + 2(2cos(1\u03c0x + 3) - 1) + 5) - 2))^2 - 1((-3(-2(2cos(1\u03c0x + 3) - 1)^2 + 2(2cos(1\u03c0x + 3) - 1) + 5) + 2)/(-1(-2(2cos(1\u03c0x + 3) - 1)^2 + 2(2cos(1\u03c0x + 3) - 1) + 5) - 2)) - 3)^2 + 4(5((-3(-2(2cos(1\u03c0x + 3) - 1)^2 + 2(2cos(1\u03c0x + 3) - 1) + 5) + 2)/(-1(-2(2cos(1\u03c0x + 3) - 1)^2 + 2(2cos(1\u03c0x + 3) - 1) + 5) - 2))^2 - 1((-3(-2(2cos(1\u03c0x + 3) - 1)^2 + 2(2cos(1\u03c0x + 3) - 1) + 5) + 2)/(-1(-2(2cos(1\u03c0x + 3) - 1)^2 + 2(2cos(1\u03c0x + 3) - 1) + 5) - 2)) - 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": "21.6", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2(3cos(3\u03c0(-2|((3((-2(-1x - 1) - 2)/(-2(-1x - 1) - 3)) - 2)/(2((-2(-1x - 1) - 2)/(-2(-1x - 1) - 3)) - 1)) - 2| - 3) + 3) + 1) - 2 and g(x) = -1(2e^(-1(-4(-3|(2x - 2)| - 1) - 5)) + 1)^2 + 3(2e^(-1(-4(-3|(2x - 2)| - 1) - 5)) + 1) between the vertical lines x = -2.4 and x = -1.8. 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) = (1(2|(-1|(1|(-3(-5x^2 + 1x + 3)^2 + 4(-5x^2 + 1x + 3) + 5) - 2| - 1) - 3| + 1) + 3| - 2) - 1)/(-1(2|(-1|(1|(-3(-5x^2 + 1x + 3)^2 + 4(-5x^2 + 1x + 3) + 5) - 2| - 1) - 3| + 1) + 3| - 2)) and g(x) = (-3(1|(-3(1e^(-2((3x + 1)/(2x + 2))))^2 - 1) - 1| - 2) - 1)/(-1(1|(-3(1e^(-2((3x + 1)/(2x + 2))))^2 - 1) - 1| - 2) - 2) from x = 0.9 to x = 1.0. 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) = 2(1((2(-4((1(3x^2 + 1x - 3) - 2)/(-3(3x^2 + 1x - 3) + 1)) + 5) + 1)/(2(-4((1(3x^2 + 1x - 3) - 2)/(-3(3x^2 + 1x - 3) + 1)) + 5))) - 1) - 1, g(x) = -2(1((-1(1(-1sin(1\u03c0x - 3)) - 5))/(3(1(-1sin(1\u03c0x - 3)) - 5) - 2))^2 - 4((-1(1(-1sin(1\u03c0x - 3)) - 5))/(3(1(-1sin(1\u03c0x - 3)) - 5) - 2)) - 1)^2 + 3(1((-1(1(-1sin(1\u03c0x - 3)) - 5))/(3(1(-1sin(1\u03c0x - 3)) - 5) - 2))^2 - 4((-1(1(-1sin(1\u03c0x - 3)) - 5))/(3(1(-1sin(1\u03c0x - 3)) - 5) - 2)) - 1) - 1, x = -1.3, 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": "1.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-1(-1|(-2|(2|(-1cos(1\u03c0(4x^2 - 1x + 3) + 1) + 1)| + 2) - 1| - 1) - 2| + 2) - 3)/(-1(-1|(-2|(2|(-1cos(1\u03c0(4x^2 - 1x + 3) + 1) + 1)| + 2) - 1| - 1) - 2| + 2) + 2) and g(x) = 2|(-5(-1|(-4(-1x - 3)) + 1| + 2)^2 + 4(-1|(-4(-1x - 3)) + 1| + 2) + 1) + 2| - 1 between the vertical lines x = -3.8 and x = -3.4. 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) = 4((1(-2|((-3(-1(1x - 4) - 1) + 2)/(2(-1(1x - 4) - 1) - 3)) - 1| - 2) - 2)/(-2(-2|((-3(-1(1x - 4) - 1) + 2)/(2(-1(1x - 4) - 1) - 3)) - 1| - 2) - 3))^2 - 3((1(-2|((-3(-1(1x - 4) - 1) + 2)/(2(-1(1x - 4) - 1) - 3)) - 1| - 2) - 2)/(-2(-2|((-3(-1(1x - 4) - 1) + 2)/(2(-1(1x - 4) - 1) - 3)) - 1| - 2) - 3)) and g(x) = 1|(-1e^(1(-4(-3|(4x) + 3| + 3)^2 - 1(-3|(4x) + 3| + 3) + 2)) - 2) - 1| - 3 from x = -0.5 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(-1(1(1(-1(4x - 5)^2 + 4(4x - 5) + 2) - 1)^2 + 3(1(-1(4x - 5)^2 + 4(4x - 5) + 2) - 1) - 1) - 3) - 2 and g(x) = -3|(1|((1(-2|(-1sin(1\u03c0x + 1) - 3) - 2| - 1) - 2)/(3(-2|(-1sin(1\u03c0x + 1) - 3) - 2| - 1) - 2)) + 2| - 1) + 2| - 3 from x = 1.0 to x = 1.3. 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": "Calculate the area enclosed between the functions f(x) = 4(-1((-1(2((2(1x^2 + 4x) - 1)/(2(1x^2 + 4x))) - 5) - 3)/(1(2((2(1x^2 + 4x) - 1)/(2(1x^2 + 4x))) - 5)))^2 + 1((-1(2((2(1x^2 + 4x) - 1)/(2(1x^2 + 4x))) - 5) - 3)/(1(2((2(1x^2 + 4x) - 1)/(2(1x^2 + 4x))) - 5))) + 2)^2 + 4(-1((-1(2((2(1x^2 + 4x) - 1)/(2(1x^2 + 4x))) - 5) - 3)/(1(2((2(1x^2 + 4x) - 1)/(2(1x^2 + 4x))) - 5)))^2 + 1((-1(2((2(1x^2 + 4x) - 1)/(2(1x^2 + 4x))) - 5) - 3)/(1(2((2(1x^2 + 4x) - 1)/(2(1x^2 + 4x))) - 5))) + 2) + 1 and g(x) = -3((2(3|((-3(4x + 5) - 1)/(1(4x + 5) - 2)) - 3| - 1) - 3)/(-1(3|((-3(4x + 5) - 1)/(1(4x + 5) - 2)) - 3| - 1) + 3)) + 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": "2.4", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2|(5((1(2((-3(-2|x + 1| + 2) + 3)/(-1(-2|x + 1| + 2) + 2)) - 1) + 3)/(-2(2((-3(-2|x + 1| + 2) + 3)/(-1(-2|x + 1| + 2) + 2)) - 1) - 1))^2 - 4((1(2((-3(-2|x + 1| + 2) + 3)/(-1(-2|x + 1| + 2) + 2)) - 1) + 3)/(-2(2((-3(-2|x + 1| + 2) + 3)/(-1(-2|x + 1| + 2) + 2)) - 1) - 1)) - 3) - 1| - 1, g(x) = 4(1|((1(-2(-2x + 5)) + 3)/(2(-2(-2x + 5)) - 1)) - 1| + 2) + 5, 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": "225.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2(3|(2(2((-3((-1x - 2)/(-2x - 1)) + 2)/(-2((-1x - 2)/(-2x - 1)) + 3))^2 - 4((-3((-1x - 2)/(-2x - 1)) + 2)/(-2((-1x - 2)/(-2x - 1)) + 3)) - 3)^2 + 3(2((-3((-1x - 2)/(-2x - 1)) + 2)/(-2((-1x - 2)/(-2x - 1)) + 3))^2 - 4((-3((-1x - 2)/(-2x - 1)) + 2)/(-2((-1x - 2)/(-2x - 1)) + 3)) - 3) + 2) - 1|)^2 - 2(3|(2(2((-3((-1x - 2)/(-2x - 1)) + 2)/(-2((-1x - 2)/(-2x - 1)) + 3))^2 - 4((-3((-1x - 2)/(-2x - 1)) + 2)/(-2((-1x - 2)/(-2x - 1)) + 3)) - 3)^2 + 3(2((-3((-1x - 2)/(-2x - 1)) + 2)/(-2((-1x - 2)/(-2x - 1)) + 3))^2 - 4((-3((-1x - 2)/(-2x - 1)) + 2)/(-2((-1x - 2)/(-2x - 1)) + 3)) - 3) + 2) - 1|) + 3 and g(x) = -2((-1((-2(-5((-2x + 2)/(-2x - 2)) + 3) - 2)/(-3(-5((-2x + 2)/(-2x - 2)) + 3) - 1)) + 1)/(-1((-2(-5((-2x + 2)/(-2x - 2)) + 3) - 2)/(-3(-5((-2x + 2)/(-2x - 2)) + 3) - 1)) + 2))^2 - 4 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": "47.6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1|(-2((2((3(-1(5x - 5)^2 + 2(5x - 5) - 1) + 3)/(-1(-1(5x - 5)^2 + 2(5x - 5) - 1) - 2)) - 3)/(1((3(-1(5x - 5)^2 + 2(5x - 5) - 1) + 3)/(-1(-1(5x - 5)^2 + 2(5x - 5) - 1) - 2)))) + 4) - 1| - 3 and g(x) = (-2(-1(1|(-1(-1x - 1)^2 + 1(-1x - 1)) - 1| - 3)) - 1)/(-2(-1(1|(-1(-1x - 1)^2 + 1(-1x - 1)) - 1| - 3)) + 3) from x = -2.5 to x = -0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "57.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-3((-2(1(-5(-2(1x^2 - 5x) - 3)^2 + 4(-2(1x^2 - 5x) - 3) - 2) - 4) + 2)/(2(1(-5(-2(1x^2 - 5x) - 3)^2 + 4(-2(1x^2 - 5x) - 3) - 2) - 4) - 3)) - 1)/(-1((-2(1(-5(-2(1x^2 - 5x) - 3)^2 + 4(-2(1x^2 - 5x) - 3) - 2) - 4) + 2)/(2(1(-5(-2(1x^2 - 5x) - 3)^2 + 4(-2(1x^2 - 5x) - 3) - 2) - 4) - 3)) + 3), g(x) = -1(-2|(5(-1(-3x^2 + 4x + 5) - 4) - 5)|)^2 + 1(-2|(5(-1(-3x^2 + 4x + 5) - 4) - 5)|) + 4, x = 2.6, 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": "3.6", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3e^(-2((1(1(4(-2(2|x| + 1) - 1)^2 - 4(-2(2|x| + 1) - 1) - 5)^2 + 2(4(-2(2|x| + 1) - 1)^2 - 4(-2(2|x| + 1) - 1) - 5) + 1) + 1)/(-2(1(4(-2(2|x| + 1) - 1)^2 - 4(-2(2|x| + 1) - 1) - 5)^2 + 2(4(-2(2|x| + 1) - 1)^2 - 4(-2(2|x| + 1) - 1) - 5) + 1) - 3))) - 1, g(x) = 3(-3((-3(2|(-3x^2 + 3x - 3) + 2| - 1) + 1)/(1(2|(-3x^2 + 3x - 3) + 2| - 1) + 3))^2 + 4((-3(2|(-3x^2 + 3x - 3) + 2| - 1) + 1)/(1(2|(-3x^2 + 3x - 3) + 2| - 1) + 3))) + 5, x = 0.2, 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": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-3(-5(4(-4((-3(-2sin(3\u03c0x - 2) - 2) - 2)/(-3(-2sin(3\u03c0x - 2) - 2))) - 2)^2 + 5(-4((-3(-2sin(3\u03c0x - 2) - 2) - 2)/(-3(-2sin(3\u03c0x - 2) - 2))) - 2) - 3) - 2) + 3)/(1(-5(4(-4((-3(-2sin(3\u03c0x - 2) - 2) - 2)/(-3(-2sin(3\u03c0x - 2) - 2))) - 2)^2 + 5(-4((-3(-2sin(3\u03c0x - 2) - 2) - 2)/(-3(-2sin(3\u03c0x - 2) - 2))) - 2) - 3) - 2)) and g(x) = -2((3((-2((1(1|x + 2| - 2) + 2)/(-2(1|x + 2| - 2))) + 1)/(-3((1(1|x + 2| - 2) + 2)/(-2(1|x + 2| - 2))) - 3)) - 1)/(1((-2((1(1|x + 2| - 2) + 2)/(-2(1|x + 2| - 2))) + 1)/(-3((1(1|x + 2| - 2) + 2)/(-2(1|x + 2| - 2))) - 3)))) - 5 from x = 2.8 to x = 4.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3(2|(3|(-3|((-3((-1x + 2)/(2x - 3)) - 1)/(-3((-1x + 2)/(2x - 3)) - 3)) + 1| + 2) - 1| - 3)| + 3) - 2 and g(x) = -1|(4(1cos(1\u03c0(1((-3x - 1)/(1x))^2 - 5)) - 2)^2 + 2(1cos(1\u03c0(1((-3x - 1)/(1x))^2 - 5)) - 2) + 5) + 3| - 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": "1.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 3((-2(-1|(-4((-3(-5x^2 - 4x - 2) + 2)/(3(-5x^2 - 4x - 2) - 2)) + 2) + 3|) + 2)/(-2(-1|(-4((-3(-5x^2 - 4x - 2) + 2)/(3(-5x^2 - 4x - 2) - 2)) + 2) + 3|) - 1)) - 2 and g(x) = 2(1|((-1(1(-3|x + 1| - 3)^2 + 4(-3|x + 1| - 3) - 1) - 2)/(1(1(-3|x + 1| - 3)^2 + 4(-3|x + 1| - 3) - 1)))| - 3) - 4 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": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1(2|(-2cos(1\u03c0(1(-5(1x + 5) - 2) - 2) + 2) - 1) + 3| + 1)^2 - 3(2|(-2cos(1\u03c0(1(-5(1x + 5) - 2) - 2) + 2) - 1) + 3| + 1) + 4, g(x) = -1|(1|(-2cos(3\u03c0(4(-5x^2 + 2x - 2) + 3) + 2) - 1) + 1| + 2) + 1| - 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": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (2((1(1|((-1(1|(-3x - 1) - 3| - 3) - 2)/(2(1|(-3x - 1) - 3| - 3) + 1)) + 2| - 2) - 3)/(3(1|((-1(1|(-3x - 1) - 3| - 3) - 2)/(2(1|(-3x - 1) - 3| - 3) + 1)) + 2| - 2) + 3)) - 1)/(3((1(1|((-1(1|(-3x - 1) - 3| - 3) - 2)/(2(1|(-3x - 1) - 3| - 3) + 1)) + 2| - 2) - 3)/(3(1|((-1(1|(-3x - 1) - 3| - 3) - 2)/(2(1|(-3x - 1) - 3| - 3) + 1)) + 2| - 2) + 3)) + 2) and g(x) = 1(-1(1cos(1\u03c0(2(-4x + 4) - 1) - 3) - 2)^2 + 2(1cos(1\u03c0(2(-4x + 4) - 1) - 3) - 2) + 5) - 3 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-2(1|(2((-3(-1(1x^2 - 1)^2 + 3(1x^2 - 1) - 3) + 1)/(3(-1(1x^2 - 1)^2 + 3(1x^2 - 1) - 3) + 3)) - 2) - 1| + 2) - 3)/(3(1|(2((-3(-1(1x^2 - 1)^2 + 3(1x^2 - 1) - 3) + 1)/(3(-1(1x^2 - 1)^2 + 3(1x^2 - 1) - 3) + 3)) - 2) - 1| + 2) - 2) and g(x) = -1|(-4(3|(-5(-5x) - 2) + 3| - 1) - 2) - 3| + 2 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": "2.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-3(-2(2(1|((2(1e^(2x)) + 2)/(-2(1e^(2x)) + 1)) + 1|) - 4) - 1) - 2)/(-1(-2(2(1|((2(1e^(2x)) + 2)/(-2(1e^(2x)) + 1)) + 1|) - 4) - 1) + 2) and g(x) = 1(1(4(-1e^(2((-3x)/(-1x + 3))) + 2)^2 + 2(-1e^(2((-3x)/(-1x + 3))) + 2) + 1)) - 3 from x = -0.8 to x = -0.1. 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) = 4(3((2(-2(-4(-2sin(2\u03c0x + 2) - 2))^2 + 5(-4(-2sin(2\u03c0x + 2) - 2)) + 3) - 2)/(2(-2(-4(-2sin(2\u03c0x + 2) - 2))^2 + 5(-4(-2sin(2\u03c0x + 2) - 2)) + 3) - 1))^2 + 5((2(-2(-4(-2sin(2\u03c0x + 2) - 2))^2 + 5(-4(-2sin(2\u03c0x + 2) - 2)) + 3) - 2)/(2(-2(-4(-2sin(2\u03c0x + 2) - 2))^2 + 5(-4(-2sin(2\u03c0x + 2) - 2)) + 3) - 1)) + 4) and g(x) = 1(2sin(2\u03c0(-1((3((1x - 3)/(-1x - 3)) - 3)/(3((1x - 3)/(-1x - 3)) - 2)) - 4) - 3) - 2)^2 - 1(2sin(2\u03c0(-1((3((1x - 3)/(-1x - 3)) - 3)/(3((1x - 3)/(-1x - 3)) - 2)) - 4) - 3) - 2) - 3 from x = -1.7 to x = -1.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1|(3(3|(-1e^(1((-3(-2|x - 1| - 1))/(-2(-2|x - 1| - 1) - 1)))) + 2| + 1)) - 3| and g(x) = -5((3((2((3(3x^2 + 5x - 1) - 2)/(1(3x^2 + 5x - 1) + 2)) + 2)/(-1((3(3x^2 + 5x - 1) - 2)/(1(3x^2 + 5x - 1) + 2)) + 2)) + 3)/(3((2((3(3x^2 + 5x - 1) - 2)/(1(3x^2 + 5x - 1) + 2)) + 2)/(-1((3(3x^2 + 5x - 1) - 2)/(1(3x^2 + 5x - 1) + 2)) + 2)) - 2)) + 4 from x = -2.0 to x = 0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "117.8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-2(-5(-3|((-2((1((-3x + 3)/(2x - 1)) - 1)/(-3((-3x + 3)/(2x - 1)) - 1)) - 3)/(1((1((-3x + 3)/(2x - 1)) - 1)/(-3((-3x + 3)/(2x - 1)) - 1)))) + 1|) + 3) + 2)/(-3(-5(-3|((-2((1((-3x + 3)/(2x - 1)) - 1)/(-3((-3x + 3)/(2x - 1)) - 1)) - 3)/(1((1((-3x + 3)/(2x - 1)) - 1)/(-3((-3x + 3)/(2x - 1)) - 1)))) + 1|) + 3) + 1) and g(x) = 3(-3sin(3\u03c0((-3((1(2|x - 1| + 1) - 1)/(1(2|x - 1| + 1) + 1)) + 1)/(-1((1(2|x - 1| + 1) - 1)/(1(2|x - 1| + 1) + 1)) - 1)) + 3) - 2)^2 + 1(-3sin(3\u03c0((-3((1(2|x - 1| + 1) - 1)/(1(2|x - 1| + 1) + 1)) + 1)/(-1((1(2|x - 1| + 1) - 1)/(1(2|x - 1| + 1) + 1)) - 1)) + 3) - 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": "8.8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-1(-3(4(-3cos(1\u03c0((2(-3x^2 - 1x + 5) - 2)/(-2(-3x^2 - 1x + 5) - 3)) + 3) + 2) - 5)^2 + 1(4(-3cos(1\u03c0((2(-3x^2 - 1x + 5) - 2)/(-2(-3x^2 - 1x + 5) - 3)) + 3) + 2) - 5) + 5) - 2)/(2(-3(4(-3cos(1\u03c0((2(-3x^2 - 1x + 5) - 2)/(-2(-3x^2 - 1x + 5) - 3)) + 3) + 2) - 5)^2 + 1(4(-3cos(1\u03c0((2(-3x^2 - 1x + 5) - 2)/(-2(-3x^2 - 1x + 5) - 3)) + 3) + 2) - 5) + 5) - 1) and g(x) = -2(-2sin(2\u03c0((1(-2((-3x - 1)/(-1x - 2)) + 2) + 3)/(3(-2((-3x - 1)/(-1x - 2)) + 2) - 2))) - 2) - 3 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": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2(-1((-1(5(2(1x^2 - 4x + 5) - 5)^2 + 5(2(1x^2 - 4x + 5) - 5) + 1) + 1)/(-3(5(2(1x^2 - 4x + 5) - 5)^2 + 5(2(1x^2 - 4x + 5) - 5) + 1) - 1))) - 2, g(x) = -1((-1(1|((-1(1x^2 + 4x - 4))/(2(1x^2 + 4x - 4) - 3)) + 3| - 1) - 2)/(2(1|((-1(1x^2 + 4x - 4))/(2(1x^2 + 4x - 4) - 3)) + 3| - 1) + 1))^2 - 5((-1(1|((-1(1x^2 + 4x - 4))/(2(1x^2 + 4x - 4) - 3)) + 3| - 1) - 2)/(2(1|((-1(1x^2 + 4x - 4))/(2(1x^2 + 4x - 4) - 3)) + 3| - 1) + 1)) + 4, x = 1.1, 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": "8.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-1(4(-4(-1((1(2x - 4) - 1)/(-2(2x - 4) + 3))) - 1)^2 - 4) + 1)/(3(4(-4(-1((1(2x - 4) - 1)/(-2(2x - 4) + 3))) - 1)^2 - 4) + 2) and g(x) = (1(-4((-1(1|(-2x + 1) + 3| + 3) + 1)/(2(1|(-2x + 1) + 3| + 3) + 2))^2 + 3((-1(1|(-2x + 1) + 3| + 3) + 1)/(2(1|(-2x + 1) + 3| + 3) + 2)) - 5) - 1)/(-2(-4((-1(1|(-2x + 1) + 3| + 3) + 1)/(2(1|(-2x + 1) + 3| + 3) + 2))^2 + 3((-1(1|(-2x + 1) + 3| + 3) + 1)/(2(1|(-2x + 1) + 3| + 3) + 2)) - 5) + 1) 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": "Calculate the area enclosed between the functions f(x) = -5((-3(-1(-1sin(3\u03c0(-2|(3|x + 1| - 3) - 2| + 2) + 1))^2 - 3(-1sin(3\u03c0(-2|(3|x + 1| - 3) - 2| + 2) + 1)) + 1) + 2)/(-2(-1(-1sin(3\u03c0(-2|(3|x + 1| - 3) - 2| + 2) + 1))^2 - 3(-1sin(3\u03c0(-2|(3|x + 1| - 3) - 2| + 2) + 1)) + 1) + 3)) + 4 and g(x) = -4((3(1((2(-1x - 1) + 2)/(-2(-1x - 1) - 3))^2 - 1((2(-1x - 1) + 2)/(-2(-1x - 1) - 3)) - 4) - 3)/(1(1((2(-1x - 1) + 2)/(-2(-1x - 1) - 3))^2 - 1((2(-1x - 1) + 2)/(-2(-1x - 1) - 3)) - 4) + 1))^2 - 2((3(1((2(-1x - 1) + 2)/(-2(-1x - 1) - 3))^2 - 1((2(-1x - 1) + 2)/(-2(-1x - 1) - 3)) - 4) - 3)/(1(1((2(-1x - 1) + 2)/(-2(-1x - 1) - 3))^2 - 1((2(-1x - 1) + 2)/(-2(-1x - 1) - 3)) - 4) + 1)) + 1 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": "4.8", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1(3cos(3\u03c0(-5(-3(-1(-2|x| - 2) - 2) + 2)^2 - 3(-3(-1(-2|x| - 2) - 2) + 2) + 3) + 1)) + 1 and g(x) = 4(-4((2((-2((-2x - 3)/(-3x)) - 3)/(-3((-2x - 3)/(-3x)) + 2)) + 2)/(1((-2((-2x - 3)/(-3x)) - 3)/(-3((-2x - 3)/(-3x)) + 2)) + 3)) - 1)^2 - 1(-4((2((-2((-2x - 3)/(-3x)) - 3)/(-3((-2x - 3)/(-3x)) + 2)) + 2)/(1((-2((-2x - 3)/(-3x)) - 3)/(-3((-2x - 3)/(-3x)) + 2)) + 3)) - 1) + 2 between the vertical lines x = -1.4 and x = -1.3. 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": "Calculate the area enclosed between the functions f(x) = -1|(-1|(2e^(-2((-2(1|(-1x - 5) + 3| - 2) + 2)/(3(1|(-1x - 5) + 3| - 2) + 2))) - 1) + 3| - 2) + 1| and g(x) = (-1(-4(-1sin(3\u03c0(-2|(1x^2 - 2x - 3) + 2| + 2) - 3) - 1)^2 - 5(-1sin(3\u03c0(-2|(1x^2 - 2x - 3) + 2| + 2) - 3) - 1) + 5) - 2)/(2(-4(-1sin(3\u03c0(-2|(1x^2 - 2x - 3) + 2| + 2) - 3) - 1)^2 - 5(-1sin(3\u03c0(-2|(1x^2 - 2x - 3) + 2| + 2) - 3) - 1) + 5) - 1) 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": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2(2cos(3\u03c0(3|(2|(-1(5x)^2 - 2(5x) + 1) - 1| + 2)| + 1) - 1)) + 5, g(x) = 3(1|((-2(2cos(1\u03c0(-5x - 4) - 2) - 2))/(1(2cos(1\u03c0(-5x - 4) - 2) - 2) + 3)) - 2| + 3) - 3, x = 3.8, 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": "1.7", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2(-1(-4(-1((-2(-3|x - 1| + 1) - 1)/(3(-3|x - 1| + 1) + 1)) + 4) + 3) - 1) and g(x) = -2|(1|(-2|((1(-2x^2 + 3x - 1) - 1)/(2(-2x^2 + 3x - 1) - 1)) - 3|) + 2| + 3) - 1| between the vertical lines x = 0.6 and x = 1.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2(-1|(-5(-4(1|((-2x - 3)/(-2x + 3)) - 1| - 3) - 2)^2 - 5(-4(1|((-2x - 3)/(-2x + 3)) - 1| - 3) - 2) + 3) + 2| + 2) + 4 and g(x) = 3cos(2\u03c0((-1(-3|(-5((1x)/(-2x - 2))^2 + 5((1x)/(-2x - 2)))| + 3) + 1)/(-1(-3|(-5((1x)/(-2x - 2))^2 + 5((1x)/(-2x - 2)))| + 3) - 3)) - 1) - 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": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 5(2|(1((-3(2|(4x^2 + 1x - 2)| - 2) + 2)/(1(2|(4x^2 + 1x - 2)| - 2) - 3)) - 5) + 1| + 1) - 1 and g(x) = 1|(3(3cos(2\u03c0((3((-3x)/(-3x + 2)))/(2((-3x)/(-3x + 2)) - 1)) - 2) - 3)^2 + 3) + 2| + 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": "3.6", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -4(3(2|((3(1|(5x^2 - 3x + 1) + 3| - 1) - 1)/(2(1|(5x^2 - 3x + 1) + 3| - 1) + 1)) - 1|) + 3) + 5, g(x) = -1(2(3|((2(3|x + 2| + 3) - 3)/(-1(3|x + 2| + 3) - 3)) - 1| + 3)), x = -3.3, 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": "2.6", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -3(-4(-2|(1|(-2|((1x + 3)/(-3x - 3)) - 1| - 3) + 2| + 1)| - 1) - 1) - 5, g(x) = -2(1(-2sin(2\u03c0((-1(3x^2 + 5x - 4) - 3)/(-1(3x^2 + 5x - 4)))) + 1) + 5)^2 + 2, 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": "4.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2|(4((-2(-3((-1(-3x + 2))/(-2(-3x + 2) + 3)) - 5) - 3)/(1(-3((-1(-3x + 2))/(-2(-3x + 2) + 3)) - 5) + 1))^2 - 3((-2(-3((-1(-3x + 2))/(-2(-3x + 2) + 3)) - 5) - 3)/(1(-3((-1(-3x + 2))/(-2(-3x + 2) + 3)) - 5) + 1)) + 3) - 1| + 2, g(x) = -1((2(2cos(2\u03c0(2(-2x + 5)^2 + 1(-2x + 5) - 5) - 2) - 3) + 3)/(-2(2cos(2\u03c0(2(-2x + 5)^2 + 1(-2x + 5) - 5) - 2) - 3) - 2)) + 3, x = 3.8, 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": "33.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -4(-2|((-2(-2(-1|(2|x| - 2) - 2| + 2)^2 - 3(-1|(2|x| - 2) - 2| + 2) + 3) - 2)/(1(-2(-1|(2|x| - 2) - 2| + 2)^2 - 3(-1|(2|x| - 2) - 2| + 2) + 3) - 3)) + 2| + 2)^2 + 3(-2|((-2(-2(-1|(2|x| - 2) - 2| + 2)^2 - 3(-1|(2|x| - 2) - 2| + 2) + 3) - 2)/(1(-2(-1|(2|x| - 2) - 2| + 2)^2 - 3(-1|(2|x| - 2) - 2| + 2) + 3) - 3)) + 2| + 2) + 5 and g(x) = (3(-2|(4(-3cos(3\u03c0((-1x + 1)/(1x + 2)) - 1))^2 + 3(-3cos(3\u03c0((-1x + 1)/(1x + 2)) - 1)) + 2) + 2| + 1))/(-1(-2|(4(-3cos(3\u03c0((-1x + 1)/(1x + 2)) - 1))^2 + 3(-3cos(3\u03c0((-1x + 1)/(1x + 2)) - 1)) + 2) + 2| + 1) + 2) from x = -1.5 to x = 1.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1742.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1sin(3\u03c0(1(-2|(-5(-3(-3|x + 1| - 2) - 3)^2 + 3(-3(-3|x + 1| - 2) - 3) + 4) - 1| + 2)^2 - 5(-2|(-5(-3(-3|x + 1| - 2) - 3)^2 + 3(-3(-3|x + 1| - 2) - 3) + 4) - 1| + 2) + 3) - 3) - 1, g(x) = (1((3(-3(2(-5x^2 - 4x - 1) + 3) - 1))/(3(-3(2(-5x^2 - 4x - 1) + 3) - 1) - 1)) + 1)/(2((3(-3(2(-5x^2 - 4x - 1) + 3) - 1))/(3(-3(2(-5x^2 - 4x - 1) + 3) - 1) - 1)) - 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -4(2((2(3(3(-1x^2 + 1x + 3) + 5)) + 3)/(-3(3(3(-1x^2 + 1x + 3) + 5)) - 2)) - 2) + 1 and g(x) = -3|(-1sin(1\u03c0(-5(-3(-1x^2 + 1x - 2) + 2) + 5) + 3) - 1) - 2| between the vertical lines x = -1.7 and x = 2.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "102.9", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1(2(-1(-1cos(1\u03c0(-2((-1x + 2)/(2x - 1))^2 - 2((-1x + 2)/(2x - 1)) - 1) - 3) - 1)^2 - 4(-1cos(1\u03c0(-2((-1x + 2)/(2x - 1))^2 - 2((-1x + 2)/(2x - 1)) - 1) - 3) - 1) + 2) + 1)^2 + 3(2(-1(-1cos(1\u03c0(-2((-1x + 2)/(2x - 1))^2 - 2((-1x + 2)/(2x - 1)) - 1) - 3) - 1)^2 - 4(-1cos(1\u03c0(-2((-1x + 2)/(2x - 1))^2 - 2((-1x + 2)/(2x - 1)) - 1) - 3) - 1) + 2) + 1) + 1 and g(x) = 4(5(3(-4((-3x - 3)/(-1x + 2)) - 4)^2 + 1(-4((-3x - 3)/(-1x + 2)) - 4) - 3)^2 - 1(3(-4((-3x - 3)/(-1x + 2)) - 4)^2 + 1(-4((-3x - 3)/(-1x + 2)) - 4) - 3) + 2)^2 - 2(5(3(-4((-3x - 3)/(-1x + 2)) - 4)^2 + 1(-4((-3x - 3)/(-1x + 2)) - 4) - 3)^2 - 1(3(-4((-3x - 3)/(-1x + 2)) - 4)^2 + 1(-4((-3x - 3)/(-1x + 2)) - 4) - 3) + 2) + 4 between the vertical lines x = -0.4 and x = -0.30000000000000004. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "412.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-3((2(2cos(2\u03c0(-2(5(-3x^2 + 1x + 4)^2 + 5(-3x^2 + 1x + 4) + 1)^2 - 4(5(-3x^2 + 1x + 4)^2 + 5(-3x^2 + 1x + 4) + 1)) + 2) - 1) + 1)/(-3(2cos(2\u03c0(-2(5(-3x^2 + 1x + 4)^2 + 5(-3x^2 + 1x + 4) + 1)^2 - 4(5(-3x^2 + 1x + 4)^2 + 5(-3x^2 + 1x + 4) + 1)) + 2) - 1) + 2)) + 1)/(1((2(2cos(2\u03c0(-2(5(-3x^2 + 1x + 4)^2 + 5(-3x^2 + 1x + 4) + 1)^2 - 4(5(-3x^2 + 1x + 4)^2 + 5(-3x^2 + 1x + 4) + 1)) + 2) - 1) + 1)/(-3(2cos(2\u03c0(-2(5(-3x^2 + 1x + 4)^2 + 5(-3x^2 + 1x + 4) + 1)^2 - 4(5(-3x^2 + 1x + 4)^2 + 5(-3x^2 + 1x + 4) + 1)) + 2) - 1) + 2))) and g(x) = -1(3((-2((-2(-3|x - 1| + 3) + 2)/(2(-3|x - 1| + 3) + 1)) - 2)/(-2((-2(-3|x - 1| + 3) + 2)/(2(-3|x - 1| + 3) + 1)) + 3))^2 - 1((-2((-2(-3|x - 1| + 3) + 2)/(2(-3|x - 1| + 3) + 1)) - 2)/(-2((-2(-3|x - 1| + 3) + 2)/(2(-3|x - 1| + 3) + 1)) + 3)) - 1) + 1 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": "0.7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2(1(-2((1(5(-2|x - 1| - 1)^2 - 1(-2|x - 1| - 1) - 4) - 1)/(-2(5(-2|x - 1| - 1)^2 - 1(-2|x - 1| - 1) - 4) + 1)) - 3)^2 - 1(-2((1(5(-2|x - 1| - 1)^2 - 1(-2|x - 1| - 1) - 4) - 1)/(-2(5(-2|x - 1| - 1)^2 - 1(-2|x - 1| - 1) - 4) + 1)) - 3))^2 - 5(1(-2((1(5(-2|x - 1| - 1)^2 - 1(-2|x - 1| - 1) - 4) - 1)/(-2(5(-2|x - 1| - 1)^2 - 1(-2|x - 1| - 1) - 4) + 1)) - 3)^2 - 1(-2((1(5(-2|x - 1| - 1)^2 - 1(-2|x - 1| - 1) - 4) - 1)/(-2(5(-2|x - 1| - 1)^2 - 1(-2|x - 1| - 1) - 4) + 1)) - 3)) - 4 and g(x) = (-1((3(-1|((1((2x - 3)/(-3x - 3)) - 2)/(-2((2x - 3)/(-3x - 3)) - 1)) - 3| + 2) + 1)/(-2(-1|((1((2x - 3)/(-3x - 3)) - 2)/(-2((2x - 3)/(-3x - 3)) - 1)) - 3| + 2) - 2)) - 3)/(2((3(-1|((1((2x - 3)/(-3x - 3)) - 2)/(-2((2x - 3)/(-3x - 3)) - 1)) - 3| + 2) + 1)/(-2(-1|((1((2x - 3)/(-3x - 3)) - 2)/(-2((2x - 3)/(-3x - 3)) - 1)) - 3| + 2) - 2)) - 3) from x = 0.0 to x = 3.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "141.6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-2(3((1(3sin(1\u03c0(-4(2|x| - 2)^2 - 1(2|x| - 2) + 4) + 1) + 2))/(1(3sin(1\u03c0(-4(2|x| - 2)^2 - 1(2|x| - 2) + 4) + 1) + 2) - 3)) + 5) + 2)/(1(3((1(3sin(1\u03c0(-4(2|x| - 2)^2 - 1(2|x| - 2) + 4) + 1) + 2))/(1(3sin(1\u03c0(-4(2|x| - 2)^2 - 1(2|x| - 2) + 4) + 1) + 2) - 3)) + 5) + 2) and g(x) = 3|(1(-3((-1(1x^2 + 4x + 1) + 2)/(2(1x^2 + 4x + 1) - 1)) - 5) + 4) - 1| + 2 from x = -2.4 to x = -2.3. 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": "Find the area of the region bounded by the curves f(x) = -1(3(4((-1(3(-1x + 5)^2 + 2(-1x + 5)) - 1)/(2(3(-1x + 5)^2 + 2(-1x + 5)) - 1))^2 - 4((-1(3(-1x + 5)^2 + 2(-1x + 5)) - 1)/(2(3(-1x + 5)^2 + 2(-1x + 5)) - 1)) - 5) + 3) - 1, g(x) = 1(3((-1(3sin(1\u03c0(2x^2 + 2x + 3) - 1) - 3) - 2)/(1(3sin(1\u03c0(2x^2 + 2x + 3) - 1) - 3) - 3)) - 4) + 5, x = 2.6, 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1(-1sin(1\u03c0(-3|(-3|((-3(-5x) - 2)/(-1(-5x))) - 3| + 2)| - 2)) + 2) - 4 and g(x) = -1((-3(1(-2((-1x - 3)/(3x - 2)) - 2) + 4))/(3(1(-2((-1x - 3)/(3x - 2)) - 2) + 4) + 3))^2 + 4((-3(1(-2((-1x - 3)/(3x - 2)) - 2) + 4))/(3(1(-2((-1x - 3)/(3x - 2)) - 2) + 4) + 3)) - 4 between the vertical lines x = -0.7 and x = -0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -3(-2(2(-1(-1((-1x - 2)/(1x))^2 + 3((-1x - 2)/(1x)) + 1) - 5)^2 - 1(-1(-1((-1x - 2)/(1x))^2 + 3((-1x - 2)/(1x)) + 1) - 5) - 1)), g(x) = 3(3sin(3\u03c0(1((-3((-2x)/(-1x)) + 3)/(2((-2x)/(-1x)) + 1)) + 5))) + 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": "18.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-1((-3(-1(-4(1|(-1x + 3) - 3| + 1) + 5)) + 1)/(-3(-1(-4(1|(-1x + 3) - 3| + 1) + 5)) + 2)) - 2)/(-1((-3(-1(-4(1|(-1x + 3) - 3| + 1) + 5)) + 1)/(-3(-1(-4(1|(-1x + 3) - 3| + 1) + 5)) + 2)) + 2) and g(x) = 2(-3e^(-1(2|(-1(1|x + 2| + 1) + 5)| - 1)) - 2)^2 - 4(-3e^(-1(2|(-1(1|x + 2| + 1) + 5)| - 1)) - 2) - 5 from x = -0.5 to x = 0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "24.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2sin(3\u03c0(-4(2((2((-2((1x - 2)/(2x + 1)) - 1)/(-1((1x - 2)/(2x + 1)) - 3)) + 1)/(-3((-2((1x - 2)/(2x + 1)) - 1)/(-1((1x - 2)/(2x + 1)) - 3)))) + 1) + 5)) - 3 and g(x) = -2|(-2((-1((-2(-2|x - 1| + 3) - 2)/(-2(-2|x - 1| + 3) + 3)) + 1)/(-3((-2(-2|x - 1| + 3) - 2)/(-2(-2|x - 1| + 3) + 3)) - 2))) + 3| - 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-1(2|(4(4(1|((-2x - 1)/(-2x + 1)) - 1| + 3)) - 3) + 3| + 1) - 3)/(-1(2|(4(4(1|((-2x - 1)/(-2x + 1)) - 1| + 3)) - 3) + 3| + 1) - 3) and g(x) = 3|(-4(-1|(1sin(3\u03c0(-5x^2 + 4x + 4)) + 2) - 1| - 1) - 4)| - 3 between the vertical lines x = 2.1 and x = 2.2. 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) = (-1((1((-2(3sin(1\u03c0(2|((-2x + 2)/(-1x + 2)) - 3| + 2) + 3) - 3) - 1)/(1(3sin(1\u03c0(2|((-2x + 2)/(-1x + 2)) - 3| + 2) + 3) - 3) + 1)) + 1)/(2((-2(3sin(1\u03c0(2|((-2x + 2)/(-1x + 2)) - 3| + 2) + 3) - 3) - 1)/(1(3sin(1\u03c0(2|((-2x + 2)/(-1x + 2)) - 3| + 2) + 3) - 3) + 1)) - 1)) + 3)/(-2((1((-2(3sin(1\u03c0(2|((-2x + 2)/(-1x + 2)) - 3| + 2) + 3) - 3) - 1)/(1(3sin(1\u03c0(2|((-2x + 2)/(-1x + 2)) - 3| + 2) + 3) - 3) + 1)) + 1)/(2((-2(3sin(1\u03c0(2|((-2x + 2)/(-1x + 2)) - 3| + 2) + 3) - 3) - 1)/(1(3sin(1\u03c0(2|((-2x + 2)/(-1x + 2)) - 3| + 2) + 3) - 3) + 1)) - 1)) + 3) and g(x) = 2((1(4((3(-3e^(1x) + 2) - 2)/(3(-3e^(1x) + 2) + 3))^2 + 5) + 1)/(3(4((3(-3e^(1x) + 2) - 2)/(3(-3e^(1x) + 2) + 3))^2 + 5) - 1)) - 4 from x = -0.3 to x = 0.8. Round 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) = 3(1((-3(1|(-5(4x - 1)^2 + 3(4x - 1) - 5) + 3| - 3))/(1(1|(-5(4x - 1)^2 + 3(4x - 1) - 5) + 3| - 3))) + 4) - 4 and g(x) = -1(-2sin(3\u03c0((-3(3|(4x^2 - 3x + 1)| - 1) + 3)/(3(3|(4x^2 - 3x + 1)| - 1) + 2)) - 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(-1(-3e^(-2((1(-4(-3|x|) - 5) - 3)/(2(-4(-3|x|) - 5) - 1))) + 3)^2 - 5(-3e^(-2((1(-4(-3|x|) - 5) - 3)/(2(-4(-3|x|) - 5) - 1))) + 3) + 3) - 2)/(2(-1(-3e^(-2((1(-4(-3|x|) - 5) - 3)/(2(-4(-3|x|) - 5) - 1))) + 3)^2 - 5(-3e^(-2((1(-4(-3|x|) - 5) - 3)/(2(-4(-3|x|) - 5) - 1))) + 3) + 3)) and g(x) = 1|((2(1(-2(3x^2 - 2x + 4)^2 - 4(3x^2 - 2x + 4) + 3) + 1) + 2)/(-1(1(-2(3x^2 - 2x + 4)^2 - 4(3x^2 - 2x + 4) + 3) + 1) - 1)) + 2| - 1 between the vertical lines x = -0.7 and x = 0.7. 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) = 5((3(1sin(2\u03c0((-1(2|(2|x - 3| + 2) - 1| + 3) - 2)/(-3(2|(2|x - 3| + 2) - 1| + 3) - 3)) - 3) + 2) - 2)/(-3(1sin(2\u03c0((-1(2|(2|x - 3| + 2) - 1| + 3) - 2)/(-3(2|(2|x - 3| + 2) - 1| + 3) - 3)) - 3) + 2))) + 3 and g(x) = (2(5(2cos(3\u03c0(-3|(1x^2 + 3x + 3) + 3| + 2) + 3) + 1)^2 - 4(2cos(3\u03c0(-3|(1x^2 + 3x + 3) + 3| + 2) + 3) + 1) - 3))/(2(5(2cos(3\u03c0(-3|(1x^2 + 3x + 3) + 3| + 2) + 3) + 1)^2 - 4(2cos(3\u03c0(-3|(1x^2 + 3x + 3) + 3| + 2) + 3) + 1) - 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-3((1(-3|((-1((3((-3x - 2)/(-1x - 1)) - 3)/(3((-3x - 2)/(-1x - 1)))))/(-2((3((-3x - 2)/(-1x - 1)) - 3)/(3((-3x - 2)/(-1x - 1)))) - 1)) - 2| + 3))/(2(-3|((-1((3((-3x - 2)/(-1x - 1)) - 3)/(3((-3x - 2)/(-1x - 1)))))/(-2((3((-3x - 2)/(-1x - 1)) - 3)/(3((-3x - 2)/(-1x - 1)))) - 1)) - 2| + 3) + 1)) + 3)/(-3((1(-3|((-1((3((-3x - 2)/(-1x - 1)) - 3)/(3((-3x - 2)/(-1x - 1)))))/(-2((3((-3x - 2)/(-1x - 1)) - 3)/(3((-3x - 2)/(-1x - 1)))) - 1)) - 2| + 3))/(2(-3|((-1((3((-3x - 2)/(-1x - 1)) - 3)/(3((-3x - 2)/(-1x - 1)))))/(-2((3((-3x - 2)/(-1x - 1)) - 3)/(3((-3x - 2)/(-1x - 1)))) - 1)) - 2| + 3) + 1)) + 1) and g(x) = -3(-3sin(2\u03c0(1((2(-3x^2 - 2x + 4) - 2)/(-1(-3x^2 - 2x + 4) - 2)) - 5) + 2))^2 + 1(-3sin(2\u03c0(1((2(-3x^2 - 2x + 4) - 2)/(-1(-3x^2 - 2x + 4) - 2)) - 5) + 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": "3.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-2(3sin(3\u03c0(1(5(2(-1x)^2 - 1(-1x) - 4)^2 + 2(2(-1x)^2 - 1(-1x) - 4))) + 2) - 2) - 3)/(-3(3sin(3\u03c0(1(5(2(-1x)^2 - 1(-1x) - 4)^2 + 2(2(-1x)^2 - 1(-1x) - 4))) + 2) - 2) - 2) and g(x) = -1|(3|(2cos(3\u03c0(-1(-3|x|)^2 - 2(-3|x|) - 2) - 2) + 2) - 3| + 2) + 3| + 3 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": "0.7", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2(1((-2(-2((2(2e^(-1x) - 1) + 1)/(3(2e^(-1x) - 1) - 2)) + 2) + 3)/(-3(-2((2(2e^(-1x) - 1) + 1)/(3(2e^(-1x) - 1) - 2)) + 2) + 4)) + 2)^2 + 5(1((-2(-2((2(2e^(-1x) - 1) + 1)/(3(2e^(-1x) - 1) - 2)) + 2) + 3)/(-3(-2((2(2e^(-1x) - 1) + 1)/(3(2e^(-1x) - 1) - 2)) + 2) + 4)) + 2) + 5, g(x) = 1|((2((1(2sin(1\u03c0((-2x + 3)/(1x + 1)) - 1)))/(-2(2sin(1\u03c0((-2x + 3)/(1x + 1)) - 1)) - 3)))/(-1((1(2sin(1\u03c0((-2x + 3)/(1x + 1)) - 1)))/(-2(2sin(1\u03c0((-2x + 3)/(1x + 1)) - 1)) - 3)) - 2)) + 3| + 3, x = 0.3, 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": "135.5", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-1((-3(-1e^(-2((-1(4(-1x^2 + 2x - 2) + 3) + 1)/(2(4(-1x^2 + 2x - 2) + 3) - 1))) - 1))/(1(-1e^(-2((-1(4(-1x^2 + 2x - 2) + 3) + 1)/(2(4(-1x^2 + 2x - 2) + 3) - 1))) - 1) - 3)) - 3)/(2((-3(-1e^(-2((-1(4(-1x^2 + 2x - 2) + 3) + 1)/(2(4(-1x^2 + 2x - 2) + 3) - 1))) - 1))/(1(-1e^(-2((-1(4(-1x^2 + 2x - 2) + 3) + 1)/(2(4(-1x^2 + 2x - 2) + 3) - 1))) - 1) - 3)) - 3), g(x) = -1((1((-1(2|(2|x + 2| - 3) + 2| + 2) - 1)/(-2(2|(2|x + 2| - 3) + 2| + 2) + 3)) + 3)/(-3((-1(2|(2|x + 2| - 3) + 2| + 2) - 1)/(-2(2|(2|x + 2| - 3) + 2| + 2) + 3)) - 1))^2 + 1, x = -2.2, 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": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1(-3sin(3\u03c0(2|(2(-5((2x - 3)/(1x + 2)) - 1) + 1) + 2| - 2) + 2) + 1)^2 + 2(-3sin(3\u03c0(2|(2(-5((2x - 3)/(1x + 2)) - 1) + 1) + 2| - 2) + 2) + 1) + 5, g(x) = 2cos(2\u03c0(-1((2(2((3x + 1)/(-1x - 2)) + 1) - 1)/(-3(2((3x + 1)/(-1x - 2)) + 1)))^2 + 2((2(2((3x + 1)/(-1x - 2)) + 1) - 1)/(-3(2((3x + 1)/(-1x - 2)) + 1))) - 1) + 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": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2(-2|(4(3(-4(-3|x - 2| + 2)^2 - 4(-3|x - 2| + 2) + 1))) + 1| - 3) - 4 and g(x) = -4(-4(-2(-1|(1|x + 2| - 1) + 1| + 2)^2 - 3(-1|(1|x + 2| - 1) + 1| + 2)) - 5)^2 - 4(-4(-2(-1|(1|x + 2| - 1) + 1| + 2)^2 - 3(-1|(1|x + 2| - 1) + 1| + 2)) - 5) - 5 between the vertical lines x = 0.7 and x = 1.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "121.7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-2(1|((2(3(-1|((-1x - 2)/(1x)) - 3| - 3)^2 - 3(-1|((-1x - 2)/(1x)) - 3| - 3) + 4) - 3)/(2(3(-1|((-1x - 2)/(1x)) - 3| - 3)^2 - 3(-1|((-1x - 2)/(1x)) - 3| - 3) + 4) - 1)) - 2| - 1) - 2)/(1(1|((2(3(-1|((-1x - 2)/(1x)) - 3| - 3)^2 - 3(-1|((-1x - 2)/(1x)) - 3| - 3) + 4) - 3)/(2(3(-1|((-1x - 2)/(1x)) - 3| - 3)^2 - 3(-1|((-1x - 2)/(1x)) - 3| - 3) + 4) - 1)) - 2| - 1)) and g(x) = -1(-3|(-1(5(1x - 3)^2 + 1(1x - 3) + 3)^2 + 4(5(1x - 3)^2 + 1(1x - 3) + 3) - 1) - 2| + 2)^2 + 2(-3|(-1(5(1x - 3)^2 + 1(1x - 3) + 3)^2 + 4(5(1x - 3)^2 + 1(1x - 3) + 3) - 1) - 2| + 2) + 4 from x = 2.3 to x = 3.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "441.9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 5(1((3(4(-3sin(1\u03c0(2x + 4) - 2) + 1) - 1) + 2)/(-3(4(-3sin(1\u03c0(2x + 4) - 2) + 1) - 1) - 1))^2 + 4((3(4(-3sin(1\u03c0(2x + 4) - 2) + 1) - 1) + 2)/(-3(4(-3sin(1\u03c0(2x + 4) - 2) + 1) - 1) - 1)) - 1) + 2 and g(x) = (-2(4(-5((2(-3x^2 + 5x - 5) - 2)/(-1(-3x^2 + 5x - 5) + 2)) + 4)) - 2)/(-1(4(-5((2(-3x^2 + 5x - 5) - 2)/(-1(-3x^2 + 5x - 5) + 2)) + 4)) + 2) from x = -3.6 to x = -3.2. 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": "Find the area of the region bounded by the curves f(x) = (-1(-4((-1((3(4((-2x)/(2x))^2 + 3((-2x)/(2x)) + 1) + 3)/(3(4((-2x)/(2x))^2 + 3((-2x)/(2x)) + 1) - 1)) + 3)/(-1((3(4((-2x)/(2x))^2 + 3((-2x)/(2x)) + 1) + 3)/(3(4((-2x)/(2x))^2 + 3((-2x)/(2x)) + 1) - 1)) + 2))^2 - 4((-1((3(4((-2x)/(2x))^2 + 3((-2x)/(2x)) + 1) + 3)/(3(4((-2x)/(2x))^2 + 3((-2x)/(2x)) + 1) - 1)) + 3)/(-1((3(4((-2x)/(2x))^2 + 3((-2x)/(2x)) + 1) + 3)/(3(4((-2x)/(2x))^2 + 3((-2x)/(2x)) + 1) - 1)) + 2)) + 3) - 3)/(-3(-4((-1((3(4((-2x)/(2x))^2 + 3((-2x)/(2x)) + 1) + 3)/(3(4((-2x)/(2x))^2 + 3((-2x)/(2x)) + 1) - 1)) + 3)/(-1((3(4((-2x)/(2x))^2 + 3((-2x)/(2x)) + 1) + 3)/(3(4((-2x)/(2x))^2 + 3((-2x)/(2x)) + 1) - 1)) + 2))^2 - 4((-1((3(4((-2x)/(2x))^2 + 3((-2x)/(2x)) + 1) + 3)/(3(4((-2x)/(2x))^2 + 3((-2x)/(2x)) + 1) - 1)) + 3)/(-1((3(4((-2x)/(2x))^2 + 3((-2x)/(2x)) + 1) + 3)/(3(4((-2x)/(2x))^2 + 3((-2x)/(2x)) + 1) - 1)) + 2)) + 3) - 3), g(x) = (1((-3(-3|(-2|(1x + 2) + 3| + 2) - 1| + 2) + 1)/(-1(-3|(-2|(1x + 2) + 3| + 2) - 1| + 2) - 1)) - 1)/(-2((-3(-3|(-2|(1x + 2) + 3| + 2) - 1| + 2) + 1)/(-1(-3|(-2|(1x + 2) + 3| + 2) - 1| + 2) - 1)) + 3), x = -4.6, 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": "5.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 3(-1(3|(-5((2(1x))/(-1(1x) + 3))^2 + 4((2(1x))/(-1(1x) + 3)) + 1) - 1| - 2) + 5) + 1 and g(x) = -2|((3(-4(1|(1x - 3) + 2| + 1)^2 + 2(1|(1x - 3) + 2| + 1) + 2) - 2)/(-2(-4(1|(1x - 3) + 2| + 1)^2 + 2(1|(1x - 3) + 2| + 1) + 2) - 1)) - 3| + 3 between the vertical lines x = -1.0 and x = 1.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "48.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3e^(1(-2(2|(1((2(1x + 1) - 2)/(-2(1x + 1) + 1)) + 2)| + 1) + 4)) - 1 and g(x) = -2|(-2cos(2\u03c0(4((1((-2x)/(3x)) - 1)/(-3((-2x)/(3x)) + 1))^2 - 5((1((-2x)/(3x)) - 1)/(-3((-2x)/(3x)) + 1)) + 2) + 2) - 2) - 1| + 2 from x = -2.6 to x = -0.8. 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": "Calculate the area enclosed between the functions f(x) = (-1((-3(-3(-1(5(-4x^2 - 1x + 5)^2 - 1)^2 - 5(5(-4x^2 - 1x + 5)^2 - 1) + 5) + 4) + 1)/(-1(-3(-1(5(-4x^2 - 1x + 5)^2 - 1)^2 - 5(5(-4x^2 - 1x + 5)^2 - 1) + 5) + 4))) - 3)/(2((-3(-3(-1(5(-4x^2 - 1x + 5)^2 - 1)^2 - 5(5(-4x^2 - 1x + 5)^2 - 1) + 5) + 4) + 1)/(-1(-3(-1(5(-4x^2 - 1x + 5)^2 - 1)^2 - 5(5(-4x^2 - 1x + 5)^2 - 1) + 5) + 4))) + 3) and g(x) = -2|(1((1(4(-4x^2 + 5x - 1)^2 - 3(-4x^2 + 5x - 1) - 3) - 2)/(3(4(-4x^2 + 5x - 1)^2 - 3(-4x^2 + 5x - 1) - 3) - 1))^2 - 5((1(4(-4x^2 + 5x - 1)^2 - 3(-4x^2 + 5x - 1) - 3) - 2)/(3(4(-4x^2 + 5x - 1)^2 - 3(-4x^2 + 5x - 1) - 3) - 1)) - 3) - 3| + 1 from x = 0.1 to x = 1.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16.4", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2(4((3(1(1|(1|x - 1| + 2) - 1|) + 3) - 1)/(-2(1(1|(1|x - 1| + 2) - 1|) + 3)))^2 + 4((3(1(1|(1|x - 1| + 2) - 1|) + 3) - 1)/(-2(1(1|(1|x - 1| + 2) - 1|) + 3))) + 5)^2 + 3(4((3(1(1|(1|x - 1| + 2) - 1|) + 3) - 1)/(-2(1(1|(1|x - 1| + 2) - 1|) + 3)))^2 + 4((3(1(1|(1|x - 1| + 2) - 1|) + 3) - 1)/(-2(1(1|(1|x - 1| + 2) - 1|) + 3))) + 5) + 3 and g(x) = (-2(2cos(2\u03c0(1|(1|((-1x - 3)/(-3x + 1)) - 3| + 1)| - 1) + 2)) + 3)/(-2(2cos(2\u03c0(1|(1|((-1x - 3)/(-3x + 1)) - 3| + 1)| - 1) + 2)) - 3) between the vertical lines x = 1.1 and x = 2.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "158.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 3((-1(1((1(2|(-2x - 2) + 3| - 1) - 2)/(2(2|(-2x - 2) + 3| - 1) - 1)) + 3) + 1)/(2(1((1(2|(-2x - 2) + 3| - 1) - 2)/(2(2|(-2x - 2) + 3| - 1) - 1)) + 3) - 1))^2 + 5((-1(1((1(2|(-2x - 2) + 3| - 1) - 2)/(2(2|(-2x - 2) + 3| - 1) - 1)) + 3) + 1)/(2(1((1(2|(-2x - 2) + 3| - 1) - 2)/(2(2|(-2x - 2) + 3| - 1) - 1)) + 3) - 1)) - 3 and g(x) = -2((-3((-3(-2cos(1\u03c0(-1|x| + 1) + 1) - 3) - 2)/(3(-2cos(1\u03c0(-1|x| + 1) + 1) - 3) + 1)) - 3)/(-3((-3(-2cos(1\u03c0(-1|x| + 1) + 1) - 3) - 2)/(3(-2cos(1\u03c0(-1|x| + 1) + 1) - 3) + 1)) - 3)) - 3 from x = 0.9 to x = 1.0. 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": "Determine the area of the region enclosed by the graphs of f(x) = 1|(-5(-5((-3((3((-1x - 2)/(1x + 3)) - 2)/(-2((-1x - 2)/(1x + 3)) + 1)) - 3)/(3((3((-1x - 2)/(1x + 3)) - 2)/(-2((-1x - 2)/(1x + 3)) + 1)) + 2))^2 + 2((-3((3((-1x - 2)/(1x + 3)) - 2)/(-2((-1x - 2)/(1x + 3)) + 1)) - 3)/(3((3((-1x - 2)/(1x + 3)) - 2)/(-2((-1x - 2)/(1x + 3)) + 1)) + 2)) + 5)^2 - 4(-5((-3((3((-1x - 2)/(1x + 3)) - 2)/(-2((-1x - 2)/(1x + 3)) + 1)) - 3)/(3((3((-1x - 2)/(1x + 3)) - 2)/(-2((-1x - 2)/(1x + 3)) + 1)) + 2))^2 + 2((-3((3((-1x - 2)/(1x + 3)) - 2)/(-2((-1x - 2)/(1x + 3)) + 1)) - 3)/(3((3((-1x - 2)/(1x + 3)) - 2)/(-2((-1x - 2)/(1x + 3)) + 1)) + 2)) + 5) + 2) + 1| and g(x) = (-2(-4((1(1|(-1e^(2x) - 3) + 3|) + 3)/(3(1|(-1e^(2x) - 3) + 3|) - 2)) - 3) - 2)/(-3(-4((1(1|(-1e^(2x) - 3) + 3|) + 3)/(3(1|(-1e^(2x) - 3) + 3|) - 2)) - 3) + 4) between the vertical lines x = -2.3 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": "Calculate the area enclosed between the functions f(x) = -5(-3(2((-3(-4(-2|x + 3| - 2) - 5) - 1)/(2(-4(-2|x + 3| - 2) - 5) + 1))) - 4) - 5 and g(x) = (1(-3(3(-1|(-2|x + 1| + 2) - 2|)^2 + 1(-1|(-2|x + 1| + 2) - 2|) - 3) - 3) - 3)/(2(-3(3(-1|(-2|x + 1| + 2) - 2|)^2 + 1(-1|(-2|x + 1| + 2) - 2|) - 3) - 3) + 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": "29.7", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (1(-2|((-2(1|(3e^(-1(-1x + 5)) + 1) - 3| + 2))/(1(1|(3e^(-1(-1x + 5)) + 1) - 3| + 2))) - 1| - 3) - 3)/(-1(-2|((-2(1|(3e^(-1(-1x + 5)) + 1) - 3| + 2))/(1(1|(3e^(-1(-1x + 5)) + 1) - 3| + 2))) - 1| - 3)), g(x) = 4((1(-4(3sin(3\u03c0(-5x^2 + 2x - 1) + 2) + 1) + 3))/(3(-4(3sin(3\u03c0(-5x^2 + 2x - 1) + 2) + 1) + 3) + 3)) + 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": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1e^(1((-1((2(2((2(3|x + 3| + 1))/(3(3|x + 3| + 1) + 2)) - 5) - 3)/(1(2((2(3|x + 3| + 1))/(3(3|x + 3| + 1) + 2)) - 5) + 1)) - 1)/(-3((2(2((2(3|x + 3| + 1))/(3(3|x + 3| + 1) + 2)) - 5) - 3)/(1(2((2(3|x + 3| + 1))/(3(3|x + 3| + 1) + 2)) - 5) + 1)) + 2))) - 1 and g(x) = -2|(-2sin(2\u03c0(1|(-1(-3x)^2 + 2(-3x) - 5) - 1|) + 3) - 3) + 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": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2(2(-2|((3((-3((2x)/(-2x - 2)) + 1)/(-3((2x)/(-2x - 2)))))/(3((-3((2x)/(-2x - 2)) + 1)/(-3((2x)/(-2x - 2)))))) + 1| - 2) + 4) - 1 and g(x) = (-3((3(-4(1|(1x + 2) - 2| - 2) - 5) + 3)/(1(-4(1|(1x + 2) - 2| - 2) - 5) - 2)))/(-2((3(-4(1|(1x + 2) - 2| - 2) - 5) + 3)/(1(-4(1|(1x + 2) - 2| - 2) - 5) - 2)) + 3) from x = -1.9 to x = 1.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "96.4", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -3(-2cos(2\u03c0(2((3(5((2x + 2)/(1x + 1))^2 + 5) - 3)/(3(5((2x + 2)/(1x + 1))^2 + 5) - 2)) - 1) - 3) - 1)^2 - 3(-2cos(2\u03c0(2((3(5((2x + 2)/(1x + 1))^2 + 5) - 3)/(3(5((2x + 2)/(1x + 1))^2 + 5) - 2)) - 1) - 3) - 1) + 2, g(x) = -5((3(3(3(-3x - 3)^2 + 5(-3x - 3))^2 + 4(3(-3x - 3)^2 + 5(-3x - 3)) + 5) - 2)/(2(3(3(-3x - 3)^2 + 5(-3x - 3))^2 + 4(3(-3x - 3)^2 + 5(-3x - 3)) + 5))) + 3, 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-1(3((3(-1cos(2\u03c0(4((-3x - 3)/(-1x + 2)) - 3) - 3) + 3) - 3)/(3(-1cos(2\u03c0(4((-3x - 3)/(-1x + 2)) - 3) - 3) + 3) - 2)) + 5) - 1)/(2(3((3(-1cos(2\u03c0(4((-3x - 3)/(-1x + 2)) - 3) - 3) + 3) - 3)/(3(-1cos(2\u03c0(4((-3x - 3)/(-1x + 2)) - 3) - 3) + 3) - 2)) + 5) + 2) and g(x) = -3(-1|((2(-3|((2x - 1)/(-3x + 1)) + 3| + 1))/(3(-3|((2x - 1)/(-3x + 1)) + 3| + 1) - 2)) - 2| + 3) + 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": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1sin(2\u03c0((-1(-5(-3(4(3x^2 - 3x) + 5) - 2) + 1) - 3)/(-3(-5(-3(4(3x^2 - 3x) + 5) - 2) + 1))) - 3) - 1 and g(x) = -1|(-3e^(-1(-1|(-5(4x + 1))| + 1)) + 1) - 2| + 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 3|(-3|(3|(-2(2|(2cos(2\u03c0x + 2) - 1) + 2| - 2)^2 - 5(2|(2cos(2\u03c0x + 2) - 1) + 2| - 2) - 1) + 3| - 2) - 2| + 2) - 2| - 1 and g(x) = 2e^(2(3((-1(-3|(-2x) - 3| + 3) + 1)/(-2(-3|(-2x) - 3| + 3) - 1))^2 + 5((-1(-3|(-2x) - 3| + 3) + 1)/(-2(-3|(-2x) - 3| + 3) - 1)) - 5)) + 3 from x = 3.9 to x = 4.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3(3((-1(-1(4((-2x + 2)/(3x - 2)) + 2)^2 - 4(4((-2x + 2)/(3x - 2)) + 2) + 2) - 2)/(3(-1(4((-2x + 2)/(3x - 2)) + 2)^2 - 4(4((-2x + 2)/(3x - 2)) + 2) + 2) + 3))^2 + 1((-1(-1(4((-2x + 2)/(3x - 2)) + 2)^2 - 4(4((-2x + 2)/(3x - 2)) + 2) + 2) - 2)/(3(-1(4((-2x + 2)/(3x - 2)) + 2)^2 - 4(4((-2x + 2)/(3x - 2)) + 2) + 2) + 3)) - 4) + 5 and g(x) = 1cos(2\u03c0(-3((-1(-1((-1x + 1)/(-2x))^2 + 3((-1x + 1)/(-2x)) - 2) - 3)/(2(-1((-1x + 1)/(-2x))^2 + 3((-1x + 1)/(-2x)) - 2) - 3)) - 3) + 2) - 1 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": "2.8", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1e^(2(-4(1(4(2(2|x + 1| - 3)^2)^2 + 2(2(2|x + 1| - 3)^2) + 3) - 3)^2 + 1(1(4(2(2|x + 1| - 3)^2)^2 + 2(2(2|x + 1| - 3)^2) + 3) - 3) - 2)) - 1 and g(x) = -2|(-3(-1(2|(-1|x + 1| + 3)| - 1) + 3)^2 - 2(-1(2|(-1|x + 1| + 3)| - 1) + 3) + 3) - 1| + 2 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": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1cos(2\u03c0((-1(-3(-5((1(1|x + 1| + 2) + 1)/(3(1|x + 1| + 2) + 3))^2 + 2((1(1|x + 1| + 2) + 1)/(3(1|x + 1| + 2) + 3)) - 2)^2 + 2(-5((1(1|x + 1| + 2) + 1)/(3(1|x + 1| + 2) + 3))^2 + 2((1(1|x + 1| + 2) + 1)/(3(1|x + 1| + 2) + 3)) - 2) - 4))/(-2(-3(-5((1(1|x + 1| + 2) + 1)/(3(1|x + 1| + 2) + 3))^2 + 2((1(1|x + 1| + 2) + 1)/(3(1|x + 1| + 2) + 3)) - 2)^2 + 2(-5((1(1|x + 1| + 2) + 1)/(3(1|x + 1| + 2) + 3))^2 + 2((1(1|x + 1| + 2) + 1)/(3(1|x + 1| + 2) + 3)) - 2) - 4) - 1)) - 2) + 1, g(x) = -5(-3((1(-3(-3x^2 - 5x - 2) - 2) - 2)/(3(-3(-3x^2 - 5x - 2) - 2) - 2)) + 2)^2 - 1(-3((1(-3(-3x^2 - 5x - 2) - 2) - 2)/(3(-3(-3x^2 - 5x - 2) - 2) - 2)) + 2) + 4, x = -1.3, 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": "Calculate the area enclosed between the functions f(x) = -4(-4(-2cos(3\u03c0(3(-1(-1|x + 1| + 1)^2 - 1(-1|x + 1| + 1))^2 - 5(-1(-1|x + 1| + 1)^2 - 1(-1|x + 1| + 1)) - 3) + 2) - 2)^2 - 5(-2cos(3\u03c0(3(-1(-1|x + 1| + 1)^2 - 1(-1|x + 1| + 1))^2 - 5(-1(-1|x + 1| + 1)^2 - 1(-1|x + 1| + 1)) - 3) + 2) - 2) + 3) + 3 and g(x) = 4(-1(-2|((1((-1x - 2)/(2x + 1)) + 2)/(-2((-1x - 2)/(2x + 1))))| + 2)^2 + 4(-2|((1((-1x - 2)/(2x + 1)) + 2)/(-2((-1x - 2)/(2x + 1))))| + 2) - 5)^2 + 4(-1(-2|((1((-1x - 2)/(2x + 1)) + 2)/(-2((-1x - 2)/(2x + 1))))| + 2)^2 + 4(-2|((1((-1x - 2)/(2x + 1)) + 2)/(-2((-1x - 2)/(2x + 1))))| + 2) - 5) - 1 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": "7.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2|((-3((2(5(-1(4x^2 + 1x + 1) + 3)^2 - 4) - 1)/(-3(5(-1(4x^2 + 1x + 1) + 3)^2 - 4) + 1)) + 1)/(3((2(5(-1(4x^2 + 1x + 1) + 3)^2 - 4) - 1)/(-3(5(-1(4x^2 + 1x + 1) + 3)^2 - 4) + 1)) + 3)) - 3| and g(x) = 1(-1|(4(4(1x) + 5) - 3) + 3|)^2 - 2(-1|(4(4(1x) + 5) - 3) + 3|) - 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (2(4(1(4(-4(-3sin(3\u03c0x + 1) + 2)^2 - 3(-3sin(3\u03c0x + 1) + 2) + 1)^2 - 4(-4(-3sin(3\u03c0x + 1) + 2)^2 - 3(-3sin(3\u03c0x + 1) + 2) + 1) + 2) - 1)^2 + 3(1(4(-4(-3sin(3\u03c0x + 1) + 2)^2 - 3(-3sin(3\u03c0x + 1) + 2) + 1)^2 - 4(-4(-3sin(3\u03c0x + 1) + 2)^2 - 3(-3sin(3\u03c0x + 1) + 2) + 1) + 2) - 1)) - 1)/(-2(4(1(4(-4(-3sin(3\u03c0x + 1) + 2)^2 - 3(-3sin(3\u03c0x + 1) + 2) + 1)^2 - 4(-4(-3sin(3\u03c0x + 1) + 2)^2 - 3(-3sin(3\u03c0x + 1) + 2) + 1) + 2) - 1)^2 + 3(1(4(-4(-3sin(3\u03c0x + 1) + 2)^2 - 3(-3sin(3\u03c0x + 1) + 2) + 1)^2 - 4(-4(-3sin(3\u03c0x + 1) + 2)^2 - 3(-3sin(3\u03c0x + 1) + 2) + 1) + 2) - 1))) and g(x) = -1|(-3(-2cos(1\u03c0(-1(-5x) + 2) + 3) + 1) + 1) - 3| + 3 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": "1.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1|(-1(-5(2cos(3\u03c0(1(-3|x + 2| - 1) - 3) - 3) - 2)^2 - 3(2cos(3\u03c0(1(-3|x + 2| - 1) - 3) - 3) - 2))^2 + 5(-5(2cos(3\u03c0(1(-3|x + 2| - 1) - 3) - 3) - 2)^2 - 3(2cos(3\u03c0(1(-3|x + 2| - 1) - 3) - 3) - 2)) - 5) + 1| - 3, g(x) = -1|(1|(1((-1(-1sin(1\u03c0x - 1) + 2) - 3)/(2(-1sin(1\u03c0x - 1) + 2) - 1)) + 4) + 2|) - 3| + 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": "122.6", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1(-2(3|(-2sin(2\u03c0(-2(-3x - 4) - 2) + 2) - 1) - 2| - 3)^2 + 5(3|(-2sin(2\u03c0(-2(-3x - 4) - 2) + 2) - 1) - 2| - 3) + 3)^2 - 5(-2(3|(-2sin(2\u03c0(-2(-3x - 4) - 2) + 2) - 1) - 2| - 3)^2 + 5(3|(-2sin(2\u03c0(-2(-3x - 4) - 2) + 2) - 1) - 2| - 3) + 3) + 2 and g(x) = (-1(3|(-2e^(2(-1((-2x + 1)/(-1x + 3))^2 - 4)) - 1) + 3| + 1) + 1)/(2(3|(-2e^(2(-1((-2x + 1)/(-1x + 3))^2 - 4)) - 1) + 3| + 1) - 1) 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": "203.7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1|((3(2|(-2|((-1(3|x + 3| - 2) - 3)/(-3(3|x + 3| - 2) + 4)) - 1| - 2) - 1| + 2) + 1)/(-3(2|(-2|((-1(3|x + 3| - 2) - 3)/(-3(3|x + 3| - 2) + 4)) - 1| - 2) - 1| + 2) - 3)) + 2| + 3 and g(x) = 3(-1|(3(1(1e^(1x) - 1)^2 - 5)) + 1| + 1) 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2sin(3\u03c0(-3|(3(1|(4((1x - 2)/(-3x + 1)) + 5) + 3| + 2)^2 + 2(1|(4((1x - 2)/(-3x + 1)) + 5) + 3| + 2) - 5) - 3| - 1)) - 3 and g(x) = -2(3((-1(1(-1cos(1\u03c0x - 1) + 2)^2 - 1(-1cos(1\u03c0x - 1) + 2) - 3) + 3)/(-3(1(-1cos(1\u03c0x - 1) + 2)^2 - 1(-1cos(1\u03c0x - 1) + 2) - 3) + 1)) - 3) - 3 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": "Calculate the area enclosed between the functions f(x) = -1|(-3(3(3sin(1\u03c0((1(-4x^2 - 4x + 1) + 2)/(2(-4x^2 - 4x + 1) + 2)) - 2) + 3)^2 + 4(3sin(1\u03c0((1(-4x^2 - 4x + 1) + 2)/(2(-4x^2 - 4x + 1) + 2)) - 2) + 3) + 5)^2 + 3(3(3sin(1\u03c0((1(-4x^2 - 4x + 1) + 2)/(2(-4x^2 - 4x + 1) + 2)) - 2) + 3)^2 + 4(3sin(1\u03c0((1(-4x^2 - 4x + 1) + 2)/(2(-4x^2 - 4x + 1) + 2)) - 2) + 3) + 5) - 4) - 1| + 1 and g(x) = -1((-2(5(-4(2x + 3)^2 - 1)^2 + 3(-4(2x + 3)^2 - 1) - 2) + 2)/(3(5(-4(2x + 3)^2 - 1)^2 + 3(-4(2x + 3)^2 - 1) - 2) - 2))^2 + 3((-2(5(-4(2x + 3)^2 - 1)^2 + 3(-4(2x + 3)^2 - 1) - 2) + 2)/(3(5(-4(2x + 3)^2 - 1)^2 + 3(-4(2x + 3)^2 - 1) - 2) - 2)) - 2 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": "20.8", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (3(1|(5(-3|(-1(-1|x| + 2) - 2) + 2| - 1)^2 - 3(-3|(-1(-1|x| + 2) - 2) + 2| - 1) + 1) - 3| - 1))/(-2(1|(5(-3|(-1(-1|x| + 2) - 2) + 2| - 1)^2 - 3(-3|(-1(-1|x| + 2) - 2) + 2| - 1) + 1) - 3| - 1) - 3), g(x) = -4((-2(2|((1(1x^2 - 5x + 4) + 2)/(-3(1x^2 - 5x + 4) - 1)) - 3|) + 3)/(3(2|((1(1x^2 - 5x + 4) + 2)/(-3(1x^2 - 5x + 4) - 1)) - 3|) + 2)) + 2, x = 3.8, 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": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -4(2((2(4(-1(1|x + 1| - 3)^2 + 2)^2) + 3)/(3(4(-1(1|x + 1| - 3)^2 + 2)^2) + 2))^2 - 2((2(4(-1(1|x + 1| - 3)^2 + 2)^2) + 3)/(3(4(-1(1|x + 1| - 3)^2 + 2)^2) + 2)) + 3)^2 + 5, g(x) = (3(3|(2|(1(3x^2 - 4x)^2 - 4(3x^2 - 4x) - 2) + 3| - 2) - 2| - 2) - 2)/(3(3|(2|(1(3x^2 - 4x)^2 - 4(3x^2 - 4x) - 2) + 3| - 2) - 2| - 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": "2.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2(2(2|(-3(-4(-4x^2 - 5x + 4) + 1)^2 + 1(-4(-4x^2 - 5x + 4) + 1) + 4)| - 2)^2 + 3(2|(-3(-4(-4x^2 - 5x + 4) + 1)^2 + 1(-4(-4x^2 - 5x + 4) + 1) + 4)| - 2) - 2) - 3 and g(x) = -3(3(-1cos(1\u03c0(3|(4x + 1) - 1| - 2)) + 1) - 4) - 5 from x = -1.8 to x = -1.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "97.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (2(5((1((3(-1((-2x - 1)/(-2x + 3)) + 2) - 3)/(-3(-1((-2x - 1)/(-2x + 3)) + 2) - 2)) + 3)/(1((3(-1((-2x - 1)/(-2x + 3)) + 2) - 3)/(-3(-1((-2x - 1)/(-2x + 3)) + 2) - 2)) - 2)) + 4) + 3)/(-1(5((1((3(-1((-2x - 1)/(-2x + 3)) + 2) - 3)/(-3(-1((-2x - 1)/(-2x + 3)) + 2) - 2)) + 3)/(1((3(-1((-2x - 1)/(-2x + 3)) + 2) - 3)/(-3(-1((-2x - 1)/(-2x + 3)) + 2) - 2)) - 2)) + 4) + 2), g(x) = -1(5(1(-1|((-2x)/(2x - 3)) + 3| - 3) + 5) + 1) + 3, x = 2.2, 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": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1|((-3(-4(2|((2(2|x - 3| + 2) + 1)/(-3(2|x - 3| + 2) + 4)) + 2| - 3)^2 + 1(2|((2(2|x - 3| + 2) + 1)/(-3(2|x - 3| + 2) + 4)) + 2| - 3) + 2) - 2)/(-2(-4(2|((2(2|x - 3| + 2) + 1)/(-3(2|x - 3| + 2) + 4)) + 2| - 3)^2 + 1(2|((2(2|x - 3| + 2) + 1)/(-3(2|x - 3| + 2) + 4)) + 2| - 3) + 2) - 3))| + 2 and g(x) = -3|(1|((2(5((1x + 1)/(1x - 3)) + 5) - 3)/(2(5((1x + 1)/(1x - 3)) + 5) - 1)) - 3| + 2) - 3| - 2 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": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3|(-1sin(2\u03c0(4((3(-5(-3x^2 - 4x - 2)^2 - 5) + 1)/(-1(-5(-3x^2 - 4x - 2)^2 - 5) + 2)) - 1) + 1) + 1) - 2| - 1 and g(x) = -1(-2(2|(2(-1|x + 3| + 2) + 4) - 3| - 1) - 1) - 1 between the vertical lines x = -0.4 and 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": "Determine the area of the region enclosed by the graphs of f(x) = 4(-3|(-3(-2|(-3(4x + 1)^2 - 4(4x + 1) - 2) + 2| + 1)^2 + 4(-2|(-3(4x + 1)^2 - 4(4x + 1) - 2) + 2| + 1)) + 3| + 2) + 2 and g(x) = -1|(-2|(-1|(3((3x - 3)/(1x + 3))^2 - 5((3x - 3)/(1x + 3)) + 3)| + 2) - 3| + 2) - 2| - 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": "2.6", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1|(5((-3(-1(-2|(4x^2 + 4x - 4) - 1| - 1)^2 - 4(-2|(4x^2 + 4x - 4) - 1| - 1) - 2) + 3)/(2(-1(-2|(4x^2 + 4x - 4) - 1| - 1)^2 - 4(-2|(4x^2 + 4x - 4) - 1| - 1) - 2))) + 5) + 1| + 1 and g(x) = -1|((2(-3(-1|((-2x + 2)/(-2x - 2)) + 1| - 3)^2 + 3) + 1)/(-1(-3(-1|((-2x + 2)/(-2x - 2)) + 1| - 3)^2 + 3) + 3)) + 3| - 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (2(-1sin(1\u03c0(3(2|(-3|((-3x + 3)/(3x + 1)) + 3|) + 1| + 3)^2 - 1(2|(-3|((-3x + 3)/(3x + 1)) + 3|) + 1| + 3) - 3) - 1) + 3) - 3)/(1(-1sin(1\u03c0(3(2|(-3|((-3x + 3)/(3x + 1)) + 3|) + 1| + 3)^2 - 1(2|(-3|((-3x + 3)/(3x + 1)) + 3|) + 1| + 3) - 3) - 1) + 3) - 2) and g(x) = -1(-2|(1cos(3\u03c0(-1(3x + 2)) + 1) + 1) + 2| + 2) - 2 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": "3.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1(1((-1(-2(1((2x)/(2x + 1))^2 - 2((2x)/(2x + 1)) - 3) - 3))/(1(-2(1((2x)/(2x + 1))^2 - 2((2x)/(2x + 1)) - 3) - 3) - 2)) - 4)^2 + 4(1((-1(-2(1((2x)/(2x + 1))^2 - 2((2x)/(2x + 1)) - 3) - 3))/(1(-2(1((2x)/(2x + 1))^2 - 2((2x)/(2x + 1)) - 3) - 3) - 2)) - 4) + 2 and g(x) = -4((2((-3(1e^(1((3x - 3)/(-1x - 2))) + 3) + 1)/(1(1e^(1((3x - 3)/(-1x - 2))) + 3) + 1)) - 1)/(-2((-3(1e^(1((3x - 3)/(-1x - 2))) + 3) + 1)/(1(1e^(1((3x - 3)/(-1x - 2))) + 3) + 1)))) + 1 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": "1.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 3sin(1\u03c0((3(-3|(-2(4(5x - 2) + 3)^2 - 5(4(5x - 2) + 3) - 3) - 2| - 3) - 1)/(1(-3|(-2(4(5x - 2) + 3)^2 - 5(4(5x - 2) + 3) - 3) - 2| - 3))) + 2) - 2 and g(x) = -3|(5(-2((-3(-4x^2 + 3x + 1) + 1)/(-3(-4x^2 + 3x + 1) + 4)) + 1) - 1) - 2| from x = 0.9 to x = 1.0. 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) = (-3(-2(1(1(-1cos(2\u03c0((-3x + 1)/(2x + 3)) + 1) - 3)^2 + 1(-1cos(2\u03c0((-3x + 1)/(2x + 3)) + 1) - 3) - 5)^2 + 2(1(-1cos(2\u03c0((-3x + 1)/(2x + 3)) + 1) - 3)^2 + 1(-1cos(2\u03c0((-3x + 1)/(2x + 3)) + 1) - 3) - 5) + 2) + 4) - 1)/(-1(-2(1(1(-1cos(2\u03c0((-3x + 1)/(2x + 3)) + 1) - 3)^2 + 1(-1cos(2\u03c0((-3x + 1)/(2x + 3)) + 1) - 3) - 5)^2 + 2(1(-1cos(2\u03c0((-3x + 1)/(2x + 3)) + 1) - 3)^2 + 1(-1cos(2\u03c0((-3x + 1)/(2x + 3)) + 1) - 3) - 5) + 2) + 4) - 1), g(x) = (1(-4(2|(3|((-2x - 3)/(1x + 2)) + 2| - 3) + 2| + 2) - 5) - 3)/(-3(-4(2|(3|((-2x - 3)/(1x + 2)) + 2| - 3) + 2| + 2) - 5) + 2), 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": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 3(3sin(2\u03c0((1(1|((1(4x^2 - 2x - 1))/(2(4x^2 - 2x - 1) - 1)) + 1| - 2) - 1)/(3(1|((1(4x^2 - 2x - 1))/(2(4x^2 - 2x - 1) - 1)) + 1| - 2) - 2)) - 2) - 1)^2 - 5(3sin(2\u03c0((1(1|((1(4x^2 - 2x - 1))/(2(4x^2 - 2x - 1) - 1)) + 1| - 2) - 1)/(3(1|((1(4x^2 - 2x - 1))/(2(4x^2 - 2x - 1) - 1)) + 1| - 2) - 2)) - 2) - 1) - 4 and g(x) = -5((3(-2(-5(1|x| - 2) - 5) - 3) - 2)/(-3(-2(-5(1|x| - 2) - 5) - 3) - 2))^2 - 4((3(-2(-5(1|x| - 2) - 5) - 3) - 2)/(-3(-2(-5(1|x| - 2) - 5) - 3) - 2)) + 4 from x = -0.5 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": "Determine the area of the region enclosed by the graphs of f(x) = -4((2((2((1(-3|((-2x)/(-2x)) - 2|) - 1)/(3(-3|((-2x)/(-2x)) - 2|) + 1)) + 3)/(1((1(-3|((-2x)/(-2x)) - 2|) - 1)/(3(-3|((-2x)/(-2x)) - 2|) + 1)) + 2)) + 1)/(1((2((1(-3|((-2x)/(-2x)) - 2|) - 1)/(3(-3|((-2x)/(-2x)) - 2|) + 1)) + 3)/(1((1(-3|((-2x)/(-2x)) - 2|) - 1)/(3(-3|((-2x)/(-2x)) - 2|) + 1)) + 2)) + 2)) + 5 and g(x) = 2((-2(2(-1(-3cos(2\u03c0x - 1) + 2) + 4)^2 - 2(-1(-3cos(2\u03c0x - 1) + 2) + 4) - 2) - 3)/(1(2(-1(-3cos(2\u03c0x - 1) + 2) + 4)^2 - 2(-1(-3cos(2\u03c0x - 1) + 2) + 4) - 2) + 1)) - 5 between the vertical lines x = -1.2 and x = -1.1. 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": "Calculate the area enclosed between the functions f(x) = (-1(1(-1|(5(1e^(1(2x^2 - 5x - 1)) + 2)^2 - 2(1e^(1(2x^2 - 5x - 1)) + 2) - 1) + 1| + 3)^2 - 2(-1|(5(1e^(1(2x^2 - 5x - 1)) + 2)^2 - 2(1e^(1(2x^2 - 5x - 1)) + 2) - 1) + 1| + 3) + 5))/(-1(1(-1|(5(1e^(1(2x^2 - 5x - 1)) + 2)^2 - 2(1e^(1(2x^2 - 5x - 1)) + 2) - 1) + 1| + 3)^2 - 2(-1|(5(1e^(1(2x^2 - 5x - 1)) + 2)^2 - 2(1e^(1(2x^2 - 5x - 1)) + 2) - 1) + 1| + 3) + 5)) and g(x) = -3|(-4(-1(-3|(-2x - 4) + 3| - 3) - 3)^2 + 5(-1(-3|(-2x - 4) + 3| - 3) - 3) + 3) + 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": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (2(-3(2|((-1(-2sin(1\u03c0(1|x - 2| + 1) - 2) - 2) - 3)/(-3(-2sin(1\u03c0(1|x - 2| + 1) - 2) - 2) - 2)) - 1| - 1)^2 - 3(2|((-1(-2sin(1\u03c0(1|x - 2| + 1) - 2) - 2) - 3)/(-3(-2sin(1\u03c0(1|x - 2| + 1) - 2) - 2) - 2)) - 1| - 1)) - 1)/(1(-3(2|((-1(-2sin(1\u03c0(1|x - 2| + 1) - 2) - 2) - 3)/(-3(-2sin(1\u03c0(1|x - 2| + 1) - 2) - 2) - 2)) - 1| - 1)^2 - 3(2|((-1(-2sin(1\u03c0(1|x - 2| + 1) - 2) - 2) - 3)/(-3(-2sin(1\u03c0(1|x - 2| + 1) - 2) - 2) - 2)) - 1| - 1)) + 2), g(x) = -3(5(-5(1|(-3|x|) - 2| - 3) - 4) - 2) - 1, x = 0.1, 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": "62.7", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-3(-1((3(2(2(-5x - 4)^2 - 4(-5x - 4) - 1)^2 - 3(2(-5x - 4)^2 - 4(-5x - 4) - 1) - 3) + 2)/(-2(2(2(-5x - 4)^2 - 4(-5x - 4) - 1)^2 - 3(2(-5x - 4)^2 - 4(-5x - 4) - 1) - 3) + 1))^2 - 2) + 1)/(1(-1((3(2(2(-5x - 4)^2 - 4(-5x - 4) - 1)^2 - 3(2(-5x - 4)^2 - 4(-5x - 4) - 1) - 3) + 2)/(-2(2(2(-5x - 4)^2 - 4(-5x - 4) - 1)^2 - 3(2(-5x - 4)^2 - 4(-5x - 4) - 1) - 3) + 1))^2 - 2) - 3), g(x) = 5(3(3(-5(3|x + 1| - 1) - 5)^2 - 2) - 5) + 5, x = -1.1, 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": "6.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (1(3((2(-2|(5((1x - 1)/(-1x - 3)) - 3) - 2| - 1) - 3)/(-2(-2|(5((1x - 1)/(-1x - 3)) - 3) - 2| - 1) - 2))^2 + 2((2(-2|(5((1x - 1)/(-1x - 3)) - 3) - 2| - 1) - 3)/(-2(-2|(5((1x - 1)/(-1x - 3)) - 3) - 2| - 1) - 2)) + 3) + 2)/(-2(3((2(-2|(5((1x - 1)/(-1x - 3)) - 3) - 2| - 1) - 3)/(-2(-2|(5((1x - 1)/(-1x - 3)) - 3) - 2| - 1) - 2))^2 + 2((2(-2|(5((1x - 1)/(-1x - 3)) - 3) - 2| - 1) - 3)/(-2(-2|(5((1x - 1)/(-1x - 3)) - 3) - 2| - 1) - 2)) + 3) - 3), g(x) = -1e^(2(1|(1(1((-2x - 1)/(-3x + 1)) - 3) - 3) + 2| - 2)) + 3, x = 0.4, 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": "Find the area of the region bounded by the curves f(x) = (3(4(3|(2(-3|(3|x + 2| - 3) + 2|)^2 + 5(-3|(3|x + 2| - 3) + 2|) - 1) + 3| - 3)^2 - 3(3|(2(-3|(3|x + 2| - 3) + 2|)^2 + 5(-3|(3|x + 2| - 3) + 2|) - 1) + 3| - 3)) + 3)/(2(4(3|(2(-3|(3|x + 2| - 3) + 2|)^2 + 5(-3|(3|x + 2| - 3) + 2|) - 1) + 3| - 3)^2 - 3(3|(2(-3|(3|x + 2| - 3) + 2|)^2 + 5(-3|(3|x + 2| - 3) + 2|) - 1) + 3| - 3)) + 2), g(x) = (-2(-2((-3((1(-3|x - 2| + 3) + 3)/(-3(-3|x - 2| + 3) + 1)) - 2)/(3((1(-3|x - 2| + 3) + 3)/(-3(-3|x - 2| + 3) + 1)) - 1)) - 5) - 1)/(3(-2((-3((1(-3|x - 2| + 3) + 3)/(-3(-3|x - 2| + 3) + 1)) - 2)/(3((1(-3|x - 2| + 3) + 3)/(-3(-3|x - 2| + 3) + 1)) - 1)) - 5) + 1), x = 0.8, 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": "5.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-2((-2(-5(3|(-2(-3x^2 - 5x + 1) - 4) + 1| - 3) + 4) - 1)/(-1(-5(3|(-2(-3x^2 - 5x + 1) - 4) + 1| - 3) + 4) - 2)) + 1)/(-1((-2(-5(3|(-2(-3x^2 - 5x + 1) - 4) + 1| - 3) + 4) - 1)/(-1(-5(3|(-2(-3x^2 - 5x + 1) - 4) + 1| - 3) + 4) - 2)) + 2), g(x) = (2(-3(-3(1(-1x^2 - 3x + 4)^2 - 4(-1x^2 - 3x + 4) + 2)^2 - 1(1(-1x^2 - 3x + 4)^2 - 4(-1x^2 - 3x + 4) + 2) + 2) + 2) - 2)/(-3(-3(-3(1(-1x^2 - 3x + 4)^2 - 4(-1x^2 - 3x + 4) + 2)^2 - 1(1(-1x^2 - 3x + 4)^2 - 4(-1x^2 - 3x + 4) + 2) + 2) + 2) + 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": "1.6", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (2(-4(4(1(-1(-5x^2 - 2x + 2) - 1) - 4) + 4) + 5) - 2)/(-1(-4(4(1(-1(-5x^2 - 2x + 2) - 1) - 4) + 4) + 5) + 2) and g(x) = 2e^(1(-2(1|(2(-3|x + 1| - 3) + 5) - 3| - 3) + 1)) + 3 between the vertical lines x = -1.3 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": "Calculate the area enclosed between the functions f(x) = 1(3|(2(4(-1sin(2\u03c0(1x - 4) + 3) + 2) - 4)^2 + 4(4(-1sin(2\u03c0(1x - 4) + 3) + 2) - 4) - 3) + 3| + 2)^2 - 4 and g(x) = -2((-3((-2(3(-1x + 1)^2 + 2(-1x + 1) - 3) - 3)/(-1(3(-1x + 1)^2 + 2(-1x + 1) - 3))) - 2)/(-3((-2(3(-1x + 1)^2 + 2(-1x + 1) - 3) - 3)/(-1(3(-1x + 1)^2 + 2(-1x + 1) - 3))) - 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": "15.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3cos(2\u03c0(-1((2(-4(4(-1x^2 - 3x + 3)^2 + 4(-1x^2 - 3x + 3))^2 - 3(4(-1x^2 - 3x + 3)^2 + 4(-1x^2 - 3x + 3)) - 4) + 3)/(2(-4(4(-1x^2 - 3x + 3)^2 + 4(-1x^2 - 3x + 3))^2 - 3(4(-1x^2 - 3x + 3)^2 + 4(-1x^2 - 3x + 3)) - 4)))^2 + 5((2(-4(4(-1x^2 - 3x + 3)^2 + 4(-1x^2 - 3x + 3))^2 - 3(4(-1x^2 - 3x + 3)^2 + 4(-1x^2 - 3x + 3)) - 4) + 3)/(2(-4(4(-1x^2 - 3x + 3)^2 + 4(-1x^2 - 3x + 3))^2 - 3(4(-1x^2 - 3x + 3)^2 + 4(-1x^2 - 3x + 3)) - 4))) - 1) - 1), g(x) = (-2(3cos(1\u03c0((-2((-3(3|x - 3|) - 1)/(-2(3|x - 3|) + 3)) - 2)/(3((-3(3|x - 3|) - 1)/(-2(3|x - 3|) + 3)))) + 2) + 2) - 1)/(-3(3cos(1\u03c0((-2((-3(3|x - 3|) - 1)/(-2(3|x - 3|) + 3)) - 2)/(3((-3(3|x - 3|) - 1)/(-2(3|x - 3|) + 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-2(3e^(1(-4(4((1(3|x + 2| + 3) + 2)/(2(3|x + 2| + 3)))^2 + 5((1(3|x + 2| + 3) + 2)/(2(3|x + 2| + 3)))) + 4)) + 2) + 2)/(-1(3e^(1(-4(4((1(3|x + 2| + 3) + 2)/(2(3|x + 2| + 3)))^2 + 5((1(3|x + 2| + 3) + 2)/(2(3|x + 2| + 3)))) + 4)) + 2) - 1) and g(x) = 3cos(2\u03c0(3(1|(-1(-3x - 2)^2 + 4(-3x - 2) + 5) - 1| + 3)) - 2) + 3 between the vertical lines x = -3.0 and x = -2.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2cos(2\u03c0(-3|(3|(-4((-2(1x - 2) + 1)/(-1(1x - 2) + 2)) + 1)| - 2) + 1| + 2) + 3) + 1 and g(x) = (2(1(-2|(-2((-3x - 2)/(2x - 3))^2 + 1((-3x - 2)/(2x - 3)) + 1) - 3| + 1) + 5) - 3)/(-2(1(-2|(-2((-3x - 2)/(2x - 3))^2 + 1((-3x - 2)/(2x - 3)) + 1) - 3| + 1) + 5)) 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) = 2(3(-2|(-1e^(2((1(-2|x - 3| - 3) + 2)/(1(-2|x - 3| - 3)))) - 1) + 2| + 1) + 5) + 1, g(x) = 3((3((3(-4(-3cos(1\u03c0x - 2) - 1) - 5) - 1)/(3(-4(-3cos(1\u03c0x - 2) - 1) - 5) + 1)) + 1)/(-2((3(-4(-3cos(1\u03c0x - 2) - 1) - 5) - 1)/(3(-4(-3cos(1\u03c0x - 2) - 1) - 5) + 1)) + 3)) + 2, x = -4.9, 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": "73.8", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2sin(1\u03c0(4(1(-2|(-2(-3|x - 1| + 2)^2 + 4(-3|x - 1| + 2)) + 3| - 3) + 5)^2 + 5) - 1) + 3, g(x) = -2|((3(-4(-2sin(3\u03c0((3x + 3)/(1x + 1)) + 3))^2 - 2(-2sin(3\u03c0((3x + 3)/(1x + 1)) + 3)) + 2) + 3)/(2(-4(-2sin(3\u03c0((3x + 3)/(1x + 1)) + 3))^2 - 2(-2sin(3\u03c0((3x + 3)/(1x + 1)) + 3)) + 2) + 3)) - 2| + 3, x = 2.1, 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -3|(1(2e^(-1(5(5(-4x - 1)^2 + 1(-4x - 1))^2 - 5(5(-4x - 1)^2 + 1(-4x - 1)) + 5)) + 1)^2 - 5(2e^(-1(5(5(-4x - 1)^2 + 1(-4x - 1))^2 - 5(5(-4x - 1)^2 + 1(-4x - 1)) + 5)) + 1) - 4) - 1| - 2, g(x) = -3|(-5(-2((-3(3x^2 + 4x + 3) + 2)/(2(3x^2 + 4x + 3) + 3))^2 + 2((-3(3x^2 + 4x + 3) + 2)/(2(3x^2 + 4x + 3) + 3)) + 3) - 4) + 3| - 1, x = -2.2, 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": "35.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-1(-3|(5((3(2|(5x^2 - 3x) + 2| - 3) + 2)/(-3(2|(5x^2 - 3x) + 2| - 3) + 1))^2 - 4) + 3| + 1) - 1)/(2(-3|(5((3(2|(5x^2 - 3x) + 2| - 3) + 2)/(-3(2|(5x^2 - 3x) + 2| - 3) + 1))^2 - 4) + 3| + 1) + 2) and g(x) = (1(-5(-2cos(3\u03c0(-1|(-1|x + 1| - 3) - 3|) + 3) - 3)^2 - 5(-2cos(3\u03c0(-1|(-1|x + 1| - 3) - 3|) + 3) - 3) + 3) + 1)/(2(-5(-2cos(3\u03c0(-1|(-1|x + 1| - 3) - 3|) + 3) - 3)^2 - 5(-2cos(3\u03c0(-1|(-1|x + 1| - 3) - 3|) + 3) - 3) + 3) + 1) from x = 1.7 to 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": "Find the area of the region bounded by the curves f(x) = -1(3|((3(-3(-1(3cos(2\u03c0x + 2) - 3)^2 - 1(3cos(2\u03c0x + 2) - 3) + 1)^2 - 1(-1(3cos(2\u03c0x + 2) - 3)^2 - 1(3cos(2\u03c0x + 2) - 3) + 1) - 5) + 3)/(-1(-3(-1(3cos(2\u03c0x + 2) - 3)^2 - 1(3cos(2\u03c0x + 2) - 3) + 1)^2 - 1(-1(3cos(2\u03c0x + 2) - 3)^2 - 1(3cos(2\u03c0x + 2) - 3) + 1) - 5) + 2)) - 3| + 2) - 4, g(x) = (3(-5(-2|((-3(-1x^2 - 4x + 2) - 3)/(-3(-1x^2 - 4x + 2) - 2))| + 1) - 1))/(-1(-5(-2|((-3(-1x^2 - 4x + 2) - 3)/(-3(-1x^2 - 4x + 2) - 2))| + 1) - 1) + 3), x = 0.6, 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": "111.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (2((1(5(-2|(-1|(1|x - 2| - 1)| - 3) + 2| - 2)) - 3)/(2(5(-2|(-1|(1|x - 2| - 1)| - 3) + 2| - 2)) + 1)))/(-2((1(5(-2|(-1|(1|x - 2| - 1)| - 3) + 2| - 2)) - 3)/(2(5(-2|(-1|(1|x - 2| - 1)| - 3) + 2| - 2)) + 1)) - 1) and g(x) = -2sin(1\u03c0(5(2|((2(1x^2 - 3x))/(1(1x^2 - 3x) - 3)) + 1| - 2)^2 + 4(2|((2(1x^2 - 3x))/(1(1x^2 - 3x) - 3)) + 1| - 2) + 5) - 1) + 1 between the vertical lines x = -2.5 and 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) = (3(5((-1(-4(-2|(-1|x - 3| + 2)| + 2) - 3) - 3)/(-1(-4(-2|(-1|x - 3| + 2)| + 2) - 3) - 2)) + 5) + 2)/(-2(5((-1(-4(-2|(-1|x - 3| + 2)| + 2) - 3) - 3)/(-1(-4(-2|(-1|x - 3| + 2)| + 2) - 3) - 2)) + 5) + 1) and g(x) = -5(-2sin(3\u03c0((1(-4(-4x - 3)^2 + 5(-4x - 3) + 5) - 2)/(3(-4(-4x - 3)^2 + 5(-4x - 3) + 5) + 3))) - 2) - 5 from x = 2.1 to x = 3.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11.8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 3|(3(-4(-1(1(-1sin(2\u03c0x + 2)) + 5) + 5) - 5) + 4) + 1| - 1 and g(x) = 1|(-2(-4(1|(2sin(1\u03c0x - 2)) - 1| - 1) - 2)^2 - 5(-4(1|(2sin(1\u03c0x - 2)) - 1| - 1) - 2) + 4) - 3| - 1 from x = 2.6 to x = 3.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "27.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3((2(5(1e^(2(3|(-3|x - 3| + 3) - 1| - 2))) + 5) + 1)/(2(5(1e^(2(3|(-3|x - 3| + 3) - 1| - 2))) + 5) - 3))^2 - 4((2(5(1e^(2(3|(-3|x - 3| + 3) - 1| - 2))) + 5) + 1)/(2(5(1e^(2(3|(-3|x - 3| + 3) - 1| - 2))) + 5) - 3)) - 1, g(x) = (-1((2(2sin(3\u03c0((1(-1x) + 1)/(3(-1x))) - 3)) + 1)/(-3(2sin(3\u03c0((1(-1x) + 1)/(3(-1x))) - 3)) - 2)) - 1)/(1((2(2sin(3\u03c0((1(-1x) + 1)/(3(-1x))) - 3)) + 1)/(-3(2sin(3\u03c0((1(-1x) + 1)/(3(-1x))) - 3)) - 2))), 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": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2|(-5((2(3|(5(2cos(3\u03c0x - 2)) - 2)| + 1) + 2)/(-3(3|(5(2cos(3\u03c0x - 2)) - 2)| + 1) + 2))^2 + 3((2(3|(5(2cos(3\u03c0x - 2)) - 2)| + 1) + 2)/(-3(3|(5(2cos(3\u03c0x - 2)) - 2)| + 1) + 2)) + 4)| - 2, g(x) = (-1(2|(-3|(-1sin(1\u03c0((2x - 1)/(2x + 3)) - 2) - 1) - 1| + 2)| - 3) - 1)/(-1(2|(-3|(-1sin(1\u03c0((2x - 1)/(2x + 3)) - 2) - 1) - 1| + 2)| - 3) + 3), x = -4.6, 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": "1.9", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2(3(-2(4(2sin(2\u03c0(2x - 3) + 2) - 1) + 1) - 4)^2 + 3(-2(4(2sin(2\u03c0(2x - 3) + 2) - 1) + 1) - 4)) - 1 and g(x) = (-3(-2sin(1\u03c0(3|(3(-4x)) + 2|) - 2) - 3))/(2(-2sin(1\u03c0(3|(3(-4x)) + 2|) - 2) - 3) + 3) between the vertical lines x = 3.1 and x = 3.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "265.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2|(-3(2|(-4(-2|(-5x^2 - 1) + 3| + 2)^2 - 4(-2|(-5x^2 - 1) + 3| + 2) + 3) - 3| + 1) + 2)| - 2 and g(x) = -2|(2|(3((2(-1x + 4) + 2)/(-1(-1x + 4) - 3))^2 - 4((2(-1x + 4) + 2)/(-1(-1x + 4) - 3)) + 3) - 3| - 2) - 2| - 1 between the vertical lines x = 0.7 and x = 0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1|(-2cos(1\u03c0(-2(2|(-3|(-1|x| + 2) + 2| - 2) - 2| - 3) - 2)) + 1) + 3| + 1 and g(x) = -3|((-2(2|((-1(1|x - 3| - 1) - 1)/(-3(1|x - 3| - 1))) - 1| - 2) + 3)/(3(2|((-1(1|x - 3| - 1) - 1)/(-3(1|x - 3| - 1))) - 1| - 2) + 3)) + 3| + 2 between the vertical lines x = 4.8 and x = 4.9. 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(3|((1(3e^(-2((-2x - 3)/(2x))) - 3) - 1)/(-1(3e^(-2((-2x - 3)/(2x))) - 3) + 2))| - 3)^2 - 4(3|((1(3e^(-2((-2x - 3)/(2x))) - 3) - 1)/(-1(3e^(-2((-2x - 3)/(2x))) - 3) + 2))| - 3) + 4))/(-1(-1(3|((1(3e^(-2((-2x - 3)/(2x))) - 3) - 1)/(-1(3e^(-2((-2x - 3)/(2x))) - 3) + 2))| - 3)^2 - 4(3|((1(3e^(-2((-2x - 3)/(2x))) - 3) - 1)/(-1(3e^(-2((-2x - 3)/(2x))) - 3) + 2))| - 3) + 4) - 3), g(x) = 4(5(-4(-3((-3x + 1)/(-2x - 2)) - 1) - 2) - 3)^2 - 5, 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": "2.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-3((-2(-4((1(2sin(3\u03c0(-2x^2 + 4x + 4) - 2) + 2) - 1)/(3(2sin(3\u03c0(-2x^2 + 4x + 4) - 2) + 2) + 1)) - 1))/(-2(-4((1(2sin(3\u03c0(-2x^2 + 4x + 4) - 2) + 2) - 1)/(3(2sin(3\u03c0(-2x^2 + 4x + 4) - 2) + 2) + 1)) - 1) - 1)) - 2)/(-2((-2(-4((1(2sin(3\u03c0(-2x^2 + 4x + 4) - 2) + 2) - 1)/(3(2sin(3\u03c0(-2x^2 + 4x + 4) - 2) + 2) + 1)) - 1))/(-2(-4((1(2sin(3\u03c0(-2x^2 + 4x + 4) - 2) + 2) - 1)/(3(2sin(3\u03c0(-2x^2 + 4x + 4) - 2) + 2) + 1)) - 1) - 1)) - 3) and g(x) = 1((2(1|(1|(-5x - 4) - 3| + 3) + 1| - 2) - 2)/(-3(1|(1|(-5x - 4) - 3| + 3) + 1| - 2) - 3)) + 3 from x = 2.5 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": "Find the area of the region bounded by the curves f(x) = 3|((1((3((-1(4(3x^2 - 2x - 3)^2 + 5(3x^2 - 2x - 3) + 4) + 2)/(1(4(3x^2 - 2x - 3)^2 + 5(3x^2 - 2x - 3) + 4))) - 1)/(-2((-1(4(3x^2 - 2x - 3)^2 + 5(3x^2 - 2x - 3) + 4) + 2)/(1(4(3x^2 - 2x - 3)^2 + 5(3x^2 - 2x - 3) + 4))))) + 3)/(-1((3((-1(4(3x^2 - 2x - 3)^2 + 5(3x^2 - 2x - 3) + 4) + 2)/(1(4(3x^2 - 2x - 3)^2 + 5(3x^2 - 2x - 3) + 4))) - 1)/(-2((-1(4(3x^2 - 2x - 3)^2 + 5(3x^2 - 2x - 3) + 4) + 2)/(1(4(3x^2 - 2x - 3)^2 + 5(3x^2 - 2x - 3) + 4))))) - 3)) + 1| + 1, g(x) = -1((2((1((-3(2|x - 2| - 1))/(-2(2|x - 2| - 1) + 1)) + 3)/(-2((-3(2|x - 2| - 1))/(-2(2|x - 2| - 1) + 1)) + 1)) - 3)/(-3((1((-3(2|x - 2| - 1))/(-2(2|x - 2| - 1) + 1)) + 3)/(-2((-3(2|x - 2| - 1))/(-2(2|x - 2| - 1) + 1)) + 1)) + 2)), x = 1.1, 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": "3.7", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2(-1((-1(1(2sin(2\u03c0(-2|x + 3| - 3) + 3) + 3)^2 - 2(2sin(2\u03c0(-2|x + 3| - 3) + 3) + 3) + 5) - 3)/(-3(1(2sin(2\u03c0(-2|x + 3| - 3) + 3) + 3)^2 - 2(2sin(2\u03c0(-2|x + 3| - 3) + 3) + 3) + 5) + 2))^2 + 5((-1(1(2sin(2\u03c0(-2|x + 3| - 3) + 3) + 3)^2 - 2(2sin(2\u03c0(-2|x + 3| - 3) + 3) + 3) + 5) - 3)/(-3(1(2sin(2\u03c0(-2|x + 3| - 3) + 3) + 3)^2 - 2(2sin(2\u03c0(-2|x + 3| - 3) + 3) + 3) + 5) + 2)) - 2)^2 + 4 and g(x) = -2((-1(4(-1sin(2\u03c0(2x^2 + 5x + 5) + 2))^2 - 1(-1sin(2\u03c0(2x^2 + 5x + 5) + 2)) - 4))/(2(4(-1sin(2\u03c0(2x^2 + 5x + 5) + 2))^2 - 1(-1sin(2\u03c0(2x^2 + 5x + 5) + 2)) - 4)))^2 + 4 between the vertical lines x = -2.5 and x = -2.2. 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) = 2cos(3\u03c0(-4(5(-2|((-1((1x - 1)/(-2x + 3)) + 3)/(1((1x - 1)/(-2x + 3)) + 3)) + 1| - 1) + 2) + 1) - 3) + 3 and g(x) = -2|((-2(-4(-4(-5x^2 + 1x + 5)^2 - 5(-5x^2 + 1x + 5) + 5)^2 - 2(-4(-5x^2 + 1x + 5)^2 - 5(-5x^2 + 1x + 5) + 5) + 5) - 2)/(-3(-4(-4(-5x^2 + 1x + 5)^2 - 5(-5x^2 + 1x + 5) + 5)^2 - 2(-4(-5x^2 + 1x + 5)^2 - 5(-5x^2 + 1x + 5) + 5) + 5) - 2)) + 3| - 2 from x = -3 to x = 3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "73.9", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3(-2|(1(-4((3(1|x - 2|) - 1)/(3(1|x - 2|) + 2))^2 - 5((3(1|x - 2|) - 1)/(3(1|x - 2|) + 2))) + 1) + 2|)^2 - 1(-2|(1(-4((3(1|x - 2|) - 1)/(3(1|x - 2|) + 2))^2 - 5((3(1|x - 2|) - 1)/(3(1|x - 2|) + 2))) + 1) + 2|) + 1 and g(x) = -4((-2((2(-2(1sin(3\u03c0x) - 1)))/(2(-2(1sin(3\u03c0x) - 1)) - 1)) - 2)/(-2((2(-2(1sin(3\u03c0x) - 1)))/(2(-2(1sin(3\u03c0x) - 1)) - 1)) + 3)) - 4 between the vertical lines x = 2.7 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": "Find the area of the region bounded by the curves f(x) = -1|(4(5(2cos(3\u03c0((1((-1x)/(1x + 1)) + 3)/(-1((-1x)/(1x + 1)) - 1)) - 3) + 1)^2 - 4) + 4) - 2| - 2, g(x) = -3|((-2(-2|((-2(3x^2 - 3x - 2) - 3)/(-1(3x^2 - 3x - 2) + 2)) + 2| - 2) + 2)/(1(-2|((-2(3x^2 - 3x - 2) - 3)/(-1(3x^2 - 3x - 2) + 2)) + 2| - 2) + 1)) + 1|, x = 4.2, 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": "15.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1((1((-1(1|(1(-2x^2 + 3x + 1) + 3) + 3| - 1) + 2)/(-2(1|(1(-2x^2 + 3x + 1) + 3) + 3| - 1) + 3)) + 3)/(-2((-1(1|(1(-2x^2 + 3x + 1) + 3) + 3| - 1) + 2)/(-2(1|(1(-2x^2 + 3x + 1) + 3) + 3| - 1) + 3)) + 3))^2 - 4((1((-1(1|(1(-2x^2 + 3x + 1) + 3) + 3| - 1) + 2)/(-2(1|(1(-2x^2 + 3x + 1) + 3) + 3| - 1) + 3)) + 3)/(-2((-1(1|(1(-2x^2 + 3x + 1) + 3) + 3| - 1) + 2)/(-2(1|(1(-2x^2 + 3x + 1) + 3) + 3| - 1) + 3)) + 3)) - 2 and g(x) = (1(-1(-3cos(3\u03c0(-5(2|x + 1| + 3) + 3) + 2) - 1)^2 - 1(-3cos(3\u03c0(-5(2|x + 1| + 3) + 3) + 2) - 1) + 3) - 3)/(3(-1(-3cos(3\u03c0(-5(2|x + 1| + 3) + 3) + 2) - 1)^2 - 1(-3cos(3\u03c0(-5(2|x + 1| + 3) + 3) + 2) - 1) + 3) - 2) 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": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3|(-3|(-2|((-3((1(2|x + 1|) - 1)/(3(2|x + 1|) + 1)) + 3)/(-3((1(2|x + 1|) - 1)/(3(2|x + 1|) + 1)) - 2)) - 1|) + 1|) + 2| + 1, g(x) = -4(-3(5(3(-2sin(1\u03c0x) + 3)^2 - 2(-2sin(1\u03c0x) + 3) + 2) + 1) - 2) - 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": "360.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (2(-1sin(3\u03c0(-3(-3|((-1(4x^2 - 3x + 1) - 2)/(-1(4x^2 - 3x + 1) - 3)) + 2| - 1) - 4) + 1) + 3) - 2)/(-3(-1sin(3\u03c0(-3(-3|((-1(4x^2 - 3x + 1) - 2)/(-1(4x^2 - 3x + 1) - 3)) + 2| - 1) - 4) + 1) + 3) - 2) and g(x) = 3(-2(4(1|(-2x^2 - 4x + 4) + 2| - 1) - 4)) - 3 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": "10.5", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3|(4(-2(2(1cos(1\u03c0(-1x^2 + 5) + 1) + 1)^2 + 3(1cos(1\u03c0(-1x^2 + 5) + 1) + 1) - 4) - 2) - 4)| - 2, g(x) = (-1(2(-4(2sin(2\u03c0(1|x + 2| + 2) - 1) - 1)^2 - 2(2sin(2\u03c0(1|x + 2| + 2) - 1) - 1) + 3) - 5) - 1)/(-1(2(-4(2sin(2\u03c0(1|x + 2| + 2) - 1) - 1)^2 - 2(2sin(2\u03c0(1|x + 2| + 2) - 1) - 1) + 3) - 5) + 3), x = -2.2, 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": "7.9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-2((-1((2(-1((-3(2|x + 1| - 3) - 2)/(3(2|x + 1| - 3)))^2 + 3((-3(2|x + 1| - 3) - 2)/(3(2|x + 1| - 3))) + 4) + 1)/(3(-1((-3(2|x + 1| - 3) - 2)/(3(2|x + 1| - 3)))^2 + 3((-3(2|x + 1| - 3) - 2)/(3(2|x + 1| - 3))) + 4) - 2)))/(-1((2(-1((-3(2|x + 1| - 3) - 2)/(3(2|x + 1| - 3)))^2 + 3((-3(2|x + 1| - 3) - 2)/(3(2|x + 1| - 3))) + 4) + 1)/(3(-1((-3(2|x + 1| - 3) - 2)/(3(2|x + 1| - 3)))^2 + 3((-3(2|x + 1| - 3) - 2)/(3(2|x + 1| - 3))) + 4) - 2)) - 1)) - 3)/(-1((-1((2(-1((-3(2|x + 1| - 3) - 2)/(3(2|x + 1| - 3)))^2 + 3((-3(2|x + 1| - 3) - 2)/(3(2|x + 1| - 3))) + 4) + 1)/(3(-1((-3(2|x + 1| - 3) - 2)/(3(2|x + 1| - 3)))^2 + 3((-3(2|x + 1| - 3) - 2)/(3(2|x + 1| - 3))) + 4) - 2)))/(-1((2(-1((-3(2|x + 1| - 3) - 2)/(3(2|x + 1| - 3)))^2 + 3((-3(2|x + 1| - 3) - 2)/(3(2|x + 1| - 3))) + 4) + 1)/(3(-1((-3(2|x + 1| - 3) - 2)/(3(2|x + 1| - 3)))^2 + 3((-3(2|x + 1| - 3) - 2)/(3(2|x + 1| - 3))) + 4) - 2)) - 1)) + 2) and g(x) = -5(-1sin(3\u03c0(-1((-3((3x)/(1x)) - 1)/(-3((3x)/(1x)) + 4))^2 + 4) - 3)) - 2 from x = -2.0 to x = -0.0. 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": "Find the area of the region bounded by the curves f(x) = -4(2((-1(3|(-1e^(-2(-5x^2 + 4x + 2)) + 3) - 1| + 1) + 3)/(1(3|(-1e^(-2(-5x^2 + 4x + 2)) + 3) - 1| + 1) + 2))^2 + 2) + 4, g(x) = -1|(-1|((3(2(-1|x - 2| - 1)^2 + 3(-1|x - 2| - 1) + 1) + 2)/(-3(2(-1|x - 2| - 1)^2 + 3(-1|x - 2| - 1) + 1))) - 3| + 1) + 3| + 2, 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": "14.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -4(-2|(-2|(2e^(1(-5(1|x| - 2) + 1))) - 1| + 1)| + 3)^2 + 4(-2|(-2|(2e^(1(-5(1|x| - 2) + 1))) - 1| + 1)| + 3) + 5, g(x) = (2((3(-3(3(4x^2 + 1x - 2)^2 + 5(4x^2 + 1x - 2) - 5)^2 + 1(3(4x^2 + 1x - 2)^2 + 5(4x^2 + 1x - 2) - 5) - 1) + 1)/(3(-3(3(4x^2 + 1x - 2)^2 + 5(4x^2 + 1x - 2) - 5)^2 + 1(3(4x^2 + 1x - 2)^2 + 5(4x^2 + 1x - 2) - 5) - 1) + 2)) - 2)/(3((3(-3(3(4x^2 + 1x - 2)^2 + 5(4x^2 + 1x - 2) - 5)^2 + 1(3(4x^2 + 1x - 2)^2 + 5(4x^2 + 1x - 2) - 5) - 1) + 1)/(3(-3(3(4x^2 + 1x - 2)^2 + 5(4x^2 + 1x - 2) - 5)^2 + 1(3(4x^2 + 1x - 2)^2 + 5(4x^2 + 1x - 2) - 5) - 1) + 2)) + 3), x = 2.4, 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": "2.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1cos(1\u03c0(5(1|(4(3|((2x - 1)/(2x - 1)) - 1| + 1)^2 + 2(3|((2x - 1)/(2x - 1)) - 1| + 1) - 2) + 3|) - 5) + 1) - 3 and g(x) = -2cos(1\u03c0(-5(-2((-2(2x + 2) - 2)/(2(2x + 2) + 3))^2 - 5((-2(2x + 2) - 2)/(2(2x + 2) + 3)) + 4)) + 3) - 3 between the vertical lines x = -1.9 and x = -1.7999999999999998. 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|(2(1|(1(5x + 5) + 5) - 2| + 3))| - 3) + 1, g(x) = 4(2|(3(-2(1x^2 + 4x + 2)^2 + 1(1x^2 + 4x + 2))^2 + 2(-2(1x^2 + 4x + 2)^2 + 1(1x^2 + 4x + 2)) + 5) - 1| - 1)^2 - 3(2|(3(-2(1x^2 + 4x + 2)^2 + 1(1x^2 + 4x + 2))^2 + 2(-2(1x^2 + 4x + 2)^2 + 1(1x^2 + 4x + 2)) + 5) - 1| - 1) + 5, x = -3.7, 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) = (-3(-5(-1sin(2\u03c0(5((-3((3x + 1)/(-2x - 2)) - 3)/(-1((3x + 1)/(-2x - 2)) + 2)) + 1) - 2)) - 4) - 2)/(-1(-5(-1sin(2\u03c0(5((-3((3x + 1)/(-2x - 2)) - 3)/(-1((3x + 1)/(-2x - 2)) + 2)) + 1) - 2)) - 4) + 2) and g(x) = (-3(5(3(-2((-2x + 1)/(3x + 2)) - 1)^2 + 2(-2((-2x + 1)/(3x + 2)) - 1) + 2)^2 + 5(3(-2((-2x + 1)/(3x + 2)) - 1)^2 + 2(-2((-2x + 1)/(3x + 2)) - 1) + 2) + 1) - 3)/(-2(5(3(-2((-2x + 1)/(3x + 2)) - 1)^2 + 2(-2((-2x + 1)/(3x + 2)) - 1) + 2)^2 + 5(3(-2((-2x + 1)/(3x + 2)) - 1)^2 + 2(-2((-2x + 1)/(3x + 2)) - 1) + 2) + 1) - 3) between the vertical lines x = -2.4 and x = -2.1. 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(-1|((1(2|(4(-4x^2 - 3x - 1) + 3) - 3|) - 3)/(-1(2|(4(-4x^2 - 3x - 1) + 3) - 3|) - 1)) + 3| + 2)^2 - 4(-1|((1(2|(4(-4x^2 - 3x - 1) + 3) - 3|) - 3)/(-1(2|(4(-4x^2 - 3x - 1) + 3) - 3|) - 1)) + 3| + 2) + 4, g(x) = (-2((1(3(2sin(1\u03c0(3|x - 1| + 3) - 2) + 3) - 3))/(2(3(2sin(1\u03c0(3|x - 1| + 3) - 2) + 3) - 3) + 2)) - 2)/(3((1(3(2sin(1\u03c0(3|x - 1| + 3) - 2) + 3) - 3))/(2(3(2sin(1\u03c0(3|x - 1| + 3) - 2) + 3) - 3) + 2)) - 2), 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 3((1((-3(-2(1|(-1x^2 - 3x + 4) - 1| + 1) + 4) + 1)/(1(-2(1|(-1x^2 - 3x + 4) - 1| + 1) + 4) + 1)) - 3)/(-1((-3(-2(1|(-1x^2 - 3x + 4) - 1| + 1) + 4) + 1)/(1(-2(1|(-1x^2 - 3x + 4) - 1| + 1) + 4) + 1)) + 2)) - 1 and g(x) = -5(2(-2(3(3e^(-1x) - 3)^2 + 3(3e^(-1x) - 3) - 5)^2 - 1(3(3e^(-1x) - 3)^2 + 3(3e^(-1x) - 3) - 5) + 1) - 5) + 1 from x = 0.5 to x = 1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "65.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1(1|(3((-3(-2e^(1((-3x + 3)/(2x))) + 3) + 2)/(-1(-2e^(1((-3x + 3)/(2x))) + 3) - 3))^2 - 5) + 2| - 2) - 4 and g(x) = -3(-4(4(1|(-1x^2 + 1x - 1) - 1| - 1) - 5)^2 + 2(4(1|(-1x^2 + 1x - 1) - 1| - 1) - 5)) - 1 between the vertical lines x = 0.0 and x = 0.4. 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": "Calculate the area enclosed between the functions f(x) = -2(3|((2(-3sin(2\u03c0(-1|(1|x - 2| - 2)| + 1) - 3) - 2) - 3)/(-3(-3sin(2\u03c0(-1|(1|x - 2| - 2)| + 1) - 3) - 2) + 4)) - 2| - 1)^2 - 2(3|((2(-3sin(2\u03c0(-1|(1|x - 2| - 2)| + 1) - 3) - 2) - 3)/(-3(-3sin(2\u03c0(-1|(1|x - 2| - 2)| + 1) - 3) - 2) + 4)) - 2| - 1) + 3 and g(x) = 5(-3|((3(4(4x - 3)^2 - 4(4x - 3) - 3) - 2)/(1(4(4x - 3)^2 - 4(4x - 3) - 3) + 2)) - 2| - 3) + 3 from x = 0.8 to x = 1.0. 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": "Calculate the area enclosed between the functions f(x) = 1((2(2(-2sin(1\u03c0(2|(-3x + 3) - 2| - 1) - 2) + 2)^2 + 1(-2sin(1\u03c0(2|(-3x + 3) - 2| - 1) - 2) + 2) - 5) + 2)/(3(2(-2sin(1\u03c0(2|(-3x + 3) - 2| - 1) - 2) + 2)^2 + 1(-2sin(1\u03c0(2|(-3x + 3) - 2| - 1) - 2) + 2) - 5) - 2))^2 + 2((2(2(-2sin(1\u03c0(2|(-3x + 3) - 2| - 1) - 2) + 2)^2 + 1(-2sin(1\u03c0(2|(-3x + 3) - 2| - 1) - 2) + 2) - 5) + 2)/(3(2(-2sin(1\u03c0(2|(-3x + 3) - 2| - 1) - 2) + 2)^2 + 1(-2sin(1\u03c0(2|(-3x + 3) - 2| - 1) - 2) + 2) - 5) - 2)) - 3 and g(x) = (-1(2|((-2(1(-3x^2 - 3x - 3)^2 - 1(-3x^2 - 3x - 3) + 2) + 1)/(3(1(-3x^2 - 3x - 3)^2 - 1(-3x^2 - 3x - 3) + 2) - 2)) + 2| - 2) + 2)/(-2(2|((-2(1(-3x^2 - 3x - 3)^2 - 1(-3x^2 - 3x - 3) + 2) + 1)/(3(1(-3x^2 - 3x - 3)^2 - 1(-3x^2 - 3x - 3) + 2) - 2)) + 2| - 2) - 2) from x = 1.8 to x = 1.9000000000000001. 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) = 3sin(1\u03c0(2|(4(4((1(-1x + 4) - 3)/(3(-1x + 4) - 2)) - 3)^2 - 2(4((1(-1x + 4) - 3)/(3(-1x + 4) - 2)) - 3) + 1) - 1| - 1) - 1) - 1 and g(x) = (-2(1(-2|(4(2|x + 1| - 2)^2 + 5(2|x + 1| - 2) + 2)| - 2) + 3) - 2)/(3(1(-2|(4(2|x + 1| - 2)^2 + 5(2|x + 1| - 2) + 2)| - 2) + 3) - 2) 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2|(1|((-2(-2((3(2sin(3\u03c0x + 3) + 3) - 2)/(1(2sin(3\u03c0x + 3) + 3) - 3)) + 4) - 3)/(-3(-2((3(2sin(3\u03c0x + 3) + 3) - 2)/(1(2sin(3\u03c0x + 3) + 3) - 3)) + 4) + 4)) + 2| - 3) - 3|, g(x) = -3|(4(-4(2((1x + 3)/(-2x - 1))^2 - 4((1x + 3)/(-2x - 1)) + 2)) + 5) - 2| + 1, 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": "0.9", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -4(1(3(4((1(-1x + 3))/(3(-1x + 3) - 2)) + 4) + 2) + 3)^2 + 4(1(3(4((1(-1x + 3))/(3(-1x + 3) - 2)) + 4) + 2) + 3) - 3, g(x) = -2|(-3|((1(1|((-2x + 1)/(1x)) - 2| - 2) + 3)/(-2(1|((-2x + 1)/(1x)) - 2| - 2) - 1)) - 3| + 1) + 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": "22.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1|(1|((1((-2(5(2x + 1)^2 + 1(2x + 1) - 4) - 1)/(2(5(2x + 1)^2 + 1(2x + 1) - 4) + 2)) - 1)/(3((-2(5(2x + 1)^2 + 1(2x + 1) - 4) - 1)/(2(5(2x + 1)^2 + 1(2x + 1) - 4) + 2)) + 2))|) - 3| and g(x) = (-1(-1cos(3\u03c0(2|(4((2x + 2)/(-1x)) - 1) - 1| - 2) - 1) + 3))/(-1(-1cos(3\u03c0(2|(4((2x + 2)/(-1x)) - 1) - 1| - 2) - 1) + 3) - 1) 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) = -2sin(1\u03c0((-3(-4(-5(4(3|x|) - 5) + 5) - 3) + 3)/(-1(-4(-5(4(3|x|) - 5) + 5) - 3) - 2)) + 1) + 1, g(x) = (-1((-1(-4(2(-5x^2 + 1x - 3)^2 - 4(-5x^2 + 1x - 3) + 3) - 5) - 3)/(1(-4(2(-5x^2 + 1x - 3)^2 - 4(-5x^2 + 1x - 3) + 3) - 5) + 1)) - 1)/(-1((-1(-4(2(-5x^2 + 1x - 3)^2 - 4(-5x^2 + 1x - 3) + 3) - 5) - 3)/(1(-4(2(-5x^2 + 1x - 3)^2 - 4(-5x^2 + 1x - 3) + 3) - 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) = -2(-1|(2cos(2\u03c0(-1(4((2x)/(-3x)) - 5) + 1) - 3) - 3) + 1| + 1)^2 - 4(-1|(2cos(2\u03c0(-1(4((2x)/(-3x)) - 5) + 1) - 3) - 3) + 1| + 1) + 4 and g(x) = 3|(4(1(-3|(1|x - 2| + 1) - 2| + 2)^2 - 4(-3|(1|x - 2| + 1) - 2| + 2))^2 - 5(1(-3|(1|x - 2| + 1) - 2| + 2)^2 - 4(-3|(1|x - 2| + 1) - 2| + 2)) - 3) - 1| between the vertical lines x = 2.2 and x = 2.4. 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) = 3|(-1|(-1|(1(-2e^(-1(-4x^2 + 1x)) - 1)^2 + 1(-2e^(-1(-4x^2 + 1x)) - 1) - 3)| + 1) + 3| - 2) + 1| - 3, g(x) = 1(2((3(-1(-3|x - 3| + 3)^2 - 3(-3|x - 3| + 3) - 3) + 1)/(2(-1(-3|x - 3| + 3)^2 - 3(-3|x - 3| + 3) - 3) - 1)) - 1)^2 + 4(2((3(-1(-3|x - 3| + 3)^2 - 3(-3|x - 3| + 3) - 3) + 1)/(2(-1(-3|x - 3| + 3)^2 - 3(-3|x - 3| + 3) - 3) - 1)) - 1) + 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": "5.6", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2|((1((-3(1|(2e^(2(2x^2 + 3x - 4)) - 2) + 1| - 2) + 1)/(2(1|(2e^(2(2x^2 + 3x - 4)) - 2) + 1| - 2) - 1)) - 1)/(-2((-3(1|(2e^(2(2x^2 + 3x - 4)) - 2) + 1| - 2) + 1)/(2(1|(2e^(2(2x^2 + 3x - 4)) - 2) + 1| - 2) - 1)) - 2)) - 1| - 2 and g(x) = -1|(5(3sin(3\u03c0(3|(-4x) + 1|) + 2)) - 5) - 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": "0.7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (3((1(3|(4(4(-1|x - 2| - 1)^2 - 3(-1|x - 2| - 1) - 3)^2 - 1(4(-1|x - 2| - 1)^2 - 3(-1|x - 2| - 1) - 3) + 1) - 3| + 1))/(-2(3|(4(4(-1|x - 2| - 1)^2 - 3(-1|x - 2| - 1) - 3)^2 - 1(4(-1|x - 2| - 1)^2 - 3(-1|x - 2| - 1) - 3) + 1) - 3| + 1))))/(3((1(3|(4(4(-1|x - 2| - 1)^2 - 3(-1|x - 2| - 1) - 3)^2 - 1(4(-1|x - 2| - 1)^2 - 3(-1|x - 2| - 1) - 3) + 1) - 3| + 1))/(-2(3|(4(4(-1|x - 2| - 1)^2 - 3(-1|x - 2| - 1) - 3)^2 - 1(4(-1|x - 2| - 1)^2 - 3(-1|x - 2| - 1) - 3) + 1) - 3| + 1))) - 2) and g(x) = 5((2(3e^(1(-2|(-4x^2 - 5x + 4) + 3| + 3)) - 2))/(-1(3e^(1(-2|(-4x^2 - 5x + 4) + 3| + 3)) - 2) - 1))^2 + 2((2(3e^(1(-2|(-4x^2 - 5x + 4) + 3| + 3)) - 2))/(-1(3e^(1(-2|(-4x^2 - 5x + 4) + 3| + 3)) - 2) - 1)) - 4 from x = 0.7 to x = 0.7999999999999999. 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|(4(4(-4(1sin(3\u03c0(3|x - 3| + 3)))^2 + 4(1sin(3\u03c0(3|x - 3| + 3))) + 2) + 1) + 2) + 3| and g(x) = -3(-5(1cos(3\u03c0(3(-4x + 1) - 3)) - 3)^2 + 2(1cos(3\u03c0(3(-4x + 1) - 3)) - 3) - 2) - 4 from x = -3.0 to x = -2.8. 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": "Determine the area of the region enclosed by the graphs of f(x) = (-3(3sin(3\u03c0(1|(-4(-2|(1|x - 3|)| - 3)^2 - 1(-2|(1|x - 3|)| - 3) - 1) - 2| + 3))) + 2)/(2(3sin(3\u03c0(1|(-4(-2|(1|x - 3|)| - 3)^2 - 1(-2|(1|x - 3|)| - 3) - 1) - 2| + 3))) - 1) and g(x) = 5(-3cos(3\u03c0(4(-2((2x - 1)/(1x + 1)) - 2)^2 + 5(-2((2x - 1)/(1x + 1)) - 2) + 4)) + 2)^2 + 4(-3cos(3\u03c0(4(-2((2x - 1)/(1x + 1)) - 2)^2 + 5(-2((2x - 1)/(1x + 1)) - 2) + 4)) + 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": "5.6", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1cos(1\u03c0(-5(2(-3(1(4x - 1) - 5)^2 - 2(1(4x - 1) - 5) - 5)^2 + 5(-3(1(4x - 1) - 5)^2 - 2(1(4x - 1) - 5) - 5) - 4)) + 2) - 3 and g(x) = -1(3((-1(1|(3x + 1) - 2| - 2) + 2)/(-3(1|(3x + 1) - 2| - 2) + 2)) + 2) - 4 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-1((-3(-1(1|((-1(-3sin(3\u03c0x - 1) - 1))/(3(-3sin(3\u03c0x - 1) - 1) - 2))| + 1) + 5) - 2)/(1(-1(1|((-1(-3sin(3\u03c0x - 1) - 1))/(3(-3sin(3\u03c0x - 1) - 1) - 2))| + 1) + 5) - 3)) - 3)/(1((-3(-1(1|((-1(-3sin(3\u03c0x - 1) - 1))/(3(-3sin(3\u03c0x - 1) - 1) - 2))| + 1) + 5) - 2)/(1(-1(1|((-1(-3sin(3\u03c0x - 1) - 1))/(3(-3sin(3\u03c0x - 1) - 1) - 2))| + 1) + 5) - 3)) - 3) and g(x) = 2|(4((-3(-1(5x^2 + 2x - 4)^2 - 3(5x^2 + 2x - 4) + 2) + 1)/(-2(-1(5x^2 + 2x - 4)^2 - 3(5x^2 + 2x - 4) + 2) - 3))^2 - 4((-3(-1(5x^2 + 2x - 4)^2 - 3(5x^2 + 2x - 4) + 2) + 1)/(-2(-1(5x^2 + 2x - 4)^2 - 3(5x^2 + 2x - 4) + 2) - 3)) - 3) + 3| - 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1e^(1(-5(1(-2(1|(-4x^2 - 1x - 1) - 1|) + 1) + 3)^2 - 3(1(-2(1|(-4x^2 - 1x - 1) - 1|) + 1) + 3) + 4)) + 1, g(x) = (2(1(2(3|(3|x| - 1) - 3| + 3)^2 - 5(3|(3|x| - 1) - 3| + 3) - 5)^2 - 3(2(3|(3|x| - 1) - 3| + 3)^2 - 5(3|(3|x| - 1) - 3| + 3) - 5) + 3) - 1)/(-1(1(2(3|(3|x| - 1) - 3| + 3)^2 - 5(3|(3|x| - 1) - 3| + 3) - 5)^2 - 3(2(3|(3|x| - 1) - 3| + 3)^2 - 5(3|(3|x| - 1) - 3| + 3) - 5) + 3) + 3), x = -1.3, 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": "2.4", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-2(2(4(-1|(1(2x - 4)) - 2| - 2)^2 + 5(-1|(1(2x - 4)) - 2| - 2) - 1)^2 + 1(4(-1|(1(2x - 4)) - 2| - 2)^2 + 5(-1|(1(2x - 4)) - 2| - 2) - 1) - 1) + 2)/(-1(2(4(-1|(1(2x - 4)) - 2| - 2)^2 + 5(-1|(1(2x - 4)) - 2| - 2) - 1)^2 + 1(4(-1|(1(2x - 4)) - 2| - 2)^2 + 5(-1|(1(2x - 4)) - 2| - 2) - 1) - 1) + 3), g(x) = -5((-1(-5(4(4x^2 - 4) + 3) + 4) + 1)/(1(-5(4(4x^2 - 4) + 3) + 4) + 3)), x = -0.9, 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": "4.4", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1((-3(-2|(-2|(-3|(2sin(1\u03c0x - 3) - 2) + 1| + 3) + 3| + 1) + 2| - 2) + 3)/(-2(-2|(-2|(-3|(2sin(1\u03c0x - 3) - 2) + 1| + 3) + 3| + 1) + 2| - 2) - 1))^2 + 2((-3(-2|(-2|(-3|(2sin(1\u03c0x - 3) - 2) + 1| + 3) + 3| + 1) + 2| - 2) + 3)/(-2(-2|(-2|(-3|(2sin(1\u03c0x - 3) - 2) + 1| + 3) + 3| + 1) + 2| - 2) - 1)) + 2 and g(x) = 2|(-5((-3((-1(-5x + 1) - 3)/(-3(-5x + 1) + 1)) + 1)/(2((-1(-5x + 1) - 3)/(-3(-5x + 1) + 1)) - 3)) + 2) + 2| + 1 between the vertical lines x = 4.1 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": "Calculate the area enclosed between the functions f(x) = (2(-4(-2(-3|(3|(-1x) - 2|) + 2| - 1)^2 - 1(-3|(3|(-1x) - 2|) + 2| - 1) + 4)^2 + 2(-2(-3|(3|(-1x) - 2|) + 2| - 1)^2 - 1(-3|(3|(-1x) - 2|) + 2| - 1) + 4) - 4) - 3)/(-3(-4(-2(-3|(3|(-1x) - 2|) + 2| - 1)^2 - 1(-3|(3|(-1x) - 2|) + 2| - 1) + 4)^2 + 2(-2(-3|(3|(-1x) - 2|) + 2| - 1)^2 - 1(-3|(3|(-1x) - 2|) + 2| - 1) + 4) - 4) - 2) and g(x) = -1(5(1|((2(5x - 2) + 3)/(-1(5x - 2) + 3)) + 1| - 2) + 2)^2 + 2(5(1|((2(5x - 2) + 3)/(-1(5x - 2) + 3)) + 1| - 2) + 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2|((-3(-2|(5(2cos(1\u03c0(3x + 1)) + 1) + 5) + 1| + 2) - 3)/(3(-2|(5(2cos(1\u03c0(3x + 1)) + 1) + 5) + 1| + 2) - 1)) + 1| and g(x) = (1(1((-1((2(1x^2 - 1x - 2) - 2)/(3(1x^2 - 1x - 2) - 2)) - 1)/(-3((2(1x^2 - 1x - 2) - 2)/(3(1x^2 - 1x - 2) - 2)) + 4)) + 4) - 3)/(-1(1((-1((2(1x^2 - 1x - 2) - 2)/(3(1x^2 - 1x - 2) - 2)) - 1)/(-3((2(1x^2 - 1x - 2) - 2)/(3(1x^2 - 1x - 2) - 2)) + 4)) + 4) + 2) from x = -3.5 to x = -3.2. 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) = -2(-1(-4(-3|(-4(-5x - 2) - 3) - 3| + 1) - 1) - 3) + 3, g(x) = 4(-3(-1cos(2\u03c0((2(-3x + 2) - 1)/(-3(-3x + 2) - 1)) - 1) - 2)^2)^2 - 3(-3(-1cos(2\u03c0((2(-3x + 2) - 1)/(-3(-3x + 2) - 1)) - 1) - 2)^2) - 3, 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": "82.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1e^(-1((-1(3|(-3(2|(2|x + 3| - 1) - 1|) + 4) - 2| + 2) - 2)/(2(3|(-3(2|(2|x + 3| - 1) - 1|) + 4) - 2| + 2) + 1))) + 1 and g(x) = 2(-2sin(3\u03c0(3(-5((-2x + 3)/(-1x + 2))^2 - 5((-2x + 3)/(-1x + 2)) + 4) + 4)) + 1) - 5 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": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 3(1|(-1(-3sin(1\u03c0(-2|((-2x)/(-1x + 3)) - 2| + 1) - 3))^2 + 4(-3sin(1\u03c0(-2|((-2x)/(-1x + 3)) - 2| + 1) - 3)) + 3) - 2| + 2)^2 + 2(1|(-1(-3sin(1\u03c0(-2|((-2x)/(-1x + 3)) - 2| + 1) - 3))^2 + 4(-3sin(1\u03c0(-2|((-2x)/(-1x + 3)) - 2| + 1) - 3)) + 3) - 2| + 2) - 4 and g(x) = 3|(2|(2cos(2\u03c0((1((3x - 2)/(3x + 3)) - 3)/(-3((3x - 2)/(3x + 3)) + 1)) - 1) + 1) + 3| - 1) + 2| + 1 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": "36.7", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (3(-3|(-1((-1((-2(-1x^2 - 5x + 1))/(-2(-1x^2 - 5x + 1) + 1)) + 2)/(-2((-2(-1x^2 - 5x + 1))/(-2(-1x^2 - 5x + 1) + 1)))) - 1) + 1| + 1))/(3(-3|(-1((-1((-2(-1x^2 - 5x + 1))/(-2(-1x^2 - 5x + 1) + 1)) + 2)/(-2((-2(-1x^2 - 5x + 1))/(-2(-1x^2 - 5x + 1) + 1)))) - 1) + 1| + 1)), g(x) = 4(2|(3|(-2|((-3x + 1)/(1x - 2)) - 1| + 1) - 1| + 1) - 2| - 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": "2.6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1(-3e^(-2((-3(-5(-1((-3x + 2)/(-2x - 3))^2 - 3((-3x + 2)/(-2x - 3)) - 4)^2 + 1(-1((-3x + 2)/(-2x - 3))^2 - 3((-3x + 2)/(-2x - 3)) - 4) + 5) - 3)/(3(-5(-1((-3x + 2)/(-2x - 3))^2 - 3((-3x + 2)/(-2x - 3)) - 4)^2 + 1(-1((-3x + 2)/(-2x - 3))^2 - 3((-3x + 2)/(-2x - 3)) - 4) + 5) - 1))) + 2) - 1 and g(x) = 4(-3|(-1(-4((2x + 1)/(-1x + 3)) - 3)^2 - 1(-4((2x + 1)/(-1x + 3)) - 3))| - 3) - 1 from x = -3.2 to x = -1.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9.8", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (2(-3(-1(-3|(1|(-1cos(3\u03c0x + 1) + 3)| - 3) + 1| + 2)^2 - 3(-3|(1|(-1cos(3\u03c0x + 1) + 3)| - 3) + 1| + 2) + 5) + 5))/(-3(-3(-1(-3|(1|(-1cos(3\u03c0x + 1) + 3)| - 3) + 1| + 2)^2 - 3(-3|(1|(-1cos(3\u03c0x + 1) + 3)| - 3) + 1| + 2) + 5) + 5) + 1), g(x) = 1|(4((3(-1((-3x + 3)/(-3x + 2)) + 1) + 1)/(3(-1((-3x + 3)/(-3x + 2)) + 1) + 1)) - 5) - 1|, x = 0.3, 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": "1.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2e^(2(2|(5((3((2((1x - 2)/(1x + 2)) + 3)/(2((1x - 2)/(1x + 2)) - 1)) - 1)/(-2((2((1x - 2)/(1x + 2)) + 3)/(2((1x - 2)/(1x + 2)) - 1)) - 1))^2 + 2) - 2| - 3)) - 1, g(x) = -4(4(3sin(3\u03c0(-5(1|x - 1|) - 1) + 2) - 3) - 2)^2 + 3(4(3sin(3\u03c0(-5(1|x - 1|) - 1) + 2) - 3) - 2) + 5, 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": "60.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 3(-2(-2|(-1((-1(-1x^2 - 1x - 5) - 2)/(-1(-1x^2 - 1x - 5))) + 4) - 3| + 2)^2 - 5(-2|(-1((-1(-1x^2 - 1x - 5) - 2)/(-1(-1x^2 - 1x - 5))) + 4) - 3| + 2) + 5) - 4 and g(x) = (3(2|((3(4(1cos(1\u03c0x + 3) - 2)^2 + 5(1cos(1\u03c0x + 3) - 2) - 5))/(2(4(1cos(1\u03c0x + 3) - 2)^2 + 5(1cos(1\u03c0x + 3) - 2) - 5) - 1)) - 3| - 1) + 2)/(3(2|((3(4(1cos(1\u03c0x + 3) - 2)^2 + 5(1cos(1\u03c0x + 3) - 2) - 5))/(2(4(1cos(1\u03c0x + 3) - 2)^2 + 5(1cos(1\u03c0x + 3) - 2) - 5) - 1)) - 3| - 1) - 1) between the vertical lines x = -4.4 and x = -0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "106.4", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 3|(2((-1(-3(3e^(-2(2x + 3)) + 2)^2 + 2(3e^(-2(2x + 3)) + 2) - 4) - 2)/(3(-3(3e^(-2(2x + 3)) + 2)^2 + 2(3e^(-2(2x + 3)) + 2) - 4) - 2))^2 - 2((-1(-3(3e^(-2(2x + 3)) + 2)^2 + 2(3e^(-2(2x + 3)) + 2) - 4) - 2)/(3(-3(3e^(-2(2x + 3)) + 2)^2 + 2(3e^(-2(2x + 3)) + 2) - 4) - 2)) + 2) - 3| + 2 and g(x) = 3(3(-3e^(-1(-4(-4x + 2)^2 + 1(-4x + 2) + 3)) + 3)^2 - 2(-3e^(-1(-4(-4x + 2)^2 + 1(-4x + 2) + 3)) + 3)) - 4 between the vertical lines x = 0.3 and x = 0.7. 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(5(-4((-1(5(-3sin(1\u03c0x - 1))^2 + 3(-3sin(1\u03c0x - 1)) - 2) - 1)/(-2(5(-3sin(1\u03c0x - 1))^2 + 3(-3sin(1\u03c0x - 1)) - 2) - 3))^2 - 2((-1(5(-3sin(1\u03c0x - 1))^2 + 3(-3sin(1\u03c0x - 1)) - 2) - 1)/(-2(5(-3sin(1\u03c0x - 1))^2 + 3(-3sin(1\u03c0x - 1)) - 2) - 3)) + 5)^2 + 2) + 3)/(-2(5(-4((-1(5(-3sin(1\u03c0x - 1))^2 + 3(-3sin(1\u03c0x - 1)) - 2) - 1)/(-2(5(-3sin(1\u03c0x - 1))^2 + 3(-3sin(1\u03c0x - 1)) - 2) - 3))^2 - 2((-1(5(-3sin(1\u03c0x - 1))^2 + 3(-3sin(1\u03c0x - 1)) - 2) - 1)/(-2(5(-3sin(1\u03c0x - 1))^2 + 3(-3sin(1\u03c0x - 1)) - 2) - 3)) + 5)^2 + 2) - 1), g(x) = 1|(-5((-2(-2|((2x + 1)/(1x)) + 3| - 1) - 2)/(-2(-2|((2x + 1)/(1x)) + 3| - 1) - 3)) + 5)| - 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -3(5((-2((2(-3cos(2\u03c0(-3|x + 1| - 3) - 1) - 1) + 3)/(1(-3cos(2\u03c0(-3|x + 1| - 3) - 1) - 1) + 1)) - 3)/(1((2(-3cos(2\u03c0(-3|x + 1| - 3) - 1) - 1) + 3)/(1(-3cos(2\u03c0(-3|x + 1| - 3) - 1) - 1) + 1)) - 2))^2 + 2((-2((2(-3cos(2\u03c0(-3|x + 1| - 3) - 1) - 1) + 3)/(1(-3cos(2\u03c0(-3|x + 1| - 3) - 1) - 1) + 1)) - 3)/(1((2(-3cos(2\u03c0(-3|x + 1| - 3) - 1) - 1) + 3)/(1(-3cos(2\u03c0(-3|x + 1| - 3) - 1) - 1) + 1)) - 2)) + 2) + 3, g(x) = (-2((-1(-2(-3|(1x + 3) - 3|) - 1) + 2)/(2(-2(-3|(1x + 3) - 3|) - 1) + 2)) - 3)/(-2((-1(-2(-3|(1x + 3) - 3|) - 1) + 2)/(2(-2(-3|(1x + 3) - 3|) - 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": "194.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2((-2(-1(-1(-2|(-1|x| - 2) + 2| - 3)^2 + 1(-2|(-1|x| - 2) + 2| - 3) + 5)^2 - 3(-1(-2|(-1|x| - 2) + 2| - 3)^2 + 1(-2|(-1|x| - 2) + 2| - 3) + 5) - 5) - 3)/(2(-1(-1(-2|(-1|x| - 2) + 2| - 3)^2 + 1(-2|(-1|x| - 2) + 2| - 3) + 5)^2 - 3(-1(-2|(-1|x| - 2) + 2| - 3)^2 + 1(-2|(-1|x| - 2) + 2| - 3) + 5) - 5) - 1))^2 + 4((-2(-1(-1(-2|(-1|x| - 2) + 2| - 3)^2 + 1(-2|(-1|x| - 2) + 2| - 3) + 5)^2 - 3(-1(-2|(-1|x| - 2) + 2| - 3)^2 + 1(-2|(-1|x| - 2) + 2| - 3) + 5) - 5) - 3)/(2(-1(-1(-2|(-1|x| - 2) + 2| - 3)^2 + 1(-2|(-1|x| - 2) + 2| - 3) + 5)^2 - 3(-1(-2|(-1|x| - 2) + 2| - 3)^2 + 1(-2|(-1|x| - 2) + 2| - 3) + 5) - 5) - 1)) + 1 and g(x) = (-2(1((2(-2|(-2x - 1) - 3| - 1) - 1)/(2(-2|(-2x - 1) - 3| - 1) + 3)) - 3))/(2(1((2(-2|(-2x - 1) - 3| - 1) - 1)/(2(-2|(-2x - 1) - 3| - 1) + 3)) - 3) + 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": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-1(-1(3cos(3\u03c0(3|(2((3x - 1)/(-1x + 2)) + 2)|) + 2) + 3) - 5) + 1)/(-1(-1(3cos(3\u03c0(3|(2((3x - 1)/(-1x + 2)) + 2)|) + 2) + 3) - 5) + 3) and g(x) = (-2(1|(1(-3cos(1\u03c0(4x + 5) - 1) + 2)^2 - 3) - 3| - 2) + 2)/(-2(1|(1(-3cos(1\u03c0(4x + 5) - 1) + 2)^2 - 3) - 3| - 2)) from x = -3.0 to 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": "Determine the area of the region enclosed by the graphs of f(x) = -1e^(1(-4(-1((-2(-1|(1x + 3) + 2| + 2))/(3(-1|(1x + 3) + 2| + 2) + 2))^2 + 2((-2(-1|(1x + 3) + 2| + 2))/(3(-1|(1x + 3) + 2| + 2) + 2)) + 1) - 4)) + 1 and g(x) = 1(-3|((-2((3(3x^2 - 4x - 4) - 3)/(-1(3x^2 - 4x - 4) + 3)) - 3)/(-2((3(3x^2 - 4x - 4) - 3)/(-1(3x^2 - 4x - 4) + 3)) - 1)) - 2|) + 1 between the vertical lines x = 0.2 and x = 2.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10.9", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1((3(-1(3|(-3sin(3\u03c0(-1|x + 3| - 2) + 1)) + 1| - 1)^2 + 1(3|(-3sin(3\u03c0(-1|x + 3| - 2) + 1)) + 1| - 1) + 2) + 2)/(-3(-1(3|(-3sin(3\u03c0(-1|x + 3| - 2) + 1)) + 1| - 1)^2 + 1(3|(-3sin(3\u03c0(-1|x + 3| - 2) + 1)) + 1| - 1) + 2) - 3)) + 2, g(x) = -2|(-4((-3(-5(-3x + 3)^2 + 3(-3x + 3) + 2) - 2)/(-1(-5(-3x + 3)^2 + 3(-3x + 3) + 2) - 3)) + 1) - 1|, x = -3.5, 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": "226.4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (1(-1(1((1(-2(2e^(2x) - 1) + 3) - 2)/(-2(-2(2e^(2x) - 1) + 3) - 1)) - 3) - 4) - 1)/(-3(-1(1((1(-2(2e^(2x) - 1) + 3) - 2)/(-2(-2(2e^(2x) - 1) + 3) - 1)) - 3) - 4)) and g(x) = 1((2(5(1(2x + 3)^2 + 4(2x + 3) + 3)) + 2)/(3(5(1(2x + 3)^2 + 4(2x + 3) + 3)) + 1)) + 2 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": "4.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (2((2(3|(-2|(1(4x^2 + 5x + 1)) + 3|) + 2| + 2) + 2)/(-1(3|(-2|(1(4x^2 + 5x + 1)) + 3|) + 2| + 2) + 2)) + 2)/(-1((2(3|(-2|(1(4x^2 + 5x + 1)) + 3|) + 2| + 2) + 2)/(-1(3|(-2|(1(4x^2 + 5x + 1)) + 3|) + 2| + 2) + 2)) + 3) and g(x) = -1sin(3\u03c0((-2((1((-2(1|x + 1| + 3) + 2)/(2(1|x + 1| + 3) + 3)) - 3)/(2((-2(1|x + 1| + 3) + 2)/(2(1|x + 1| + 3) + 3)) - 3)) - 2)/(3((1((-2(1|x + 1| + 3) + 2)/(2(1|x + 1| + 3) + 3)) - 3)/(2((-2(1|x + 1| + 3) + 2)/(2(1|x + 1| + 3) + 3)) - 3)) - 2)) - 2) - 1 between the vertical lines x = -0.3 and x = 0.8. 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": "Calculate the area enclosed between the functions f(x) = 4(-1((-2(-5(-1(5x + 1) + 4) - 4) + 1)/(-3(-5(-1(5x + 1) + 4) - 4) + 1))^2 + 5((-2(-5(-1(5x + 1) + 4) - 4) + 1)/(-3(-5(-1(5x + 1) + 4) - 4) + 1)) + 3) - 2 and g(x) = 5(4(2|(5(-2|x - 3| + 3)^2 - 5(-2|x - 3| + 3) - 5) - 3| + 1) - 4) - 2 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": "1.9", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 5(2sin(2\u03c0(4(2|(3|(1|x - 1| - 2) - 3| - 2)| + 1)^2 - 2) - 2) + 2) - 5 and g(x) = (1(1(2(3|(-1|x + 1| + 3) + 2|))^2 - 3) + 3)/(3(1(2(3|(-1|x + 1| + 3) + 2|))^2 - 3) + 2) 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": "0.7", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1(5(4((2(-1|(3x - 3) + 2| - 1) + 2)/(-3(-1|(3x - 3) + 2| - 1) + 1)) + 2) + 3) + 1 and g(x) = 2cos(1\u03c0(5(2|(3(-4x^2 + 2x + 3)^2 + 5(-4x^2 + 2x + 3) + 3) - 1| + 2)^2 - 4(2|(3(-4x^2 + 2x + 3)^2 + 5(-4x^2 + 2x + 3) + 3) - 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1(-1|(2|(2((-1(1|x - 3| - 1) - 1)/(-2(1|x - 3| - 1) - 3)) + 4) - 3| - 1) - 1| + 2)^2 - 4(-1|(2|(2((-1(1|x - 3| - 1) - 1)/(-2(1|x - 3| - 1) - 3)) + 4) - 3| - 1) - 1| + 2) + 5, g(x) = 2cos(3\u03c0(-1|((-1(5(2|x - 2| - 1)^2 + 5(2|x - 2| - 1) - 4) - 2)/(-2(5(2|x - 2| - 1)^2 + 5(2|x - 2| - 1) - 4) - 1)) - 3| - 3) + 2) + 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) = -5((3(3(-1((1(-3|x + 1| - 3) + 3)/(2(-3|x + 1| - 3) + 3)) - 4)^2 - 1(-1((1(-3|x + 1| - 3) + 3)/(2(-3|x + 1| - 3) + 3)) - 4) - 4) - 2)/(1(3(-1((1(-3|x + 1| - 3) + 3)/(2(-3|x + 1| - 3) + 3)) - 4)^2 - 1(-1((1(-3|x + 1| - 3) + 3)/(2(-3|x + 1| - 3) + 3)) - 4) - 4) + 3)) and g(x) = -4(2(2cos(1\u03c0((1(2x + 1) + 2)/(-1(2x + 1) + 2)) - 1) + 3) - 3)^2 + 3(2(2cos(1\u03c0((1(2x + 1) + 2)/(-1(2x + 1) + 2)) - 1) + 3) - 3) + 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": "5.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1e^(-1((1(5(5(3|(-4x + 2)| - 1) - 3) + 2) + 1)/(2(5(5(3|(-4x + 2)| - 1) - 3) + 2) + 3))) and g(x) = (1(-3|(-1(-5(-1x - 1) + 1)^2 + 3) - 3| + 2) + 2)/(-1(-3|(-1(-5(-1x - 1) + 1)^2 + 3) - 3| + 2) - 2) 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2(2|(2sin(1\u03c0(-4(-3((-3x - 2)/(-1x + 2)) - 5)^2 + 3(-3((-3x - 2)/(-1x + 2)) - 5) - 1) - 1) + 2) - 1|) - 5 and g(x) = 1((-2(3cos(2\u03c0(1|((-2x + 1)/(-3x - 3)) - 1| - 1)) - 2) + 2)/(-1(3cos(2\u03c0(1|((-2x + 1)/(-3x - 3)) - 1| - 1)) - 2) + 3))^2 - 5((-2(3cos(2\u03c0(1|((-2x + 1)/(-3x - 3)) - 1| - 1)) - 2) + 2)/(-1(3cos(2\u03c0(1|((-2x + 1)/(-3x - 3)) - 1| - 1)) - 2) + 3)) from x = 3.1 to x = 3.2. 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) = 2((2(1(1(5(-1|x - 2| - 1)^2 + 3(-1|x - 2| - 1) - 3)^2 - 5(5(-1|x - 2| - 1)^2 + 3(-1|x - 2| - 1) - 3) + 4)^2 - 5(1(5(-1|x - 2| - 1)^2 + 3(-1|x - 2| - 1) - 3)^2 - 5(5(-1|x - 2| - 1)^2 + 3(-1|x - 2| - 1) - 3) + 4) - 5))/(-1(1(1(5(-1|x - 2| - 1)^2 + 3(-1|x - 2| - 1) - 3)^2 - 5(5(-1|x - 2| - 1)^2 + 3(-1|x - 2| - 1) - 3) + 4)^2 - 5(1(5(-1|x - 2| - 1)^2 + 3(-1|x - 2| - 1) - 3)^2 - 5(5(-1|x - 2| - 1)^2 + 3(-1|x - 2| - 1) - 3) + 4) - 5) - 3))^2 + 4((2(1(1(5(-1|x - 2| - 1)^2 + 3(-1|x - 2| - 1) - 3)^2 - 5(5(-1|x - 2| - 1)^2 + 3(-1|x - 2| - 1) - 3) + 4)^2 - 5(1(5(-1|x - 2| - 1)^2 + 3(-1|x - 2| - 1) - 3)^2 - 5(5(-1|x - 2| - 1)^2 + 3(-1|x - 2| - 1) - 3) + 4) - 5))/(-1(1(1(5(-1|x - 2| - 1)^2 + 3(-1|x - 2| - 1) - 3)^2 - 5(5(-1|x - 2| - 1)^2 + 3(-1|x - 2| - 1) - 3) + 4)^2 - 5(1(5(-1|x - 2| - 1)^2 + 3(-1|x - 2| - 1) - 3)^2 - 5(5(-1|x - 2| - 1)^2 + 3(-1|x - 2| - 1) - 3) + 4) - 5) - 3)) + 2, g(x) = (-3(1|(3((2(1|x + 3|))/(3(1|x + 3|) - 1)) - 4) - 1| - 2) + 2)/(2(1|(3((2(1|x + 3|))/(3(1|x + 3|) - 1)) - 4) - 1| - 2) - 3), 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": "Calculate the area enclosed between the functions f(x) = 2sin(2\u03c0(2|(5(-2|(1|(1x^2 + 1x + 2) + 1| - 1) + 2| - 1)^2 + 5(-2|(1|(1x^2 + 1x + 2) + 1| - 1) + 2| - 1) - 2) + 2| - 1) + 1) - 1 and g(x) = 2cos(2\u03c0((-2(1(-2((1x + 3)/(2x - 3)) - 2) - 4))/(-2(1(-2((1x + 3)/(2x - 3)) - 2) - 4))) - 3) from x = -4.7 to x = -4.6000000000000005. 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((-1(4(-1(-3x + 4)^2 - 5(-3x + 4) - 5) + 2) - 3)/(3(4(-1(-3x + 4)^2 - 5(-3x + 4) - 5) + 2) - 2)) - 3) + 2| + 1, g(x) = -4((-3(5(-1(1|x - 2|)^2 + 4)^2 + 3(-1(1|x - 2|)^2 + 4) + 5) + 3)/(3(5(-1(1|x - 2|)^2 + 4)^2 + 3(-1(1|x - 2|)^2 + 4) + 5))) - 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1(5((-1(3((1(-5x^2 + 3x + 5) + 3)/(3(-5x^2 + 3x + 5) + 3))) + 1)/(-3(3((1(-5x^2 + 3x + 5) + 3)/(3(-5x^2 + 3x + 5) + 3))) - 2)) + 3) - 4, g(x) = 1sin(3\u03c0(-1|(-3|(2|(1|x - 1| + 3) + 1| + 2) - 3| - 1) - 1| + 3)) + 3, x = -1.0, 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": "Calculate the area enclosed between the functions f(x) = (1(5(-1sin(1\u03c0(3(5(2|x + 3| + 2)^2 + 3(2|x + 3| + 2) + 3) + 3) + 3) - 2)) - 1)/(-3(5(-1sin(1\u03c0(3(5(2|x + 3| + 2)^2 + 3(2|x + 3| + 2) + 3) + 3) + 3) - 2)) - 2) and g(x) = 1(-2cos(2\u03c0(1(-2|((-2x - 1)/(2x)) - 2| + 2) - 3) + 2) - 1)^2 - 3(-2cos(2\u03c0(1(-2|((-2x - 1)/(2x)) - 2| + 2) - 3) + 2) - 1) + 1 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": "0.7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-3(2(-3|(1|(-3(1x - 5) + 5)| + 2) + 3| + 2)^2 - 4(-3|(1|(-3(1x - 5) + 5)| + 2) + 3| + 2) - 4))/(-1(2(-3|(1|(-3(1x - 5) + 5)| + 2) + 3| + 2)^2 - 4(-3|(1|(-3(1x - 5) + 5)| + 2) + 3| + 2) - 4) + 2) and g(x) = (-1(-1(3(3(1sin(3\u03c0x + 3) + 2)^2 - 5(1sin(3\u03c0x + 3) + 2) - 5)^2 + 3(3(1sin(3\u03c0x + 3) + 2)^2 - 5(1sin(3\u03c0x + 3) + 2) - 5) - 4) + 3) + 1)/(2(-1(3(3(1sin(3\u03c0x + 3) + 2)^2 - 5(1sin(3\u03c0x + 3) + 2) - 5)^2 + 3(3(1sin(3\u03c0x + 3) + 2)^2 - 5(1sin(3\u03c0x + 3) + 2) - 5) - 4) + 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": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 4(-1cos(3\u03c0(-5((2(5(-2|x + 3| + 2) - 3) + 1)/(-2(5(-2|x + 3| + 2) - 3) + 3)) + 2) + 1) - 1)^2 + 1(-1cos(3\u03c0(-5((2(5(-2|x + 3| + 2) - 3) + 1)/(-2(5(-2|x + 3| + 2) - 3) + 3)) + 2) + 1) - 1) - 3 and g(x) = (3(-1|((-1(-2(-1x - 3)^2 + 5(-1x - 3) - 4) + 2)/(2(-2(-1x - 3)^2 + 5(-1x - 3) - 4) - 3)) + 2| - 3) - 1)/(1(-1|((-1(-2(-1x - 3)^2 + 5(-1x - 3) - 4) + 2)/(2(-2(-1x - 3)^2 + 5(-1x - 3) - 4) - 3)) + 2| - 3) - 2) 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2((-3(3|(1(-5((-2x + 1)/(-2x - 1))^2 - 5((-2x + 1)/(-2x - 1)) + 3)^2 + 5(-5((-2x + 1)/(-2x - 1))^2 - 5((-2x + 1)/(-2x - 1)) + 3) + 4) - 1| - 2) - 1)/(-3(3|(1(-5((-2x + 1)/(-2x - 1))^2 - 5((-2x + 1)/(-2x - 1)) + 3)^2 + 5(-5((-2x + 1)/(-2x - 1))^2 - 5((-2x + 1)/(-2x - 1)) + 3) + 4) - 1| - 2) - 3)) - 1 and g(x) = -2|(-2|((-2(1cos(2\u03c0((2x + 1)/(-2x - 1)) - 2) + 1) - 1)/(3(1cos(2\u03c0((2x + 1)/(-2x - 1)) - 2) + 1) + 3))| - 3)| 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": "7.4", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-2((3((-3(-3sin(2\u03c0(-1(-2|x - 2| + 1) - 2) - 2) - 3) + 3)/(3(-3sin(2\u03c0(-1(-2|x - 2| + 1) - 2) - 2) - 3) + 1)) + 3)/(1((-3(-3sin(2\u03c0(-1(-2|x - 2| + 1) - 2) - 2) - 3) + 3)/(3(-3sin(2\u03c0(-1(-2|x - 2| + 1) - 2) - 2) - 3) + 1)) + 3)))/(1((3((-3(-3sin(2\u03c0(-1(-2|x - 2| + 1) - 2) - 2) - 3) + 3)/(3(-3sin(2\u03c0(-1(-2|x - 2| + 1) - 2) - 2) - 3) + 1)) + 3)/(1((-3(-3sin(2\u03c0(-1(-2|x - 2| + 1) - 2) - 2) - 3) + 3)/(3(-3sin(2\u03c0(-1(-2|x - 2| + 1) - 2) - 2) - 3) + 1)) + 3)) + 3), g(x) = 1(-3|((1((-2(-4x^2 + 1))/(1(-4x^2 + 1) + 1)) + 2)/(1((-2(-4x^2 + 1))/(1(-4x^2 + 1) + 1)) + 2)) + 1| + 3) + 4, 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-3(-4((3(1cos(1\u03c0((2(1x - 4) + 1)/(1(1x - 4) + 1)) - 1) + 3) - 2)/(1(1cos(1\u03c0((2(1x - 4) + 1)/(1(1x - 4) + 1)) - 1) + 3) + 2)) - 5))/(-2(-4((3(1cos(1\u03c0((2(1x - 4) + 1)/(1(1x - 4) + 1)) - 1) + 3) - 2)/(1(1cos(1\u03c0((2(1x - 4) + 1)/(1(1x - 4) + 1)) - 1) + 3) + 2)) - 5) - 3) and g(x) = 1(-2|(-1cos(3\u03c0(-1(3|x| - 3)^2 - 5(3|x| - 3) + 5)) + 1) - 3| + 2) + 4 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3|((-2(2|((-2(-2e^(-1(3x^2 + 5x - 3)) - 1))/(-1(-2e^(-1(3x^2 + 5x - 3)) - 1) - 1))| - 2) - 1)/(1(2|((-2(-2e^(-1(3x^2 + 5x - 3)) - 1))/(-1(-2e^(-1(3x^2 + 5x - 3)) - 1) - 1))| - 2) - 2)) - 2| - 1, g(x) = 1e^(2(2(2(-1|(1x^2 + 4x + 1) - 3| + 3)^2 + 2(-1|(1x^2 + 4x + 1) - 3| + 3) + 1) + 2)), 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": "32.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (1(4(1(-2|(1(-2e^(-2x) - 3) + 1) + 2| + 1) + 3) + 3))/(-1(4(1(-2|(1(-2e^(-2x) - 3) + 1) + 2| + 1) + 3) + 3) + 2), g(x) = -1(1cos(1\u03c0(-5(2((1x + 2)/(3x + 2)))^2 - 5(2((1x + 2)/(3x + 2))) - 2) + 3) + 2)^2 + 5(1cos(1\u03c0(-5(2((1x + 2)/(3x + 2)))^2 - 5(2((1x + 2)/(3x + 2))) - 2) + 3) + 2) - 5, 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1(-1|(1sin(2\u03c0((2(3(-5x)^2 - 2(-5x)) - 2)/(-1(3(-5x)^2 - 2(-5x)) + 2)) + 2) + 1) - 3| - 2) + 1 and g(x) = 2cos(3\u03c0((-2(3(-2|((-2x + 3)/(3x)) + 3| + 3) - 2) + 3)/(-1(3(-2|((-2x + 3)/(3x)) + 3| + 3) - 2))) + 1) - 3 between the vertical lines x = 0.2 and x = 0.30000000000000004. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "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(1|((-2(-2((1x - 2)/(-2x - 1)) - 5) - 1)/(1(-2((1x - 2)/(-2x - 1)) - 5))) - 1| + 1) + 2) + 4 and g(x) = -2|(5(-1e^(-1(-1(-5x^2 + 3x)^2 - 3(-5x^2 + 3x) + 5)) - 1)^2 - 2(-1e^(-1(-1(-5x^2 + 3x)^2 - 3(-5x^2 + 3x) + 5)) - 1)) - 3| + 1 between the vertical lines x = 0.2 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": "Determine the area of the region enclosed by the graphs of f(x) = -2(2((-1(-2|(-3|(-1|x + 3| + 1) + 3| + 3) + 1| + 3) + 1)/(-1(-2|(-3|(-1|x + 3| + 1) + 3| + 3) + 1| + 3) - 1))^2 - 2((-1(-2|(-3|(-1|x + 3| + 1) + 3| + 3) + 1| + 3) + 1)/(-1(-2|(-3|(-1|x + 3| + 1) + 3| + 3) + 1| + 3) - 1)) - 4)^2 - 5(2((-1(-2|(-3|(-1|x + 3| + 1) + 3| + 3) + 1| + 3) + 1)/(-1(-2|(-3|(-1|x + 3| + 1) + 3| + 3) + 1| + 3) - 1))^2 - 2((-1(-2|(-3|(-1|x + 3| + 1) + 3| + 3) + 1| + 3) + 1)/(-1(-2|(-3|(-1|x + 3| + 1) + 3| + 3) + 1| + 3) - 1)) - 4) - 3 and g(x) = -1(-5(-2sin(3\u03c0((3(-1|x + 3| + 3) - 1)/(2(-1|x + 3| + 3) - 1)) + 2) - 1)^2 - 4(-2sin(3\u03c0((3(-1|x + 3| + 3) - 1)/(2(-1|x + 3| + 3) - 1)) + 2) - 1) + 1)^2 + 5(-5(-2sin(3\u03c0((3(-1|x + 3| + 3) - 1)/(2(-1|x + 3| + 3) - 1)) + 2) - 1)^2 - 4(-2sin(3\u03c0((3(-1|x + 3| + 3) - 1)/(2(-1|x + 3| + 3) - 1)) + 2) - 1) + 1) + 2 between the vertical lines x = -0.4 and x = -0.30000000000000004. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "27.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1(-4(-3|((1(4(-2|x| - 3) + 3) + 1)/(-1(4(-2|x| - 3) + 3) - 3)) + 2| + 2)^2 - 1(-3|((1(4(-2|x| - 3) + 3) + 1)/(-1(4(-2|x| - 3) + 3) - 3)) + 2| + 2) + 1) + 3 and g(x) = 2(4(3e^(-2(-3(1x^2 - 4x)^2 + 5(1x^2 - 4x))) - 3) - 4) + 2 between the vertical lines x = 4.0 and x = 4.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2(2|((-2(3((2((-3x + 2)/(-3x - 2)) + 3)/(-1((-3x + 2)/(-3x - 2)) + 2)) - 3) + 3)/(-3(3((2((-3x + 2)/(-3x - 2)) + 3)/(-1((-3x + 2)/(-3x - 2)) + 2)) - 3) + 1)) - 1| + 1) - 5 and g(x) = (3(-2|(-2(4(-1cos(2\u03c0x - 3))^2 + 1(-1cos(2\u03c0x - 3)) - 4)^2 + 2(4(-1cos(2\u03c0x - 3))^2 + 1(-1cos(2\u03c0x - 3)) - 4) - 5) + 1| - 3) + 1)/(2(-2|(-2(4(-1cos(2\u03c0x - 3))^2 + 1(-1cos(2\u03c0x - 3)) - 4)^2 + 2(4(-1cos(2\u03c0x - 3))^2 + 1(-1cos(2\u03c0x - 3)) - 4) - 5) + 1| - 3) - 1) 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": "30.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (2(-3cos(3\u03c0(-2|(-2|(4(1|x + 2| + 2)) - 1| - 1) + 3|) + 1) - 1) - 3)/(1(-3cos(3\u03c0(-2|(-2|(4(1|x + 2| + 2)) - 1| - 1) + 3|) + 1) - 1) - 3) and g(x) = -5(1e^(-1(-4(-2(4x^2 - 5x + 5)^2 - 2(4x^2 - 5x + 5) - 2) - 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|((2(-1(-3cos(1\u03c0(3|(-4x - 1) - 2| + 1) - 3) - 3) + 1) - 1)/(-2(-1(-3cos(1\u03c0(3|(-4x - 1) - 2| + 1) - 3) - 3) + 1))) + 3| + 2 and g(x) = (1(1|(-5(2|((-1x + 3)/(-2x - 3)) + 2| + 1) - 2) - 3| - 2) - 3)/(-2(1|(-5(2|((-1x + 3)/(-2x - 3)) + 2| + 1) - 2) - 3| - 2) + 3) from x = 2.2 to x = 2.3. 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) = -3sin(3\u03c0(1|(-1(1(4(-4x^2 - 2x - 3) + 2)^2 - 5(4(-4x^2 - 2x - 3) + 2) - 2) - 5)| + 3) + 3) + 1 and g(x) = (1(-2(-3|(1cos(3\u03c0(-1|x - 2| + 3) + 3) + 2) - 1|) - 4) - 2)/(1(-2(-3|(1cos(3\u03c0(-1|x - 2| + 3) + 3) + 2) - 1|) - 4)) 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": "Find the area of the region bounded by the curves f(x) = -2|(-1(5(3((3(3x + 5) + 2)/(3(3x + 5) + 1))^2 + 5((3(3x + 5) + 2)/(3(3x + 5) + 1)) - 1) - 1) + 5) + 1| - 1, g(x) = -2|(2|((-2(-1(-2cos(3\u03c0x) + 1)^2 - 4))/(-1(-1(-2cos(3\u03c0x) + 1)^2 - 4) - 2))|) + 3| - 1, 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": "2.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3|(4((-3(3sin(1\u03c0(-3(1|x + 3| + 1)^2 - 2(1|x + 3| + 1) - 2))))/(-2(3sin(1\u03c0(-3(1|x + 3| + 1)^2 - 2(1|x + 3| + 1) - 2))) + 1))^2 + 1((-3(3sin(1\u03c0(-3(1|x + 3| + 1)^2 - 2(1|x + 3| + 1) - 2))))/(-2(3sin(1\u03c0(-3(1|x + 3| + 1)^2 - 2(1|x + 3| + 1) - 2))) + 1)) + 3) - 2| and g(x) = -5((2(-1|(-2((3x - 2)/(2x + 2)) - 2) - 3| - 2) - 3)/(-1(-1|(-2((3x - 2)/(2x + 2)) - 2) - 3| - 2)))^2 - 3((2(-1|(-2((3x - 2)/(2x + 2)) - 2) - 3| - 2) - 3)/(-1(-1|(-2((3x - 2)/(2x + 2)) - 2) - 3| - 2))) - 2 between the vertical lines x = 4.2 and x = 4.3. 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": "Find the area of the region bounded by the curves f(x) = 1((-1((1(2|((1((1x)/(3x + 2)) + 1)/(3((1x)/(3x + 2)) - 2)) - 1|))/(1(2|((1((1x)/(3x + 2)) + 1)/(3((1x)/(3x + 2)) - 2)) - 1|) + 3)) + 3)/(-1((1(2|((1((1x)/(3x + 2)) + 1)/(3((1x)/(3x + 2)) - 2)) - 1|))/(1(2|((1((1x)/(3x + 2)) + 1)/(3((1x)/(3x + 2)) - 2)) - 1|) + 3)) + 2))^2 - 2((-1((1(2|((1((1x)/(3x + 2)) + 1)/(3((1x)/(3x + 2)) - 2)) - 1|))/(1(2|((1((1x)/(3x + 2)) + 1)/(3((1x)/(3x + 2)) - 2)) - 1|) + 3)) + 3)/(-1((1(2|((1((1x)/(3x + 2)) + 1)/(3((1x)/(3x + 2)) - 2)) - 1|))/(1(2|((1((1x)/(3x + 2)) + 1)/(3((1x)/(3x + 2)) - 2)) - 1|) + 3)) + 2)), g(x) = (-1((1(-5(3|((2x - 3)/(-1x - 2)) - 2|)^2 + 2) - 1)/(1(-5(3|((2x - 3)/(-1x - 2)) - 2|)^2 + 2) - 3)))/(-1((1(-5(3|((2x - 3)/(-1x - 2)) - 2|)^2 + 2) - 1)/(1(-5(3|((2x - 3)/(-1x - 2)) - 2|)^2 + 2) - 3)) + 2), 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2(-1(-2((-3(2(3x) - 2) - 2)/(2(2(3x) - 2) + 2))^2 + 5((-3(2(3x) - 2) - 2)/(2(2(3x) - 2) + 2)) + 4)^2 + 3(-2((-3(2(3x) - 2) - 2)/(2(2(3x) - 2) + 2))^2 + 5((-3(2(3x) - 2) - 2)/(2(2(3x) - 2) + 2)) + 4) - 1) + 2 and g(x) = (1(2(1cos(1\u03c0(2|(5x + 4) - 2| - 3) - 3) - 2)^2 - 5(1cos(1\u03c0(2|(5x + 4) - 2| - 3) - 3) - 2) - 4) - 2)/(3(2(1cos(1\u03c0(2|(5x + 4) - 2| - 3) - 3) - 2)^2 - 5(1cos(1\u03c0(2|(5x + 4) - 2| - 3) - 3) - 2) - 4) - 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": "1.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 3sin(2\u03c0(3|(1(3(-1(3|x + 1| - 2)^2 - 4(3|x + 1| - 2) + 3) - 4)^2 + 5(3(-1(3|x + 1| - 2)^2 - 4(3|x + 1| - 2) + 3) - 4) + 1) - 2| + 3) - 3) - 1 and g(x) = 3sin(1\u03c0(2((-1(-4(4x^2 + 3x - 3) + 4) - 3)/(-1(-4(4x^2 + 3x - 3) + 4) - 3)) + 1) + 1) between the vertical lines x = -2.5 and 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) = 2|(2sin(2\u03c0((2(-2|(-5((2x - 2)/(2x + 3)) - 2) + 2| - 2) - 2)/(-2(-2|(-5((2x - 2)/(2x + 3)) - 2) + 2| - 2) - 1)) - 2) - 2)| + 2, g(x) = (1(3|(3|((2(-2|x - 3| - 2) + 2)/(-1(-2|x - 3| - 2) - 3)) + 2| - 3)| - 2) - 2)/(-1(3|(3|((2(-2|x - 3| - 2) + 2)/(-1(-2|x - 3| - 2) - 3)) + 2| - 3)| - 2) - 1), x = 0.1, 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": "43.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 3cos(1\u03c0(3|(-1((-1(2(-4x - 2) + 2) + 1)/(1(2(-4x - 2) + 2) - 3)) + 2) + 3| - 1) - 3) + 2 and g(x) = 1|(3|(-2(4(-2|x + 1| + 2)^2 + 5(-2|x + 1| + 2) - 1)^2 - 5(4(-2|x + 1| + 2)^2 + 5(-2|x + 1| + 2) - 1) - 4) + 2| - 2) + 3| - 1 between the vertical lines x = -2.5 and x = -2.2. 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": "Calculate the area enclosed between the functions f(x) = (-1(3((-3(3|(4(3sin(1\u03c0x + 3) - 2) - 3) + 3| + 1))/(3(3|(4(3sin(1\u03c0x + 3) - 2) - 3) + 3| + 1) - 1))^2 - 5((-3(3|(4(3sin(1\u03c0x + 3) - 2) - 3) + 3| + 1))/(3(3|(4(3sin(1\u03c0x + 3) - 2) - 3) + 3| + 1) - 1)) + 1) - 2)/(2(3((-3(3|(4(3sin(1\u03c0x + 3) - 2) - 3) + 3| + 1))/(3(3|(4(3sin(1\u03c0x + 3) - 2) - 3) + 3| + 1) - 1))^2 - 5((-3(3|(4(3sin(1\u03c0x + 3) - 2) - 3) + 3| + 1))/(3(3|(4(3sin(1\u03c0x + 3) - 2) - 3) + 3| + 1) - 1)) + 1) + 1) and g(x) = (1(1|(3(5((-1x + 3)/(-3x + 1))^2 - 5((-1x + 3)/(-3x + 1)))^2 - 2(5((-1x + 3)/(-3x + 1))^2 - 5((-1x + 3)/(-3x + 1))) - 5)|) - 3)/(3(1|(3(5((-1x + 3)/(-3x + 1))^2 - 5((-1x + 3)/(-3x + 1)))^2 - 2(5((-1x + 3)/(-3x + 1))^2 - 5((-1x + 3)/(-3x + 1))) - 5)|) + 2) from x = -0.6 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": "Determine the area of the region enclosed by the graphs of f(x) = 1sin(2\u03c0(2|(1|((1(-2(2x - 4) + 3) - 1)/(2(-2(2x - 4) + 3) + 2)) + 1| - 1) - 2| - 3) - 2) + 1 and g(x) = -3cos(2\u03c0(3(-3(3|(1x - 1)| + 2) + 5)) + 1) between the vertical lines x = 3.7 and 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": "Find the area of the region bounded by the curves f(x) = 1(4((2(-2|(1|((2x + 2)/(-1x + 3))|)| - 3) - 2)/(-3(-2|(1|((2x + 2)/(-1x + 3))|)| - 3) + 2)) + 2)^2 - 4(4((2(-2|(1|((2x + 2)/(-1x + 3))|)| - 3) - 2)/(-3(-2|(1|((2x + 2)/(-1x + 3))|)| - 3) + 2)) + 2) + 2, g(x) = 1|(-1(1((-2(2|x + 3|) + 3)/(2(2|x + 3|) - 1)) - 4)) - 3| + 1, x = -3.1, 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": "Calculate the area enclosed between the functions f(x) = -4(-2|(-2sin(2\u03c0(3(3(-4x^2 + 4x - 2)^2 + 1(-4x^2 + 4x - 2) + 5) - 3)) - 2) + 1|) - 4 and g(x) = (-3(1((1(-2|(2x^2 + 1) - 1|) + 1)/(-2(-2|(2x^2 + 1) - 1|) - 2)) - 2) + 1)/(3(1((1(-2|(2x^2 + 1) - 1|) + 1)/(-2(-2|(2x^2 + 1) - 1|) - 2)) - 2) + 2) from x = 3.5 to x = 3.6. 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|(5((2(-1sin(2\u03c0(2|((1x + 3)/(-2x - 1)) + 2|) + 3) - 3))/(-3(-1sin(2\u03c0(2|((1x + 3)/(-2x - 1)) + 2|) + 3) - 3) - 1)) + 5) + 3| + 1 and g(x) = -5(-4(3(-3|(-1x + 4) - 2|) + 1)^2 - 4(3(-3|(-1x + 4) - 2|) + 1) - 1)^2 + 5(-4(3(-3|(-1x + 4) - 2|) + 1)^2 - 4(3(-3|(-1x + 4) - 2|) + 1) - 1) + 2 from x = 1.9 to x = 2.1. 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) = -4(2(-3sin(3\u03c0(-2|(1|((-1x)/(-1x + 2))| - 2) - 2| - 1)) - 1)^2 + 1(-3sin(3\u03c0(-2|(1|((-1x)/(-1x + 2))| - 2) - 2| - 1)) - 1) - 3) + 4 and g(x) = (1(-2|(3|(-3|(1e^(-1x) - 3)| + 1) + 1| + 1)| - 3) + 1)/(-2(-2|(3|(-3|(1e^(-1x) - 3)| + 1) + 1| + 1)| - 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": "3.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2|(3sin(1\u03c0(-2(1(3(-2x^2 - 1x - 3) + 2) + 2)^2 - 4(1(3(-2x^2 - 1x - 3) + 2) + 2) - 4) - 3)) + 3| + 3, g(x) = (1(-2cos(3\u03c0((2((-1(1x^2 - 4x) - 3)/(1(1x^2 - 4x) + 1)) - 1)/(-2((-1(1x^2 - 4x) - 3)/(1(1x^2 - 4x) + 1)) - 3)) - 2) - 1) - 3)/(-3(-2cos(3\u03c0((2((-1(1x^2 - 4x) - 3)/(1(1x^2 - 4x) + 1)) - 1)/(-2((-1(1x^2 - 4x) - 3)/(1(1x^2 - 4x) + 1)) - 3)) - 2) - 1) - 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": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 4((2(-4(1|(-3((-3x + 2)/(1x + 2))^2 - 3((-3x + 2)/(1x + 2)) - 4) - 1| + 1)^2 - 4(1|(-3((-3x + 2)/(1x + 2))^2 - 3((-3x + 2)/(1x + 2)) - 4) - 1| + 1)) + 2)/(3(-4(1|(-3((-3x + 2)/(1x + 2))^2 - 3((-3x + 2)/(1x + 2)) - 4) - 1| + 1)^2 - 4(1|(-3((-3x + 2)/(1x + 2))^2 - 3((-3x + 2)/(1x + 2)) - 4) - 1| + 1))))^2 - 4((2(-4(1|(-3((-3x + 2)/(1x + 2))^2 - 3((-3x + 2)/(1x + 2)) - 4) - 1| + 1)^2 - 4(1|(-3((-3x + 2)/(1x + 2))^2 - 3((-3x + 2)/(1x + 2)) - 4) - 1| + 1)) + 2)/(3(-4(1|(-3((-3x + 2)/(1x + 2))^2 - 3((-3x + 2)/(1x + 2)) - 4) - 1| + 1)^2 - 4(1|(-3((-3x + 2)/(1x + 2))^2 - 3((-3x + 2)/(1x + 2)) - 4) - 1| + 1)))) - 2, g(x) = 5(-4(-1|((1(4x - 3) - 3)/(-1(4x - 3) + 2)) + 1| + 1) + 2) - 3, x = 0.8, 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": "227.5", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-3(2(1(-3cos(2\u03c0(1|(-1x^2 + 5x - 5) + 1|) - 1) - 1) - 2)^2 + 3(1(-3cos(2\u03c0(1|(-1x^2 + 5x - 5) + 1|) - 1) - 1) - 2) - 5) + 1)/(-2(2(1(-3cos(2\u03c0(1|(-1x^2 + 5x - 5) + 1|) - 1) - 1) - 2)^2 + 3(1(-3cos(2\u03c0(1|(-1x^2 + 5x - 5) + 1|) - 1) - 1) - 2) - 5) + 3), g(x) = 4(5(3|(-3|(1x^2 - 2x - 1) - 1|) + 3| - 2) + 4)^2 - 3(5(3|(-3|(1x^2 - 2x - 1) - 1|) + 3| - 2) + 4) + 1, x = 3.0, 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": "14.4", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1(3((3(-5(-4(-3x^2 - 4x) - 4)^2 + 3(-4(-3x^2 - 4x) - 4) + 3) - 3)/(2(-5(-4(-3x^2 - 4x) - 4)^2 + 3(-4(-3x^2 - 4x) - 4) + 3) + 1)) + 4) + 1, g(x) = -2|(2|((-1(-5(-4x^2 - 1x - 5)^2 + 3(-4x^2 - 1x - 5) - 4) + 2)/(-1(-5(-4x^2 - 1x - 5)^2 + 3(-4x^2 - 1x - 5) - 4) - 2)) - 3| + 1)| + 1, 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": "1.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1(-1|(-1((2(1((1x + 2)/(2x - 3))^2 - 3((1x + 2)/(2x - 3)) + 1) + 3)/(1(1((1x + 2)/(2x - 3))^2 - 3((1x + 2)/(2x - 3)) + 1) + 1)) - 5)| + 2)^2 - 5(-1|(-1((2(1((1x + 2)/(2x - 3))^2 - 3((1x + 2)/(2x - 3)) + 1) + 3)/(1(1((1x + 2)/(2x - 3))^2 - 3((1x + 2)/(2x - 3)) + 1) + 1)) - 5)| + 2) and g(x) = 2sin(1\u03c0(-3(1((2(-1|x| - 2) + 1)/(-2(-1|x| - 2) - 1))^2 + 4((2(-1|x| - 2) + 1)/(-2(-1|x| - 2) - 1)) - 5) + 3) + 3) + 2 from x = 3.7 to x = 4.3. 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": "Find the area of the region bounded by the curves f(x) = (2((3(1|((1(-5(-3|x + 2| + 2) + 3) - 3)/(-2(-5(-3|x + 2| + 2) + 3) + 1)) - 1| - 2))/(-1(1|((1(-5(-3|x + 2| + 2) + 3) - 3)/(-2(-5(-3|x + 2| + 2) + 3) + 1)) - 1| - 2) + 2)) - 3)/(-3((3(1|((1(-5(-3|x + 2| + 2) + 3) - 3)/(-2(-5(-3|x + 2| + 2) + 3) + 1)) - 1| - 2))/(-1(1|((1(-5(-3|x + 2| + 2) + 3) - 3)/(-2(-5(-3|x + 2| + 2) + 3) + 1)) - 1| - 2) + 2)) + 2), g(x) = -1(3sin(1\u03c0((1((3((-1x - 1)/(1x)) - 2)/(-2((-1x - 1)/(1x)) - 3)) + 2)/(1((3((-1x - 1)/(1x)) - 2)/(-2((-1x - 1)/(1x)) - 3)) - 2)))) + 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": "3.5", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2|((3(1|(-5(2cos(3\u03c0(-3|x - 3| + 2)) + 1) + 5)| - 2))/(-2(1|(-5(2cos(3\u03c0(-3|x - 3| + 2)) + 1) + 5)| - 2) - 2)) - 1| - 1, g(x) = 1(-3(-1|(-5(-1x^2 + 3x - 1) + 3) + 2| + 3) + 3)^2 - 4(-3(-1|(-5(-1x^2 + 3x - 1) + 3) + 2| + 3) + 3) + 4, x = 1.7, 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": "18.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3(-3|(-4(5((1(2x^2 - 5x + 2))/(-3(2x^2 - 5x + 2) - 2))^2 - 2((1(2x^2 - 5x + 2))/(-3(2x^2 - 5x + 2) - 2)) - 5) - 1) + 3| + 1) + 1 and g(x) = 1cos(1\u03c0(-2|(5((2(2|x - 2| - 3))/(-1(2|x - 2| - 3) + 3)) + 1) - 3| - 1) - 3) - 1 between the vertical lines x = 1.1 and x = 1.2000000000000002. 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) = 4(-2(2|(-3((2(-3|x + 2| + 1) + 3)/(-1(-3|x + 2| + 1) + 3)) - 5) + 1| + 2)) - 2 and g(x) = -4(2cos(2\u03c0(-1((3((2x + 3)/(-2x - 3)) - 1)/(2((2x + 3)/(-2x - 3)) - 1)) - 4)) - 2)^2 - 1(2cos(2\u03c0(-1((3((2x + 3)/(-2x - 3)) - 1)/(2((2x + 3)/(-2x - 3)) - 1)) - 4)) - 2) between the vertical lines x = -4.4 and x = 0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "213.9", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1((3(3(5(1((-2x)/(2x - 1))^2 + 3((-2x)/(2x - 1)) - 3)^2 + 5(1((-2x)/(2x - 1))^2 + 3((-2x)/(2x - 1)) - 3) + 1) - 4) - 1)/(2(3(5(1((-2x)/(2x - 1))^2 + 3((-2x)/(2x - 1)) - 3)^2 + 5(1((-2x)/(2x - 1))^2 + 3((-2x)/(2x - 1)) - 3) + 1) - 4) - 3))^2 + 5((3(3(5(1((-2x)/(2x - 1))^2 + 3((-2x)/(2x - 1)) - 3)^2 + 5(1((-2x)/(2x - 1))^2 + 3((-2x)/(2x - 1)) - 3) + 1) - 4) - 1)/(2(3(5(1((-2x)/(2x - 1))^2 + 3((-2x)/(2x - 1)) - 3)^2 + 5(1((-2x)/(2x - 1))^2 + 3((-2x)/(2x - 1)) - 3) + 1) - 4) - 3)) - 5 and g(x) = (2(-1((-2(-3e^(-2(-5x^2 - 1x + 5))) + 2)/(-2(-3e^(-2(-5x^2 - 1x + 5))))) - 4) - 2)/(1(-1((-2(-3e^(-2(-5x^2 - 1x + 5))) + 2)/(-2(-3e^(-2(-5x^2 - 1x + 5))))) - 4) + 2) 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": "1.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2(3|(-2(1(-2|((-1x + 1)/(1x + 2))| - 1))^2 + 3(1(-2|((-1x + 1)/(1x + 2))| - 1)) + 3) + 2| - 2)^2 + 5(3|(-2(1(-2|((-1x + 1)/(1x + 2))| - 1))^2 + 3(1(-2|((-1x + 1)/(1x + 2))| - 1)) + 3) + 2| - 2) - 1 and g(x) = 1e^(2(-3((2(-2(2x - 1)^2 + 3(2x - 1) - 3) + 1)/(-2(-2(2x - 1)^2 + 3(2x - 1) - 3) + 1))^2 + 2((2(-2(2x - 1)^2 + 3(2x - 1) - 3) + 1)/(-2(-2(2x - 1)^2 + 3(2x - 1) - 3) + 1)))) between the vertical lines x = 0.8 and x = 1.2. 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(5(3cos(3\u03c0(-3(-1|((-3x + 2)/(-2x - 3))| + 1) + 4) - 2) - 2) + 3)^2 + 5(5(3cos(3\u03c0(-3(-1|((-3x + 2)/(-2x - 3))| + 1) + 4) - 2) - 2) + 3) - 2, g(x) = -1(2|(-3(5(1x - 2) + 1)^2 + 3(5(1x - 2) + 1)) - 2| + 1)^2 + 5(2|(-3(5(1x - 2) + 1)^2 + 3(5(1x - 2) + 1)) - 2| + 1) + 4, 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": "1.6", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -3(-1sin(2\u03c0(-2|(-1|(2|(1|x - 2| - 2) - 3| + 2) + 1| - 3) - 3| + 3) - 3) + 1)^2 + 5(-1sin(2\u03c0(-2|(-1|(2|(1|x - 2| - 2) - 3| + 2) + 1| - 3) - 3| + 3) - 3) + 1) + 1, g(x) = 2(-3(1cos(3\u03c0(-1(-1|x + 3| - 1)^2 - 4(-1|x + 3| - 1) + 3) - 2) + 2)^2 + 5(1cos(3\u03c0(-1(-1|x + 3| - 1)^2 - 4(-1|x + 3| - 1) + 3) - 2) + 2) + 3)^2 - 5(-3(1cos(3\u03c0(-1(-1|x + 3| - 1)^2 - 4(-1|x + 3| - 1) + 3) - 2) + 2)^2 + 5(1cos(3\u03c0(-1(-1|x + 3| - 1)^2 - 4(-1|x + 3| - 1) + 3) - 2) + 2) + 3) - 5, 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": "5.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 4((-3((-1((1(-3(3x + 3)^2 + 5(3x + 3) - 2) + 2)/(3(-3(3x + 3)^2 + 5(3x + 3) - 2) - 1)) - 3)/(2((1(-3(3x + 3)^2 + 5(3x + 3) - 2) + 2)/(3(-3(3x + 3)^2 + 5(3x + 3) - 2) - 1)) - 1)) - 3)/(3((-1((1(-3(3x + 3)^2 + 5(3x + 3) - 2) + 2)/(3(-3(3x + 3)^2 + 5(3x + 3) - 2) - 1)) - 3)/(2((1(-3(3x + 3)^2 + 5(3x + 3) - 2) + 2)/(3(-3(3x + 3)^2 + 5(3x + 3) - 2) - 1)) - 1)) + 2)) - 2 and g(x) = -2|(3((-1(3|(-5x + 3) - 1| - 3) + 1)/(2(3|(-5x + 3) - 1| - 3) - 3)) - 4) - 2| 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": "2.7", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2((-1((-1(-4((2(-4x) - 2)/(2(-4x) - 3))^2 - 5((2(-4x) - 2)/(2(-4x) - 3)) + 3) + 1)/(-1(-4((2(-4x) - 2)/(2(-4x) - 3))^2 - 5((2(-4x) - 2)/(2(-4x) - 3)) + 3) - 1)) + 3)/(1((-1(-4((2(-4x) - 2)/(2(-4x) - 3))^2 - 5((2(-4x) - 2)/(2(-4x) - 3)) + 3) + 1)/(-1(-4((2(-4x) - 2)/(2(-4x) - 3))^2 - 5((2(-4x) - 2)/(2(-4x) - 3)) + 3) - 1)) + 2))^2 + 3((-1((-1(-4((2(-4x) - 2)/(2(-4x) - 3))^2 - 5((2(-4x) - 2)/(2(-4x) - 3)) + 3) + 1)/(-1(-4((2(-4x) - 2)/(2(-4x) - 3))^2 - 5((2(-4x) - 2)/(2(-4x) - 3)) + 3) - 1)) + 3)/(1((-1(-4((2(-4x) - 2)/(2(-4x) - 3))^2 - 5((2(-4x) - 2)/(2(-4x) - 3)) + 3) + 1)/(-1(-4((2(-4x) - 2)/(2(-4x) - 3))^2 - 5((2(-4x) - 2)/(2(-4x) - 3)) + 3) - 1)) + 2)) - 4 and g(x) = -3cos(1\u03c0(4(-2|(-1|(2|x - 1|) - 1| - 1) - 3| - 1) - 4) - 1) - 1 between the vertical lines x = -2.3 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": "Find the area of the region bounded by the curves f(x) = (2((3((-1(3(2e^(-1(3|x + 2| + 2)) - 3) - 3))/(3(3(2e^(-1(3|x + 2| + 2)) - 3) - 3) - 2)) - 1)/(2((-1(3(2e^(-1(3|x + 2| + 2)) - 3) - 3))/(3(3(2e^(-1(3|x + 2| + 2)) - 3) - 3) - 2)) - 1)) - 3)/(1((3((-1(3(2e^(-1(3|x + 2| + 2)) - 3) - 3))/(3(3(2e^(-1(3|x + 2| + 2)) - 3) - 3) - 2)) - 1)/(2((-1(3(2e^(-1(3|x + 2| + 2)) - 3) - 3))/(3(3(2e^(-1(3|x + 2| + 2)) - 3) - 3) - 2)) - 1)) - 2), g(x) = 1(-1((-3(-5(5x + 4)^2 - 2(5x + 4) + 1) + 3)/(3(-5(5x + 4)^2 - 2(5x + 4) + 1) + 1))^2 - 2((-3(-5(5x + 4)^2 - 2(5x + 4) + 1) + 3)/(3(-5(5x + 4)^2 - 2(5x + 4) + 1) + 1)) + 4) + 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": "152.8", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1((-3(-1sin(2\u03c0((2(-2|(-2|x| + 1) + 3| - 3) - 2)/(-3(-2|(-2|x| + 1) + 3| - 3) + 2)) - 1) - 1) - 1)/(1(-1sin(2\u03c0((2(-2|(-2|x| + 1) + 3| - 3) - 2)/(-3(-2|(-2|x| + 1) + 3| - 3) + 2)) - 1) - 1) + 1)) + 3, g(x) = 2|(5((3(5(-1x + 5) - 2) - 3)/(1(5(-1x + 5) - 2) + 3)) - 2) - 1| - 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": "Determine the area of the region enclosed by the graphs of f(x) = 5((-2((-2(5((-1(-2|x - 1|) - 2)/(2(-2|x - 1|)))^2 - 2((-1(-2|x - 1|) - 2)/(2(-2|x - 1|))) - 5) + 2)/(3(5((-1(-2|x - 1|) - 2)/(2(-2|x - 1|)))^2 - 2((-1(-2|x - 1|) - 2)/(2(-2|x - 1|))) - 5))) + 3)/(-2((-2(5((-1(-2|x - 1|) - 2)/(2(-2|x - 1|)))^2 - 2((-1(-2|x - 1|) - 2)/(2(-2|x - 1|))) - 5) + 2)/(3(5((-1(-2|x - 1|) - 2)/(2(-2|x - 1|)))^2 - 2((-1(-2|x - 1|) - 2)/(2(-2|x - 1|))) - 5))) - 2))^2 + 5((-2((-2(5((-1(-2|x - 1|) - 2)/(2(-2|x - 1|)))^2 - 2((-1(-2|x - 1|) - 2)/(2(-2|x - 1|))) - 5) + 2)/(3(5((-1(-2|x - 1|) - 2)/(2(-2|x - 1|)))^2 - 2((-1(-2|x - 1|) - 2)/(2(-2|x - 1|))) - 5))) + 3)/(-2((-2(5((-1(-2|x - 1|) - 2)/(2(-2|x - 1|)))^2 - 2((-1(-2|x - 1|) - 2)/(2(-2|x - 1|))) - 5) + 2)/(3(5((-1(-2|x - 1|) - 2)/(2(-2|x - 1|)))^2 - 2((-1(-2|x - 1|) - 2)/(2(-2|x - 1|))) - 5))) - 2)) + 2 and g(x) = 2|(3((1(4(-2e^(2x) - 3)^2 - 4(-2e^(2x) - 3) - 2) - 3)/(3(4(-2e^(2x) - 3)^2 - 4(-2e^(2x) - 3) - 2) - 2)) - 2) - 1| + 2 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": "5.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (3(3|(2cos(1\u03c0(-4(-2|(3x - 1) - 2|) + 2) - 2)) + 1|) - 1)/(1(3|(2cos(1\u03c0(-4(-2|(3x - 1) - 2|) + 2) - 2)) + 1|)), g(x) = -5(1|(-1((-2(-1x^2 + 3x + 4) + 3)/(-2(-1x^2 + 3x + 4))) + 3) - 2|)^2 - 5(1|(-1((-2(-1x^2 + 3x + 4) + 3)/(-2(-1x^2 + 3x + 4))) + 3) - 2|) - 3, 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": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2|((-2(-3(4(-1|(1x^2 + 4x - 3) - 3| + 2) + 2)) + 1)/(1(-3(4(-1|(1x^2 + 4x - 3) - 3| + 2) + 2)) - 2))| - 1 and g(x) = (-2(1(-5((1((-3x + 2)/(-2x)) - 1)/(3((-3x + 2)/(-2x)) + 1)) + 3) - 1) - 2)/(2(1(-5((1((-3x + 2)/(-2x)) - 1)/(3((-3x + 2)/(-2x)) + 1)) + 3) - 1) - 3) from x = -4.7 to x = -0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "49.6", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1((-1((3(1(4(-3|x| + 1)^2 - 3(-3|x| + 1) + 1)^2 - 5(4(-3|x| + 1)^2 - 3(-3|x| + 1) + 1) - 4) + 3)/(-1(1(4(-3|x| + 1)^2 - 3(-3|x| + 1) + 1)^2 - 5(4(-3|x| + 1)^2 - 3(-3|x| + 1) + 1) - 4) + 2)) + 3)/(-2((3(1(4(-3|x| + 1)^2 - 3(-3|x| + 1) + 1)^2 - 5(4(-3|x| + 1)^2 - 3(-3|x| + 1) + 1) - 4) + 3)/(-1(1(4(-3|x| + 1)^2 - 3(-3|x| + 1) + 1)^2 - 5(4(-3|x| + 1)^2 - 3(-3|x| + 1) + 1) - 4) + 2)) + 1))^2 - 2, g(x) = (-2(3((2(-2|(-1|x - 2| - 1) + 2| + 2) + 3)/(-3(-2|(-1|x - 2| - 1) + 2| + 2) - 1))^2 + 5((2(-2|(-1|x - 2| - 1) + 2| + 2) + 3)/(-3(-2|(-1|x - 2| - 1) + 2| + 2) - 1)) - 2) + 2)/(1(3((2(-2|(-1|x - 2| - 1) + 2| + 2) + 3)/(-3(-2|(-1|x - 2| - 1) + 2| + 2) - 1))^2 + 5((2(-2|(-1|x - 2| - 1) + 2| + 2) + 3)/(-3(-2|(-1|x - 2| - 1) + 2| + 2) - 1)) - 2) - 2), x = 2.2, 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": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 3cos(2\u03c0(-4(-1(2(-2(3|x + 2| - 2))^2 - 1(-2(3|x + 2| - 2)) - 4) + 3) - 2) - 2) + 2 and g(x) = 1cos(1\u03c0((2(2(-3|(1|x - 2| + 1) + 1| - 2) + 4) + 2)/(2(2(-3|(1|x - 2| + 1) + 1| - 2) + 4) + 1)) + 2) - 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": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3((2((-2(-2|(3|(2e^(-2x) + 1) + 3|) - 2| + 1))/(-3(-2|(3|(2e^(-2x) + 1) + 3|) - 2| + 1) + 4)) - 2)/(3((-2(-2|(3|(2e^(-2x) + 1) + 3|) - 2| + 1))/(-3(-2|(3|(2e^(-2x) + 1) + 3|) - 2| + 1) + 4))))^2 - 1((2((-2(-2|(3|(2e^(-2x) + 1) + 3|) - 2| + 1))/(-3(-2|(3|(2e^(-2x) + 1) + 3|) - 2| + 1) + 4)) - 2)/(3((-2(-2|(3|(2e^(-2x) + 1) + 3|) - 2| + 1))/(-3(-2|(3|(2e^(-2x) + 1) + 3|) - 2| + 1) + 4)))) - 2 and g(x) = -1|((-1(1|(4((2x + 3)/(1x))^2 - 2((2x + 3)/(1x)) - 3) + 1| - 1) + 2)/(2(1|(4((2x + 3)/(1x))^2 - 2((2x + 3)/(1x)) - 3) + 1| - 1) - 3)) - 2| - 1 between the vertical lines x = -4.6 and x = -1.0. 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": "Find the area of the region bounded by the curves f(x) = (-3(4(-4(-1(-2|(2|x + 2| - 1) + 1| + 2) - 2)^2 - 2)^2 - 2) + 2)/(-2(4(-4(-1(-2|(2|x + 2| - 1) + 1| + 2) - 2)^2 - 2)^2 - 2) - 3), g(x) = -3(3cos(1\u03c0(-1|(-4(2|x| - 1) + 2) + 2| + 3) + 1) + 3)^2 + 5(3cos(1\u03c0(-1|(-4(2|x| - 1) + 2) + 2| + 3) + 1) + 3) + 1, x = -3.0, 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": "6.6", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -3|(-3e^(-1(4(-2|((-1(1x - 3) + 1)/(-1(1x - 3) + 2)) - 1| - 2)^2 + 3(-2|((-1(1x - 3) + 1)/(-1(1x - 3) + 2)) - 1| - 2) - 4)) - 3) + 1| + 1, g(x) = -2(-1|(-5(-2(2|x + 1| - 2) + 1) - 3)|)^2 - 3(-1|(-5(-2(2|x + 1| - 2) + 1) - 3)|) - 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": "Calculate the area enclosed between the functions f(x) = (3(-1(1(-3cos(3\u03c0((-3(5x^2 + 1x + 3) - 2)/(-2(5x^2 + 1x + 3) + 3)) - 2) - 2)^2 + 4(-3cos(3\u03c0((-3(5x^2 + 1x + 3) - 2)/(-2(5x^2 + 1x + 3) + 3)) - 2) - 2) + 4)^2 + 4(1(-3cos(3\u03c0((-3(5x^2 + 1x + 3) - 2)/(-2(5x^2 + 1x + 3) + 3)) - 2) - 2)^2 + 4(-3cos(3\u03c0((-3(5x^2 + 1x + 3) - 2)/(-2(5x^2 + 1x + 3) + 3)) - 2) - 2) + 4) - 5) + 3)/(-1(-1(1(-3cos(3\u03c0((-3(5x^2 + 1x + 3) - 2)/(-2(5x^2 + 1x + 3) + 3)) - 2) - 2)^2 + 4(-3cos(3\u03c0((-3(5x^2 + 1x + 3) - 2)/(-2(5x^2 + 1x + 3) + 3)) - 2) - 2) + 4)^2 + 4(1(-3cos(3\u03c0((-3(5x^2 + 1x + 3) - 2)/(-2(5x^2 + 1x + 3) + 3)) - 2) - 2)^2 + 4(-3cos(3\u03c0((-3(5x^2 + 1x + 3) - 2)/(-2(5x^2 + 1x + 3) + 3)) - 2) - 2) + 4) - 5) + 2) and g(x) = -1(-3((1(3|(-3x - 5) + 2| - 3))/(3(3|(-3x - 5) + 2| - 3) - 2))^2 + 3((1(3|(-3x - 5) + 2| - 3))/(3(3|(-3x - 5) + 2| - 3) - 2)) + 2) - 2 from x = -0.6 to x = -0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "43.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 3(-2e^(1(-3(2(3|(-5x - 1) - 1| - 1) - 1)^2 - 4(2(3|(-5x - 1) - 1| - 1) - 1) - 1)) + 2)^2 - 3(-2e^(1(-3(2(3|(-5x - 1) - 1| - 1) - 1)^2 - 4(2(3|(-5x - 1) - 1| - 1) - 1) - 1)) + 2) + 2 and g(x) = 2(-2e^(1(4(1|(2x + 1) + 2| - 2) + 1)) + 3)^2 + 5(-2e^(1(4(1|(2x + 1) + 2| - 2) + 1)) + 3) - 5 between the vertical lines x = -2.3 and x = -0.7. 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": "Calculate the area enclosed between the functions f(x) = 4(3cos(2\u03c0(-5((1(3|(1x) - 3| - 3) + 2)/(2(3|(1x) - 3| - 3) + 1)) - 1)) + 2) - 5 and g(x) = (-3(-4(4((1(2sin(3\u03c0x) - 3) + 3)/(-3(2sin(3\u03c0x) - 3) - 2))^2 - 3((1(2sin(3\u03c0x) - 3) + 3)/(-3(2sin(3\u03c0x) - 3) - 2)) - 4) + 2) + 2)/(-1(-4(4((1(2sin(3\u03c0x) - 3) + 3)/(-3(2sin(3\u03c0x) - 3) - 2))^2 - 3((1(2sin(3\u03c0x) - 3) + 3)/(-3(2sin(3\u03c0x) - 3) - 2)) - 4) + 2) + 2) from x = 3.5 to x = 3.6. 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": "Determine the area of the region enclosed by the graphs of f(x) = (2((-1(-3(3(2|(1|x - 3|) - 1| - 2) + 4)^2 + 1(3(2|(1|x - 3|) - 1| - 2) + 4) + 4) + 1)/(-3(-3(3(2|(1|x - 3|) - 1| - 2) + 4)^2 + 1(3(2|(1|x - 3|) - 1| - 2) + 4) + 4) - 2)) - 2)/(2((-1(-3(3(2|(1|x - 3|) - 1| - 2) + 4)^2 + 1(3(2|(1|x - 3|) - 1| - 2) + 4) + 4) + 1)/(-3(-3(3(2|(1|x - 3|) - 1| - 2) + 4)^2 + 1(3(2|(1|x - 3|) - 1| - 2) + 4) + 4) - 2)) - 1) and g(x) = -2((-2(-5(2e^(1((2x + 2)/(-3x - 1))) - 2) - 1) - 3)/(-1(-5(2e^(1((2x + 2)/(-3x - 1))) - 2) - 1) + 2)) - 4 between the vertical lines x = 3.9 and x = 4.1. 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|(2|(1(-1e^(-1(-1|(1x^2 - 4x - 3) + 2| - 3)) - 1) + 3) + 2| + 3) - 2| + 3, g(x) = 1|(-4(-3|(3|(1cos(3\u03c0x + 1) - 1) - 3| + 2) - 3| + 3) + 3) - 3| + 1, x = 4.1, 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": "14.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-2(1(-3((-2(1((1x - 3)/(1x + 2))) - 3)/(3(1((1x - 3)/(1x + 2))) - 2)) + 4) - 5) - 1)/(1(1(-3((-2(1((1x - 3)/(1x + 2))) - 3)/(3(1((1x - 3)/(1x + 2))) - 2)) + 4) - 5) - 2) and g(x) = -3|(1|(3(-1|((2x - 3)/(2x))| + 2)^2 + 4(-1|((2x - 3)/(2x))| + 2) - 4) + 1| - 2) - 1| + 3 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-2((-3(-2|(1(-3e^(-1(1|x - 2| + 1)) - 2)^2 + 4(-3e^(-1(1|x - 2| + 1)) - 2) + 4) - 1|) + 2)/(-3(-2|(1(-3e^(-1(1|x - 2| + 1)) - 2)^2 + 4(-3e^(-1(1|x - 2| + 1)) - 2) + 4) - 1|) - 3)) - 2)/(3((-3(-2|(1(-3e^(-1(1|x - 2| + 1)) - 2)^2 + 4(-3e^(-1(1|x - 2| + 1)) - 2) + 4) - 1|) + 2)/(-3(-2|(1(-3e^(-1(1|x - 2| + 1)) - 2)^2 + 4(-3e^(-1(1|x - 2| + 1)) - 2) + 4) - 1|) - 3)) + 3) and g(x) = -2(3(-2(-1((-3x - 2)/(-1x - 1)) + 1) + 3) + 3)^2 - 3(3(-2(-1((-3x - 2)/(-1x - 1)) + 1) + 3) + 3) + 3 between the vertical lines x = -0.8 and x = -0.7. 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) = (3(1(-1sin(1\u03c0(2(4(-3x^2 + 3x - 3)^2 - 4(-3x^2 + 3x - 3) - 3)^2 - 4(4(-3x^2 + 3x - 3)^2 - 4(-3x^2 + 3x - 3) - 3) + 1) - 3) + 2)^2 + 4(-1sin(1\u03c0(2(4(-3x^2 + 3x - 3)^2 - 4(-3x^2 + 3x - 3) - 3)^2 - 4(4(-3x^2 + 3x - 3)^2 - 4(-3x^2 + 3x - 3) - 3) + 1) - 3) + 2)) + 2)/(1(1(-1sin(1\u03c0(2(4(-3x^2 + 3x - 3)^2 - 4(-3x^2 + 3x - 3) - 3)^2 - 4(4(-3x^2 + 3x - 3)^2 - 4(-3x^2 + 3x - 3) - 3) + 1) - 3) + 2)^2 + 4(-1sin(1\u03c0(2(4(-3x^2 + 3x - 3)^2 - 4(-3x^2 + 3x - 3) - 3)^2 - 4(4(-3x^2 + 3x - 3)^2 - 4(-3x^2 + 3x - 3) - 3) + 1) - 3) + 2)) - 3), g(x) = 3|((3(-2cos(1\u03c0(5(1x^2 - 5x - 3)^2 - 5(1x^2 - 5x - 3) - 4) + 3) - 3) - 2)/(-1(-2cos(1\u03c0(5(1x^2 - 5x - 3)^2 - 5(1x^2 - 5x - 3) - 4) + 3) - 3) + 2)) + 1| + 3, 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 5(-3|(-1(-3(1e^(2(5x + 1)) - 3) - 3) + 4) + 2| - 1)^2 + 2(-3|(-1(-3(1e^(2(5x + 1)) - 3) - 3) + 4) + 2| - 1) + 5 and g(x) = (3(-4(1sin(3\u03c0(3|((-1x + 3)/(-3x - 1))| - 3) - 1) - 2) - 5) - 1)/(-2(-4(1sin(3\u03c0(3|((-1x + 3)/(-3x - 1))| - 3) - 1) - 2) - 5) - 1) between the vertical lines x = -1.2 and x = -1.1. 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) = (-2((3((-1(5(-5(-1|x + 3| - 3)^2 + 3(-1|x + 3| - 3) + 2) - 4) - 1)/(-3(5(-5(-1|x + 3| - 3)^2 + 3(-1|x + 3| - 3) + 2) - 4) + 4)) + 1)/(1((-1(5(-5(-1|x + 3| - 3)^2 + 3(-1|x + 3| - 3) + 2) - 4) - 1)/(-3(5(-5(-1|x + 3| - 3)^2 + 3(-1|x + 3| - 3) + 2) - 4) + 4)) - 2)) + 1)/(2((3((-1(5(-5(-1|x + 3| - 3)^2 + 3(-1|x + 3| - 3) + 2) - 4) - 1)/(-3(5(-5(-1|x + 3| - 3)^2 + 3(-1|x + 3| - 3) + 2) - 4) + 4)) + 1)/(1((-1(5(-5(-1|x + 3| - 3)^2 + 3(-1|x + 3| - 3) + 2) - 4) - 1)/(-3(5(-5(-1|x + 3| - 3)^2 + 3(-1|x + 3| - 3) + 2) - 4) + 4)) - 2)) + 2) and g(x) = -2((1(-1cos(2\u03c0(3(-3x^2 - 1)^2 - 2(-3x^2 - 1)) + 2) + 1) - 1)/(-1(-1cos(2\u03c0(3(-3x^2 - 1)^2 - 2(-3x^2 - 1)) + 2) + 1))) - 1 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": "447.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2|(1|(1sin(2\u03c0(-2(1(-4x^2 - 2x - 3) - 2)^2 + 4(1(-4x^2 - 2x - 3) - 2) + 3) + 1) - 1)|)| - 2 and g(x) = (2(-5(-2|(-4(1|x - 3| + 3) - 3) + 3| + 1)^2 - 1(-2|(-4(1|x - 3| + 3) - 3) + 3| + 1) - 2) + 3)/(2(-5(-2|(-4(1|x - 3| + 3) - 3) + 3| + 1)^2 - 1(-2|(-4(1|x - 3| + 3) - 3) + 3| + 1) - 2)) 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": "Calculate the area enclosed between the functions f(x) = (2(-4(-1(-3(3(-2e^(2x) + 1) + 4)^2 - 3(3(-2e^(2x) + 1) + 4) + 3) - 5)^2 - 1(-1(-3(3(-2e^(2x) + 1) + 4)^2 - 3(3(-2e^(2x) + 1) + 4) + 3) - 5) - 1) + 2)/(1(-4(-1(-3(3(-2e^(2x) + 1) + 4)^2 - 3(3(-2e^(2x) + 1) + 4) + 3) - 5)^2 - 1(-1(-3(3(-2e^(2x) + 1) + 4)^2 - 3(3(-2e^(2x) + 1) + 4) + 3) - 5) - 1) + 3) and g(x) = (1((-3((1(2|(5x + 2) + 2| - 1) - 3)/(-1(2|(5x + 2) + 2| - 1) - 1)))/(-2((1(2|(5x + 2) + 2| - 1) - 3)/(-1(2|(5x + 2) + 2| - 1) - 1)) - 3)) + 1)/(2((-3((1(2|(5x + 2) + 2| - 1) - 3)/(-1(2|(5x + 2) + 2| - 1) - 1)))/(-2((1(2|(5x + 2) + 2| - 1) - 3)/(-1(2|(5x + 2) + 2| - 1) - 1)) - 3)) - 1) from x = -0.0 to 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": "Determine the area of the region enclosed by the graphs of f(x) = (3(-1(2|(-3sin(2\u03c0(-5(-2|x - 1| + 2) + 5) - 3) + 2) - 2| + 2)^2 + 3(2|(-3sin(2\u03c0(-5(-2|x - 1| + 2) + 5) - 3) + 2) - 2| + 2) + 5) - 3)/(3(-1(2|(-3sin(2\u03c0(-5(-2|x - 1| + 2) + 5) - 3) + 2) - 2| + 2)^2 + 3(2|(-3sin(2\u03c0(-5(-2|x - 1| + 2) + 5) - 3) + 2) - 2| + 2) + 5) + 3) and g(x) = 3|(3(2|((-2(-3|x + 2| + 1))/(-1(-3|x + 2| + 1) + 3)) - 2| + 3) - 4) + 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": "3.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2(1(-4((-3(-2(-3|x + 2| + 1) - 1) - 3)/(-2(-2(-3|x + 2| + 1) - 1) - 3))^2 - 4((-3(-2(-3|x + 2| + 1) - 1) - 3)/(-2(-2(-3|x + 2| + 1) - 1) - 3))) + 5) - 5, g(x) = (2(-1e^(1(1|(4(3x - 1) - 5) + 2| + 3)) - 3) + 3)/(2(-1e^(1(1|(4(3x - 1) - 5) + 2| + 3)) - 3) + 1), x = -2.3, 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": "22.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1sin(2\u03c0(-2((-1((-1(2|(-2|x - 1| + 3) + 2| + 2) - 1)/(-3(2|(-2|x - 1| + 3) + 2| + 2) - 2)))/(-3((-1(2|(-2|x - 1| + 3) + 2| + 2) - 1)/(-3(2|(-2|x - 1| + 3) + 2| + 2) - 2)) - 2))^2 + 3((-1((-1(2|(-2|x - 1| + 3) + 2| + 2) - 1)/(-3(2|(-2|x - 1| + 3) + 2| + 2) - 2)))/(-3((-1(2|(-2|x - 1| + 3) + 2| + 2) - 1)/(-3(2|(-2|x - 1| + 3) + 2| + 2) - 2)) - 2)) - 1) - 2) + 2 and g(x) = 1(2|(-4(1(1|x| + 2)^2 - 2(1|x| + 2))) + 1| + 1) - 5 from x = -0.4 to x = 0.4. 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(-1|((-1(-1|(-1|(-3cos(1\u03c0x - 1) - 2) - 2| + 2) + 1| + 1) - 1)/(1(-1|(-1|(-3cos(1\u03c0x - 1) - 2) - 2| + 2) + 1| + 1))) + 3| + 2)^2 + 4(-1|((-1(-1|(-1|(-3cos(1\u03c0x - 1) - 2) - 2| + 2) + 1| + 1) - 1)/(1(-1|(-1|(-3cos(1\u03c0x - 1) - 2) - 2| + 2) + 1| + 1))) + 3| + 2) + 3 and g(x) = -1|(-5(-3sin(2\u03c0(5(5x^2 + 4x + 2)^2 - 2(5x^2 + 4x + 2) + 1) - 2) + 2) - 4) - 3| + 2 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": "1.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (3(-4(-2|(4(-2e^(2(2|x - 2| - 2)) - 1)^2 + 1(-2e^(2(2|x - 2| - 2)) - 1) + 3) + 1| - 1)^2 - 4(-2|(4(-2e^(2(2|x - 2| - 2)) - 1)^2 + 1(-2e^(2(2|x - 2| - 2)) - 1) + 3) + 1| - 1) + 1) + 2)/(-3(-4(-2|(4(-2e^(2(2|x - 2| - 2)) - 1)^2 + 1(-2e^(2(2|x - 2| - 2)) - 1) + 3) + 1| - 1)^2 - 4(-2|(4(-2e^(2(2|x - 2| - 2)) - 1)^2 + 1(-2e^(2(2|x - 2| - 2)) - 1) + 3) + 1| - 1) + 1) + 2) and g(x) = -1(3cos(1\u03c0(1(-3((-2x + 1)/(-2x + 3)) - 3)^2 - 3(-3((-2x + 1)/(-2x + 3)) - 3) + 4)) + 3) - 1 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": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1|(-1|(1(-2|(-1(-3|x + 2|) - 3) + 3| - 3) - 2)|) + 3| - 2 and g(x) = (3((1(-3((1((1x + 1)/(3x - 1)) - 2)/(3((1x + 1)/(3x - 1)) - 2))^2 - 3((1((1x + 1)/(3x - 1)) - 2)/(3((1x + 1)/(3x - 1)) - 2)) + 3) + 1)/(-1(-3((1((1x + 1)/(3x - 1)) - 2)/(3((1x + 1)/(3x - 1)) - 2))^2 - 3((1((1x + 1)/(3x - 1)) - 2)/(3((1x + 1)/(3x - 1)) - 2)) + 3) - 2)) - 1)/(3((1(-3((1((1x + 1)/(3x - 1)) - 2)/(3((1x + 1)/(3x - 1)) - 2))^2 - 3((1((1x + 1)/(3x - 1)) - 2)/(3((1x + 1)/(3x - 1)) - 2)) + 3) + 1)/(-1(-3((1((1x + 1)/(3x - 1)) - 2)/(3((1x + 1)/(3x - 1)) - 2))^2 - 3((1((1x + 1)/(3x - 1)) - 2)/(3((1x + 1)/(3x - 1)) - 2)) + 3) - 2)) - 1) from x = -2.2 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) = -3(2|(-2sin(3\u03c0(-3|((-2(5x + 4) + 3)/(3(5x + 4) + 1))| - 1) - 1) + 3)| + 3) + 4 and g(x) = -4(2sin(1\u03c0(3|(-1|(-1x)| + 2)| - 2)))^2 - 5(2sin(1\u03c0(3|(-1|(-1x)| + 2)| - 2))) + 2 from x = -2.2 to x = -2.1. 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) = 3(-4(-1(2((-2(1|x - 2| - 1))/(-3(1|x - 2| - 1) - 1)))^2 + 4(2((-2(1|x - 2| - 1))/(-3(1|x - 2| - 1) - 1))) - 1)) + 2, g(x) = 4((2((-1(-3(-3x - 3) + 4) - 3)/(2(-3(-3x - 3) + 4) + 1)) - 1)/(2((-1(-3(-3x - 3) + 4) - 3)/(2(-3(-3x - 3) + 4) + 1)) + 1))^2 + 2((2((-1(-3(-3x - 3) + 4) - 3)/(2(-3(-3x - 3) + 4) + 1)) - 1)/(2((-1(-3(-3x - 3) + 4) - 3)/(2(-3(-3x - 3) + 4) + 1)) + 1)) + 1, x = 2.6, 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": "-270.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-1((1(1(2|(-5(1e^(1x))^2 - 5) - 3| + 3)) + 3)/(1(1(2|(-5(1e^(1x))^2 - 5) - 3| + 3)))) + 2)/(-2((1(1(2|(-5(1e^(1x))^2 - 5) - 3| + 3)) + 3)/(1(1(2|(-5(1e^(1x))^2 - 5) - 3| + 3)))) + 3) and g(x) = 2e^(2(4(2|(3|((-3x - 1)/(-1x + 2)) + 1|) + 1| - 2) - 4)) + 1 from x = 0.2 to x = 0.3. 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(3cos(2\u03c0((3((3(3x^2 - 3x + 5) - 3)/(-1(3x^2 - 3x + 5) - 1)) - 2)/(-2((3(3x^2 - 3x + 5) - 3)/(-1(3x^2 - 3x + 5) - 1)) - 2)) - 1) - 2) - 4) - 3| + 1, g(x) = (2(-5((1(3(-1x^2 - 2x + 1) - 1) - 1)/(-3(3(-1x^2 - 2x + 1) - 1)))^2 - 4((1(3(-1x^2 - 2x + 1) - 1) - 1)/(-3(3(-1x^2 - 2x + 1) - 1))) - 2) - 1)/(-2(-5((1(3(-1x^2 - 2x + 1) - 1) - 1)/(-3(3(-1x^2 - 2x + 1) - 1)))^2 - 4((1(3(-1x^2 - 2x + 1) - 1) - 1)/(-3(3(-1x^2 - 2x + 1) - 1))) - 2) + 3), 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": "Calculate the area enclosed between the functions f(x) = 3|(-2cos(2\u03c0(1((-2((1(2|x + 2| + 3) - 3)/(3(2|x + 2| + 3) - 2)))/(-3((1(2|x + 2| + 3) - 3)/(3(2|x + 2| + 3) - 2)) - 1))^2 - 1((-2((1(2|x + 2| + 3) - 3)/(3(2|x + 2| + 3) - 2)))/(-3((1(2|x + 2| + 3) - 3)/(3(2|x + 2| + 3) - 2)) - 1)) - 5) - 1) - 3) + 2| - 1 and g(x) = 2sin(1\u03c0(2|(-1|((1((-3x + 2)/(2x)) + 3)/(-3((-3x + 2)/(2x)) + 2)) - 2| - 2) + 3| + 2)) + 2 from x = -1.6 to x = 3.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1((3((2(4(-1|((3x + 1)/(-3x - 2)) + 2| + 3)^2 - 1(-1|((3x + 1)/(-3x - 2)) + 2| + 3) - 4) + 2)/(-3(4(-1|((3x + 1)/(-3x - 2)) + 2| + 3)^2 - 1(-1|((3x + 1)/(-3x - 2)) + 2| + 3) - 4) + 1)) + 3)/(-1((2(4(-1|((3x + 1)/(-3x - 2)) + 2| + 3)^2 - 1(-1|((3x + 1)/(-3x - 2)) + 2| + 3) - 4) + 2)/(-3(4(-1|((3x + 1)/(-3x - 2)) + 2| + 3)^2 - 1(-1|((3x + 1)/(-3x - 2)) + 2| + 3) - 4) + 1)))) - 3 and g(x) = -1sin(2\u03c0((1(1((-1(3|x + 3| - 2) + 3)/(-3(3|x + 3| - 2) - 3)) + 5) + 3)/(-1(1((-1(3|x + 3| - 2) + 3)/(-3(3|x + 3| - 2) - 3)) + 5) + 2)) + 1) + 2 between the vertical lines x = -0.8 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": "Calculate the area enclosed between the functions f(x) = (2(-1(-2|(-3(-1(1x - 2)^2 - 4(1x - 2) + 1)) + 3|) - 5) - 2)/(2(-1(-2|(-3(-1(1x - 2)^2 - 4(1x - 2) + 1)) + 3|) - 5) - 1) and g(x) = 1(1|(-3|(2(-1|x - 2| + 2) - 1) - 2| - 2) - 3| + 1) - 5 from x = 1.8 to x = 2.2. 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": "Calculate the area enclosed between the functions f(x) = 2sin(1\u03c0(3|(-1(2(2|((3x - 1)/(-3x - 2)) + 3| - 3)^2 - 2)) - 2| - 1) + 2) - 2 and g(x) = -3(1(5(-4(1x + 4) - 3)^2 + 3(-4(1x + 4) - 3) - 3) - 1) - 1 from x = -4.9 to x = -4.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2(3(-2(1(5(3|x| - 1) + 3) + 2) + 4) + 4)^2 + 5(3(-2(1(5(3|x| - 1) + 3) + 2) + 4) + 4) - 5 and g(x) = 3cos(1\u03c0(-1|(-1(3|((-1x - 2)/(-1x + 2)) + 3| - 3)^2 + 2(3|((-1x - 2)/(-1x + 2)) + 3| - 3) - 4) + 2| - 2)) - 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": "1.6", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 3sin(2\u03c0((1(-2(2(-2(1x + 2)^2 - 1(1x + 2) + 5))^2 + 5(2(-2(1x + 2)^2 - 1(1x + 2) + 5)) - 4) + 2)/(3(-2(2(-2(1x + 2)^2 - 1(1x + 2) + 5))^2 + 5(2(-2(1x + 2)^2 - 1(1x + 2) + 5)) - 4) - 2)) + 2) - 1 and g(x) = (1(-1|(2|(-1|(1x) + 3| - 1) + 3| + 2) - 3| - 2) - 2)/(-2(-1|(2|(-1|(1x) + 3| - 1) + 3| + 2) - 3| - 2) - 1) between the vertical lines x = -3.9 and x = -3.6. 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) = -1|(2(-3|((-1(-1(4x + 1) + 1) + 3)/(-2(-1(4x + 1) + 1) + 3)) + 1| + 3) - 3) - 1| + 1 and g(x) = (-3(5(1|(-2|(1x - 1) - 1| + 1) - 1|)^2 + 4(1|(-2|(1x - 1) - 1| + 1) - 1|) - 2) + 2)/(-2(5(1|(-2|(1x - 1) - 1| + 1) - 1|)^2 + 4(1|(-2|(1x - 1) - 1| + 1) - 1|) - 2) + 3) from x = 1.7 to x = 2.3. 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": "Determine the area of the region enclosed by the graphs of f(x) = 2(1(3cos(3\u03c0((-3(4((-2x + 1)/(-2x - 2))^2 + 4((-2x + 1)/(-2x - 2)) + 2) + 3)/(-1(4((-2x + 1)/(-2x - 2))^2 + 4((-2x + 1)/(-2x - 2)) + 2) + 2)) - 2) - 1)^2 - 2(3cos(3\u03c0((-3(4((-2x + 1)/(-2x - 2))^2 + 4((-2x + 1)/(-2x - 2)) + 2) + 3)/(-1(4((-2x + 1)/(-2x - 2))^2 + 4((-2x + 1)/(-2x - 2)) + 2) + 2)) - 2) - 1) - 3) + 2 and g(x) = 1|(2sin(2\u03c0(-1(5((-2x + 1)/(1x + 3)) + 2)^2 + 2) + 2) - 2) + 2| 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": "1.6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2|(-2|(-2|((1(-4((-2x)/(-3x + 4)) + 3) - 2)/(-2(-4((-2x)/(-3x + 4)) + 3) - 3)) + 3|) + 2|) + 3| - 2 and g(x) = (-2(1e^(-1(5((1(-4x^2 + 4x) - 1)/(-3(-4x^2 + 4x) + 1))^2 + 2((1(-4x^2 + 4x) - 1)/(-3(-4x^2 + 4x) + 1)) - 1)) - 2) - 1)/(2(1e^(-1(5((1(-4x^2 + 4x) - 1)/(-3(-4x^2 + 4x) + 1))^2 + 2((1(-4x^2 + 4x) - 1)/(-3(-4x^2 + 4x) + 1)) - 1)) - 2) - 3) from x = 2.6 to x = 2.8. 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) = (-2(-1(-1|((-1(1(-5x^2 - 3x - 3)^2 + 4(-5x^2 - 3x - 3)) + 2)/(-3(1(-5x^2 - 3x - 3)^2 + 4(-5x^2 - 3x - 3)) + 1)) - 1| + 3) + 5) + 3)/(2(-1(-1|((-1(1(-5x^2 - 3x - 3)^2 + 4(-5x^2 - 3x - 3)) + 2)/(-3(1(-5x^2 - 3x - 3)^2 + 4(-5x^2 - 3x - 3)) + 1)) - 1| + 3) + 5) + 1) and g(x) = (1(5(-3sin(3\u03c0(3|(-2|x|) + 2| - 3) - 2) + 2) - 4) + 2)/(-1(5(-3sin(3\u03c0(3|(-2|x|) + 2| - 3) - 2) + 2) - 4) - 3) from x = 4.9 to x = 5.0. 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) = 2sin(3\u03c0(2(-3(-4(-1|(2|x - 3| + 1) + 3|)^2 + 4(-1|(2|x - 3| + 1) + 3|) - 2)^2 - 3(-4(-1|(2|x - 3| + 1) + 3|)^2 + 4(-1|(2|x - 3| + 1) + 3|) - 2)) - 4) - 3) + 1, g(x) = (1(-3|((-2(-2|((1x)/(2x)) + 2| - 3))/(-3(-2|((1x)/(2x)) + 2| - 3))) - 3| - 1) + 2)/(1(-3|((-2(-2|((1x)/(2x)) + 2| - 3))/(-3(-2|((1x)/(2x)) + 2| - 3))) - 3| - 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-1((2(-2(3|(2|(-4x^2 - 5x + 4) - 3| + 1) - 1|)^2 - 1(3|(2|(-4x^2 - 5x + 4) - 3| + 1) - 1|) + 3) - 2)/(1(-2(3|(2|(-4x^2 - 5x + 4) - 3| + 1) - 1|)^2 - 1(3|(2|(-4x^2 - 5x + 4) - 3| + 1) - 1|) + 3) - 3)) - 1)/(-3((2(-2(3|(2|(-4x^2 - 5x + 4) - 3| + 1) - 1|)^2 - 1(3|(2|(-4x^2 - 5x + 4) - 3| + 1) - 1|) + 3) - 2)/(1(-2(3|(2|(-4x^2 - 5x + 4) - 3| + 1) - 1|)^2 - 1(3|(2|(-4x^2 - 5x + 4) - 3| + 1) - 1|) + 3) - 3)) - 1), g(x) = -4((3(1((-3(2|x| - 2) - 1)/(-1(2|x| - 2) + 2))^2 - 3((-3(2|x| - 2) - 1)/(-1(2|x| - 2) + 2)) - 3) - 2)/(-2(1((-3(2|x| - 2) - 1)/(-1(2|x| - 2) + 2))^2 - 3((-3(2|x| - 2) - 1)/(-1(2|x| - 2) + 2)) - 3) + 1)) - 1, x = -1.1, 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": "10.9", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3((2(-2((3(4(-5x - 1)^2 + 1(-5x - 1) + 5) - 3)/(1(4(-5x - 1)^2 + 1(-5x - 1) + 5) - 3))^2 - 2((3(4(-5x - 1)^2 + 1(-5x - 1) + 5) - 3)/(1(4(-5x - 1)^2 + 1(-5x - 1) + 5) - 3)) - 5) - 2)/(-1(-2((3(4(-5x - 1)^2 + 1(-5x - 1) + 5) - 3)/(1(4(-5x - 1)^2 + 1(-5x - 1) + 5) - 3))^2 - 2((3(4(-5x - 1)^2 + 1(-5x - 1) + 5) - 3)/(1(4(-5x - 1)^2 + 1(-5x - 1) + 5) - 3)) - 5) + 2)) + 3 and g(x) = 2|(-1|(-3(-2|(-2x + 5) - 2| + 1)^2 - 1(-2|(-2x + 5) - 2| + 1) + 3) - 3| + 2) - 1| - 3 between the vertical lines x = 0.8 and x = 2.2. 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": "Calculate the area enclosed between the functions f(x) = -1|(-1(-3|(-2|((-1(2sin(3\u03c0x + 2) + 2) - 2)/(-2(2sin(3\u03c0x + 2) + 2) + 3)) - 3| - 1) + 2| - 2) - 3) - 1| + 1 and g(x) = (-2(2cos(1\u03c0(-2(1(1x^2 - 1) - 5)) + 1)) + 1)/(2(2cos(1\u03c0(-2(1(1x^2 - 1) - 5)) + 1)) + 1) from x = 2.5 to x = 2.6. 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(1|(-3(-2cos(1\u03c0(-1(2x + 4)^2 + 4(2x + 4) - 4) - 3) - 2)) - 2|) - 2, g(x) = 2(2(2|((-2(4x + 3) + 1)/(-3(4x + 3) - 2))|) - 4) - 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": "53.8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1|(-5(-2cos(1\u03c0(-3|(-3|(-3x^2 + 5x + 2) - 2| - 1) + 2| + 3)) + 1) - 4)| + 2 and g(x) = (-1((1(-5(1cos(3\u03c0(1|x + 2| - 3)) - 3)^2 - 3(1cos(3\u03c0(1|x + 2| - 3)) - 3) - 4) - 3)/(-2(-5(1cos(3\u03c0(1|x + 2| - 3)) - 3)^2 - 3(1cos(3\u03c0(1|x + 2| - 3)) - 3) - 4) + 3)) + 3)/(-3((1(-5(1cos(3\u03c0(1|x + 2| - 3)) - 3)^2 - 3(1cos(3\u03c0(1|x + 2| - 3)) - 3) - 4) - 3)/(-2(-5(1cos(3\u03c0(1|x + 2| - 3)) - 3)^2 - 3(1cos(3\u03c0(1|x + 2| - 3)) - 3) - 4) + 3))) from x = 3.2 to x = 3.3000000000000003. 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) = -4(3((1((2(-2(-1|x - 1| + 1)^2 - 3(-1|x - 1| + 1) - 2) - 3)/(1(-2(-1|x - 1| + 1)^2 - 3(-1|x - 1| + 1) - 2) + 3)) + 2)/(-1((2(-2(-1|x - 1| + 1)^2 - 3(-1|x - 1| + 1) - 2) - 3)/(1(-2(-1|x - 1| + 1)^2 - 3(-1|x - 1| + 1) - 2) + 3)) + 2))^2 + 2((1((2(-2(-1|x - 1| + 1)^2 - 3(-1|x - 1| + 1) - 2) - 3)/(1(-2(-1|x - 1| + 1)^2 - 3(-1|x - 1| + 1) - 2) + 3)) + 2)/(-1((2(-2(-1|x - 1| + 1)^2 - 3(-1|x - 1| + 1) - 2) - 3)/(1(-2(-1|x - 1| + 1)^2 - 3(-1|x - 1| + 1) - 2) + 3)) + 2)) - 1) and g(x) = -2|(1sin(2\u03c0(3|(3((-1x - 1)/(2x + 1)) - 5)| - 3) - 2) + 1) - 2| between the vertical lines x = 0.4 and x = 1.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1((2((2(-1|((1((1x + 1)/(1x)))/(-2((1x + 1)/(1x)) - 1)) + 2| + 3))/(-1(-1|((1((1x + 1)/(1x)))/(-2((1x + 1)/(1x)) - 1)) + 2| + 3) + 2)) + 3)/(3((2(-1|((1((1x + 1)/(1x)))/(-2((1x + 1)/(1x)) - 1)) + 2| + 3))/(-1(-1|((1((1x + 1)/(1x)))/(-2((1x + 1)/(1x)) - 1)) + 2| + 3) + 2)) + 2)) + 1 and g(x) = 1|(-5(-2cos(1\u03c0((2(3x + 4) - 2)/(-1(3x + 4) - 3)) + 2) + 2) + 1) + 2| - 3 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (3(-3|(-4(-2e^(1((-2(-1x - 4) - 1)/(1(-1x - 4) - 3))))) + 1| - 2) - 1)/(3(-3|(-4(-2e^(1((-2(-1x - 4) - 1)/(1(-1x - 4) - 3))))) + 1| - 2) + 3) and g(x) = -4(-4(-2|(-2|(-5x + 3) + 2| + 2) - 1| + 1) - 4) - 4 between the vertical lines x = 1.0 and x = 1.2. 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(-4(5(3((1(-1x + 2) + 1)/(-2(-1x + 2) + 3)) - 3) - 1) - 5) - 1)/(3(-4(5(3((1(-1x + 2) + 1)/(-2(-1x + 2) + 3)) - 3) - 1) - 5) - 2) and g(x) = (2(-3e^(1((1(1(-4x^2 + 5x)^2 - 2(-4x^2 + 5x) - 2) - 3)/(1(1(-4x^2 + 5x)^2 - 2(-4x^2 + 5x) - 2) + 2))) - 1) + 2)/(2(-3e^(1((1(1(-4x^2 + 5x)^2 - 2(-4x^2 + 5x) - 2) - 3)/(1(1(-4x^2 + 5x)^2 - 2(-4x^2 + 5x) - 2) + 2))) - 1) + 2) from x = -0.0 to x = 1.4. 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|(4(-2e^(-1(-1(5x + 2) - 3)) + 1)^2 - 2(-2e^(-1(-1(5x + 2) - 3)) + 1) - 4) - 2| - 3) + 1)/(3(3|(4(-2e^(-1(-1(5x + 2) - 3)) + 1)^2 - 2(-2e^(-1(-1(5x + 2) - 3)) + 1) - 4) - 2| - 3) + 1), g(x) = -2|(-4((2(-2cos(1\u03c0(1x^2 - 2x + 2) + 2) - 2) + 3)/(2(-2cos(1\u03c0(1x^2 - 2x + 2) + 2) - 2) + 2))^2 + 4) - 2| + 1, x = -3.3, and x = -3.1999999999999997. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2(-2(-1sin(1\u03c0(-1(-1((-2x - 2)/(3x - 2))^2 + 3((-2x - 2)/(3x - 2)) + 5)^2 - 1(-1((-2x - 2)/(3x - 2))^2 + 3((-2x - 2)/(3x - 2)) + 5) - 1) - 1) - 3) + 5)^2 - 1(-2(-1sin(1\u03c0(-1(-1((-2x - 2)/(3x - 2))^2 + 3((-2x - 2)/(3x - 2)) + 5)^2 - 1(-1((-2x - 2)/(3x - 2))^2 + 3((-2x - 2)/(3x - 2)) + 5) - 1) - 1) - 3) + 5) + 5 and g(x) = 4(-1(-1(1(3x^2 - 5x - 5) - 3)^2 + 4(1(3x^2 - 5x - 5) - 3) + 5) - 1) - 2 between the vertical lines x = -0.4 and x = -0.30000000000000004. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6.7", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1(-4(-3sin(3\u03c0(-2(3(5x - 3)^2 - 3(5x - 3) - 2)^2 - 3(3(5x - 3)^2 - 3(5x - 3) - 2) - 5)) + 2)^2 + 1(-3sin(3\u03c0(-2(3(5x - 3)^2 - 3(5x - 3) - 2)^2 - 3(3(5x - 3)^2 - 3(5x - 3) - 2) - 5)) + 2) - 3) + 5, g(x) = -2|(3(2|(-4((2x - 2)/(2x - 3)) - 2) - 3| + 3) - 1) + 1| - 3, 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": "4.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (2((2(-1(4(2|(-2x + 3) + 2| + 3)) + 1) - 2)/(-3(-1(4(2|(-2x + 3) + 2| + 3)) + 1) - 1)) + 3)/(3((2(-1(4(2|(-2x + 3) + 2| + 3)) + 1) - 2)/(-3(-1(4(2|(-2x + 3) + 2| + 3)) + 1) - 1))) and g(x) = -2cos(2\u03c0(-5(-2(-3|((2x - 2)/(2x)) - 3| - 2)^2 - 2(-3|((2x - 2)/(2x)) - 3| - 2) + 1) + 1) + 1) + 1 from x = -4.1 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) = -5((-3(3cos(2\u03c0(1(2((3x + 1)/(-1x + 2)) + 3) + 2)) - 3) - 3)/(3(3cos(2\u03c0(1(2((3x + 1)/(-1x + 2)) + 3) + 2)) - 3) + 1)) + 5 and g(x) = 5(-2sin(3\u03c0(4(-2|(-3x^2 + 2) + 3|)^2 + 1) - 1) + 1) - 4 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": "2.8", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2(-3(1cos(1\u03c0(2|(-2(-5x - 5) + 1) - 3| - 1) + 2) + 1)^2 + 2(1cos(1\u03c0(2|(-2(-5x - 5) + 1) - 3| - 1) + 2) + 1) - 2) + 2 and g(x) = 1(1|((1(4((-3x + 2)/(-1x + 2)) - 2))/(-1(4((-3x + 2)/(-1x + 2)) - 2) + 2)) + 1| + 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": "11.5", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1|(3|(3cos(3\u03c0(3(-4((3x + 1)/(-2x + 3))^2 - 2((3x + 1)/(-2x + 3)) - 3) - 2) + 3) + 2) - 3| - 3) - 3| - 3, g(x) = -3cos(3\u03c0((3((-2((-3(1|x + 2| - 1) + 3)/(-2(1|x + 2| - 1) - 3)) + 1)/(1((-3(1|x + 2| - 1) + 3)/(-2(1|x + 2| - 1) - 3)))) + 1)/(-2((-2((-3(1|x + 2| - 1) + 3)/(-2(1|x + 2| - 1) - 3)) + 1)/(1((-3(1|x + 2| - 1) + 3)/(-2(1|x + 2| - 1) - 3)))) + 3)) - 3) - 2, 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": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 5((-1((1(-3(2(-3|x - 2| - 1) + 1) + 3) - 1)/(1(-3(2(-3|x - 2| - 1) + 1) + 3) - 3)) + 2)/(-2((1(-3(2(-3|x - 2| - 1) + 1) + 3) - 1)/(1(-3(2(-3|x - 2| - 1) + 1) + 3) - 3)) - 1)) - 4, g(x) = -3|((2(1((1(2x + 3) - 3)/(1(2x + 3) - 2)) + 2) - 3)/(2(1((1(2x + 3) - 3)/(1(2x + 3) - 2)) + 2) - 1)) - 2| + 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": "5.7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-3(5(3(1|(-3((-1x)/(3x - 1)) - 1) + 2| - 1) - 2) - 4) - 1)/(-1(5(3(1|(-3((-1x)/(3x - 1)) - 1) + 2| - 1) - 2) - 4) - 3) and g(x) = (3(-4(-2|(1(-1x + 4) + 4) + 1| - 3)^2 - 2(-2|(1(-1x + 4) + 4) + 1| - 3) + 3) + 2)/(-1(-4(-2|(1(-1x + 4) + 4) + 1| - 3)^2 - 2(-2|(1(-1x + 4) + 4) + 1| - 3) + 3) + 2) from x = -1.5 to x = 0.2. 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(-3sin(1\u03c0((-2(-4(-2(-1x^2 - 5x - 5)^2 + 5(-1x^2 - 5x - 5) + 3)^2 + 1(-2(-1x^2 - 5x - 5)^2 + 5(-1x^2 - 5x - 5) + 3) - 5) - 2)/(-2(-4(-2(-1x^2 - 5x - 5)^2 + 5(-1x^2 - 5x - 5) + 3)^2 + 1(-2(-1x^2 - 5x - 5)^2 + 5(-1x^2 - 5x - 5) + 3) - 5))) - 1) - 1) - 2)/(1(-3sin(1\u03c0((-2(-4(-2(-1x^2 - 5x - 5)^2 + 5(-1x^2 - 5x - 5) + 3)^2 + 1(-2(-1x^2 - 5x - 5)^2 + 5(-1x^2 - 5x - 5) + 3) - 5) - 2)/(-2(-4(-2(-1x^2 - 5x - 5)^2 + 5(-1x^2 - 5x - 5) + 3)^2 + 1(-2(-1x^2 - 5x - 5)^2 + 5(-1x^2 - 5x - 5) + 3) - 5))) - 1) - 1) + 3) and g(x) = 1((1(-3(-3((-1x - 1)/(-2x))^2 - 1((-1x - 1)/(-2x)) + 1)^2 + 4) + 1)/(2(-3(-3((-1x - 1)/(-2x))^2 - 1((-1x - 1)/(-2x)) + 1)^2 + 4) + 1))^2 - 3((1(-3(-3((-1x - 1)/(-2x))^2 - 1((-1x - 1)/(-2x)) + 1)^2 + 4) + 1)/(2(-3(-3((-1x - 1)/(-2x))^2 - 1((-1x - 1)/(-2x)) + 1)^2 + 4) + 1)) - 5 between the vertical lines x = -3.8 and x = -1.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3(3((-3(-2|((1(-2|x| - 3) - 2)/(-1(-2|x| - 3) - 2)) + 2| + 1) + 1)/(1(-2|((1(-2|x| - 3) - 2)/(-1(-2|x| - 3) - 2)) + 2| + 1) + 3)) + 1)^2 + 5(3((-3(-2|((1(-2|x| - 3) - 2)/(-1(-2|x| - 3) - 2)) + 2| + 1) + 1)/(1(-2|((1(-2|x| - 3) - 2)/(-1(-2|x| - 3) - 2)) + 2| + 1) + 3)) + 1) + 5 and g(x) = -2(-2(3(3|(-1x^2 + 3x + 4) - 2| - 2) - 3) - 4)^2 - 4(-2(3(3|(-1x^2 + 3x + 4) - 2| - 2) - 3) - 4) + 5 between the vertical lines x = 3.7 and x = 3.8. 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": "Calculate the area enclosed between the functions f(x) = 3(1(-1(-1|(1(-5x^2 + 1x + 5)^2 - 2(-5x^2 + 1x + 5) - 2) + 3|) + 4)^2 - 1(-1(-1|(1(-5x^2 + 1x + 5)^2 - 2(-5x^2 + 1x + 5) - 2) + 3|) + 4) + 1) - 1 and g(x) = -3(-4(2|((2((-2x - 1)/(-2x + 3)) + 1)/(-1((-2x - 1)/(-2x + 3)) - 3)) - 3|)^2 + 5(2|((2((-2x - 1)/(-2x + 3)) + 1)/(-1((-2x - 1)/(-2x + 3)) - 3)) - 3|) + 2) - 1 from x = -1.1 to x = -0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "205.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (2(1(5(-2e^(-1(-2(3|x + 3| - 2) - 2)) - 1))^2 - 1(5(-2e^(-1(-2(3|x + 3| - 2) - 2)) - 1)) + 3))/(-2(1(5(-2e^(-1(-2(3|x + 3| - 2) - 2)) - 1))^2 - 1(5(-2e^(-1(-2(3|x + 3| - 2) - 2)) - 1)) + 3) + 3) and g(x) = 4(1((-3((-2(-2cos(3\u03c0x - 3) - 2) - 1)/(-3(-2cos(3\u03c0x - 3) - 2))) - 1)/(3((-2(-2cos(3\u03c0x - 3) - 2) - 1)/(-3(-2cos(3\u03c0x - 3) - 2))) + 3)) - 3) - 5 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": "2.5", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (1((-1((2((-3(1|(2e^(1x) + 3) + 2| - 1) + 2)/(-2(1|(2e^(1x) + 3) + 2| - 1) - 2)) + 3)/(3((-3(1|(2e^(1x) + 3) + 2| - 1) + 2)/(-2(1|(2e^(1x) + 3) + 2| - 1) - 2)) - 2)) + 3)/(-2((2((-3(1|(2e^(1x) + 3) + 2| - 1) + 2)/(-2(1|(2e^(1x) + 3) + 2| - 1) - 2)) + 3)/(3((-3(1|(2e^(1x) + 3) + 2| - 1) + 2)/(-2(1|(2e^(1x) + 3) + 2| - 1) - 2)) - 2)) - 3)) - 2)/(-1((-1((2((-3(1|(2e^(1x) + 3) + 2| - 1) + 2)/(-2(1|(2e^(1x) + 3) + 2| - 1) - 2)) + 3)/(3((-3(1|(2e^(1x) + 3) + 2| - 1) + 2)/(-2(1|(2e^(1x) + 3) + 2| - 1) - 2)) - 2)) + 3)/(-2((2((-3(1|(2e^(1x) + 3) + 2| - 1) + 2)/(-2(1|(2e^(1x) + 3) + 2| - 1) - 2)) + 3)/(3((-3(1|(2e^(1x) + 3) + 2| - 1) + 2)/(-2(1|(2e^(1x) + 3) + 2| - 1) - 2)) - 2)) - 3)) - 2), g(x) = 1(-3sin(3\u03c0(3|(-2|(3x^2 + 5x - 3) - 1| - 2) - 3| - 3) + 3) - 1)^2 - 2(-3sin(3\u03c0(3|(-2|(3x^2 + 5x - 3) - 1| - 2) - 3| - 3) + 3) - 1) - 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": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (1(-5(-1(1|(3(-5x^2 - 2x - 5) - 2) - 1| - 2)^2 - 1(1|(3(-5x^2 - 2x - 5) - 2) - 1| - 2) + 4) - 5) + 3)/(-3(-5(-1(1|(3(-5x^2 - 2x - 5) - 2) - 1| - 2)^2 - 1(1|(3(-5x^2 - 2x - 5) - 2) - 1| - 2) + 4) - 5) - 1), g(x) = 5((3(1|((2(-2x^2 - 3x - 2) - 3)/(1(-2x^2 - 3x - 2) + 1)) - 3| + 2) - 1)/(-2(1|((2(-2x^2 - 3x - 2) - 3)/(1(-2x^2 - 3x - 2) + 1)) - 3| + 2) - 1)) + 5, x = -2.8, 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": "Determine the area of the region enclosed by the graphs of f(x) = 4((1(-3e^(1(-2|(4((-1x + 2)/(2x - 1))^2 + 2((-1x + 2)/(2x - 1)) + 5) - 1| + 3))))/(3(-3e^(1(-2|(4((-1x + 2)/(2x - 1))^2 + 2((-1x + 2)/(2x - 1)) + 5) - 1| + 3))) - 1)) - 2 and g(x) = 3cos(3\u03c0(-3(3((2(-1x^2 - 3x + 2) - 3)/(-3(-1x^2 - 3x + 2) + 2))^2 + 4((2(-1x^2 - 3x + 2) - 3)/(-3(-1x^2 - 3x + 2) + 2)) + 2) - 2) + 3) + 1 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": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (3(4(1(1|(-2|(-3x + 2) + 1| + 2) - 2|)^2 - 3(1|(-2|(-3x + 2) + 1| + 2) - 2|) + 3)^2 + 3(1(1|(-2|(-3x + 2) + 1| + 2) - 2|)^2 - 3(1|(-2|(-3x + 2) + 1| + 2) - 2|) + 3) - 5) - 3)/(-3(4(1(1|(-2|(-3x + 2) + 1| + 2) - 2|)^2 - 3(1|(-2|(-3x + 2) + 1| + 2) - 2|) + 3)^2 + 3(1(1|(-2|(-3x + 2) + 1| + 2) - 2|)^2 - 3(1|(-2|(-3x + 2) + 1| + 2) - 2|) + 3) - 5)), g(x) = 2(-3|(2|(-4(5x + 2)^2 + 1) - 2| - 2) - 2| + 2), 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": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2|(3((2(-4(-4(1|x + 1| - 1)^2 - 3(1|x + 1| - 1) + 2)^2 - 5(-4(1|x + 1| - 1)^2 - 3(1|x + 1| - 1) + 2)) + 2)/(-2(-4(-4(1|x + 1| - 1)^2 - 3(1|x + 1| - 1) + 2)^2 - 5(-4(1|x + 1| - 1)^2 - 3(1|x + 1| - 1) + 2)) + 3)) + 3) + 1| + 3 and g(x) = 3(-5((2(4(3|x|) + 2) + 2)/(2(4(3|x|) + 2) + 1))^2 + 3((2(4(3|x|) + 2) + 2)/(2(4(3|x|) + 2) + 1)) + 1) - 1 from x = -2.4 to x = 0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 5((2(3(-4(-1cos(2\u03c0(-2x - 2) + 3) + 2) + 2)^2 + 4(-4(-1cos(2\u03c0(-2x - 2) + 3) + 2) + 2) - 4) - 3)/(-3(3(-4(-1cos(2\u03c0(-2x - 2) + 3) + 2) + 2)^2 + 4(-4(-1cos(2\u03c0(-2x - 2) + 3) + 2) + 2) - 4) + 4))^2 + 5((2(3(-4(-1cos(2\u03c0(-2x - 2) + 3) + 2) + 2)^2 + 4(-4(-1cos(2\u03c0(-2x - 2) + 3) + 2) + 2) - 4) - 3)/(-3(3(-4(-1cos(2\u03c0(-2x - 2) + 3) + 2) + 2)^2 + 4(-4(-1cos(2\u03c0(-2x - 2) + 3) + 2) + 2) - 4) + 4)) - 3 and g(x) = 1|(-2|((-2(2sin(2\u03c0(-4x^2 + 3x + 4)) - 1))/(1(2sin(2\u03c0(-4x^2 + 3x + 4)) - 1) + 1)) - 1| + 1) - 1| from x = 0.7 to x = 0.8. 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": "Calculate the area enclosed between the functions f(x) = 5((-1(3((-1(-5((3x - 2)/(-1x - 2)) + 2) + 3)/(3(-5((3x - 2)/(-1x - 2)) + 2) - 2))^2 + 2((-1(-5((3x - 2)/(-1x - 2)) + 2) + 3)/(3(-5((3x - 2)/(-1x - 2)) + 2) - 2)) - 4) - 1)/(-1(3((-1(-5((3x - 2)/(-1x - 2)) + 2) + 3)/(3(-5((3x - 2)/(-1x - 2)) + 2) - 2))^2 + 2((-1(-5((3x - 2)/(-1x - 2)) + 2) + 3)/(3(-5((3x - 2)/(-1x - 2)) + 2) - 2)) - 4) + 3)) + 2 and g(x) = 1|(-1|(-3(-2|((-1x - 3)/(-2x - 1)) + 3| + 3)^2 - 2(-2|((-1x - 3)/(-2x - 1)) + 3| + 3) + 5)| + 2) + 2| + 2 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": "17.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1|(1(-1sin(3\u03c0(-1|(3(5x^2 + 1)^2 - 5(5x^2 + 1) + 4) - 2| + 3) + 1) - 2)^2 + 4) + 1| + 2 and g(x) = 1(-1|(4(3|(-3x^2 + 2x + 3) + 1| - 2)^2 + 3(3|(-3x^2 + 2x + 3) + 1| - 2) + 2) - 2| + 3) - 2 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": "0.7", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3|((-1(-2((1(2sin(2\u03c0(-1x - 4) - 3)) - 2)/(2(2sin(2\u03c0(-1x - 4) - 3)) + 2)) - 2))/(-3(-2((1(2sin(2\u03c0(-1x - 4) - 3)) - 2)/(2(2sin(2\u03c0(-1x - 4) - 3)) + 2)) - 2) + 2)) - 1| - 3 and g(x) = -3(-3|((-3(1((1x + 1)/(2x - 3))) - 1)/(-2(1((1x + 1)/(2x - 3))))) + 3| + 2)^2 + 2(-3|((-3(1((1x + 1)/(2x - 3))) - 1)/(-2(1((1x + 1)/(2x - 3))))) + 3| + 2) - 1 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": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2((-2(1(-5(1cos(3\u03c0(4x^2 + 1x + 5) - 1) + 3) + 2) + 1) + 1)/(-1(1(-5(1cos(3\u03c0(4x^2 + 1x + 5) - 1) + 3) + 2) + 1) - 2))^2 + 3((-2(1(-5(1cos(3\u03c0(4x^2 + 1x + 5) - 1) + 3) + 2) + 1) + 1)/(-1(1(-5(1cos(3\u03c0(4x^2 + 1x + 5) - 1) + 3) + 2) + 1) - 2)) + 3, g(x) = -2|(5(1|(3(2x^2 + 4x)^2 - 5(2x^2 + 4x) - 1) + 1|)^2 + 1(1|(3(2x^2 + 4x)^2 - 5(2x^2 + 4x) - 1) + 1|) - 5) + 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": "5.6", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-1((1(4(-1e^(-1((-1((2x)/(2x + 2)) + 2)/(1((2x)/(2x + 2)) - 3))) - 1) + 5))/(-1(4(-1e^(-1((-1((2x)/(2x + 2)) + 2)/(1((2x)/(2x + 2)) - 3))) - 1) + 5) - 1)) - 3)/(-3((1(4(-1e^(-1((-1((2x)/(2x + 2)) + 2)/(1((2x)/(2x + 2)) - 3))) - 1) + 5))/(-1(4(-1e^(-1((-1((2x)/(2x + 2)) + 2)/(1((2x)/(2x + 2)) - 3))) - 1) + 5) - 1)) - 3) and g(x) = 5(1|(-4((-2(1x^2 + 1) - 2)/(-2(1x^2 + 1) + 3)) + 2) + 3| - 1)^2 - 5(1|(-4((-2(1x^2 + 1) - 2)/(-2(1x^2 + 1) + 3)) + 2) + 3| - 1) - 4 between the vertical lines x = 1.9 and 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": "Calculate the area enclosed between the functions f(x) = -3((-2(-2(1(3cos(2\u03c0(-4x^2 + 2x - 1) + 1) - 1) + 2) + 4) + 2)/(-3(-2(1(3cos(2\u03c0(-4x^2 + 2x - 1) + 1) - 1) + 2) + 4) - 3))^2 - 4((-2(-2(1(3cos(2\u03c0(-4x^2 + 2x - 1) + 1) - 1) + 2) + 4) + 2)/(-3(-2(1(3cos(2\u03c0(-4x^2 + 2x - 1) + 1) - 1) + 2) + 4) - 3)) + 4 and g(x) = (2(1|(2(-3(-3|x + 3| - 3)^2 + 4(-3|x + 3| - 3) - 3) - 4) + 2| - 2) + 1)/(-3(1|(2(-3(-3|x + 3| - 3)^2 + 4(-3|x + 3| - 3) - 3) - 4) + 2| - 2) + 1) from x = -1.7 to x = -1.5999999999999999. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "24.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3sin(2\u03c0(-1(-3|((-2((1(3|x - 2| - 2) - 1)/(-2(3|x - 2| - 2))) + 2)/(2((1(3|x - 2| - 2) - 1)/(-2(3|x - 2| - 2))) - 1)) + 2| - 3))) - 1 and g(x) = (3(1(-2|(4(2x - 2)^2 - 5(2x - 2) - 5) - 2| - 2)) + 3)/(2(1(-2|(4(2x - 2)^2 - 5(2x - 2) - 5) - 2| - 2)) + 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": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 3(-1|(1(2|(5((1x - 1)/(3x - 2)) + 3) + 3| - 1) - 2) - 3| + 3)^2 - 5(-1|(1(2|(5((1x - 1)/(3x - 2)) + 3) + 3| - 1) - 2) - 3| + 3) + 3 and g(x) = 1|(1cos(3\u03c0(3(-2|(-2x^2 + 5x + 4) - 2| + 2) - 3) - 3) - 3)| - 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": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1(2|(2|(3(-1sin(3\u03c0(-2x^2 + 1) - 1))^2 - 2(-1sin(3\u03c0(-2x^2 + 1) - 1)) - 3) + 3| + 3)| + 1) - 1, g(x) = -3|((3(-1|(-2|((-3x + 3)/(-3x - 2)) + 2| - 3)| + 3) + 2)/(-2(-1|(-2|((-3x + 3)/(-3x - 2)) + 2| - 3)| + 3))) - 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": "2.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 3e^(-2(5((-2((-3((-2(3|x - 3|) + 1)/(-3(3|x - 3|) - 3)))/(-1((-2(3|x - 3|) + 1)/(-3(3|x - 3|) - 3)) + 2)) + 1)/(-2((-3((-2(3|x - 3|) + 1)/(-3(3|x - 3|) - 3)))/(-1((-2(3|x - 3|) + 1)/(-3(3|x - 3|) - 3)) + 2)) + 3))^2 + 3((-2((-3((-2(3|x - 3|) + 1)/(-3(3|x - 3|) - 3)))/(-1((-2(3|x - 3|) + 1)/(-3(3|x - 3|) - 3)) + 2)) + 1)/(-2((-3((-2(3|x - 3|) + 1)/(-3(3|x - 3|) - 3)))/(-1((-2(3|x - 3|) + 1)/(-3(3|x - 3|) - 3)) + 2)) + 3)) - 3)) + 2 and g(x) = -5(-1|(-3(-2|(-1cos(2\u03c0x - 2) + 1) - 2| + 2)^2 + 2(-2|(-1cos(2\u03c0x - 2) + 1) - 2| + 2) + 1) + 2| + 2) - 3 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": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -3((-1(-4(2sin(1\u03c0(3(-4x^2 + 1x - 5)^2 + 3(-4x^2 + 1x - 5) + 1) + 3) + 3) + 1) + 1)/(-1(-4(2sin(1\u03c0(3(-4x^2 + 1x - 5)^2 + 3(-4x^2 + 1x - 5) + 1) + 3) + 3) + 1) + 3))^2 - 5((-1(-4(2sin(1\u03c0(3(-4x^2 + 1x - 5)^2 + 3(-4x^2 + 1x - 5) + 1) + 3) + 3) + 1) + 1)/(-1(-4(2sin(1\u03c0(3(-4x^2 + 1x - 5)^2 + 3(-4x^2 + 1x - 5) + 1) + 3) + 3) + 1) + 3)) - 3, g(x) = -2|(-4(3|(-1|(-2|x + 1| - 2) + 1| + 1) + 1| - 2) + 2)| + 1, 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": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1(-4(-1|((1(-3|(1|x + 2| - 3) + 2| - 1) + 3)/(-1(-3|(1|x + 2| - 3) + 2| - 1) + 3)) + 3|)^2 + 5(-1|((1(-3|(1|x + 2| - 3) + 2| - 1) + 3)/(-1(-3|(1|x + 2| - 3) + 2| - 1) + 3)) + 3|)) - 1 and g(x) = -2(-1e^(2(-3(-2(2x + 3)^2 - 4(2x + 3)) - 2)) + 1) + 5 between the vertical lines x = -2.6 and x = -1.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "55.9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2((-1(-5(-2(2cos(3\u03c0(-3|x + 3| - 1) + 3) + 2)^2 - 2(2cos(3\u03c0(-3|x + 3| - 1) + 3) + 2) + 3)^2 + 1(-2(2cos(3\u03c0(-3|x + 3| - 1) + 3) + 2)^2 - 2(2cos(3\u03c0(-3|x + 3| - 1) + 3) + 2) + 3) + 1) - 2)/(-1(-5(-2(2cos(3\u03c0(-3|x + 3| - 1) + 3) + 2)^2 - 2(2cos(3\u03c0(-3|x + 3| - 1) + 3) + 2) + 3)^2 + 1(-2(2cos(3\u03c0(-3|x + 3| - 1) + 3) + 2)^2 - 2(2cos(3\u03c0(-3|x + 3| - 1) + 3) + 2) + 3) + 1))) - 5 and g(x) = 1(-1(1((1(-1x) - 3)/(-2(-1x) + 3))^2 + 2((1(-1x) - 3)/(-2(-1x) + 3)) - 4)^2 - 1(1((1(-1x) - 3)/(-2(-1x) + 3))^2 + 2((1(-1x) - 3)/(-2(-1x) + 3)) - 4)) - 1 from x = -4.2 to x = -4.0. 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) = -2e^(2((2(-3((-1((3(1x - 2))/(-3(1x - 2) + 4)) - 3)/(2((3(1x - 2))/(-3(1x - 2) + 4)) + 2))^2 - 1((-1((3(1x - 2))/(-3(1x - 2) + 4)) - 3)/(2((3(1x - 2))/(-3(1x - 2) + 4)) + 2))) + 3)/(-3(-3((-1((3(1x - 2))/(-3(1x - 2) + 4)) - 3)/(2((3(1x - 2))/(-3(1x - 2) + 4)) + 2))^2 - 1((-1((3(1x - 2))/(-3(1x - 2) + 4)) - 3)/(2((3(1x - 2))/(-3(1x - 2) + 4)) + 2))) + 4))) - 1 and g(x) = -3((-3(4(-2|(2|x + 3| - 1) + 2| + 1)^2 + 1(-2|(2|x + 3| - 1) + 2| + 1) - 5) + 2)/(-3(4(-2|(2|x + 3| - 1) + 2| + 1)^2 + 1(-2|(2|x + 3| - 1) + 2| + 1) - 5) - 1))^2 + 3((-3(4(-2|(2|x + 3| - 1) + 2| + 1)^2 + 1(-2|(2|x + 3| - 1) + 2| + 1) - 5) + 2)/(-3(4(-2|(2|x + 3| - 1) + 2| + 1)^2 + 1(-2|(2|x + 3| - 1) + 2| + 1) - 5) - 1)) - 3 from x = 2.8 to x = 4.8. 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": "Find the area of the region bounded by the curves f(x) = (1(-1(-3|((2(1|(4x^2 + 4x + 1) + 3| + 2) + 2)/(-3(1|(4x^2 + 4x + 1) + 3| + 2) - 3))| + 2)^2 - 2) + 2)/(1(-1(-3|((2(1|(4x^2 + 4x + 1) + 3| + 2) + 2)/(-3(1|(4x^2 + 4x + 1) + 3| + 2) - 3))| + 2)^2 - 2) - 2), g(x) = -3sin(1\u03c0(-2(-1(-2|(-2|x - 1| - 2) + 3|)^2 - 2(-2|(-2|x - 1| - 2) + 3|) - 5)^2 + 4) + 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": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1sin(3\u03c0(4(-1((2(-3|(-1|x + 2| + 1) + 2| + 2) - 3)/(3(-3|(-1|x + 2| + 1) + 2| + 2) - 1))^2 + 1((2(-3|(-1|x + 2| + 1) + 2| + 2) - 3)/(3(-3|(-1|x + 2| + 1) + 2| + 2) - 1)) + 5)^2 + 2(-1((2(-3|(-1|x + 2| + 1) + 2| + 2) - 3)/(3(-3|(-1|x + 2| + 1) + 2| + 2) - 1))^2 + 1((2(-3|(-1|x + 2| + 1) + 2| + 2) - 3)/(3(-3|(-1|x + 2| + 1) + 2| + 2) - 1)) + 5) + 4) - 1) + 1, g(x) = 3|(4(-5((-3(-1e^(-1x) + 3) + 3)/(1(-1e^(-1x) + 3) + 2))^2 + 3((-3(-1e^(-1x) + 3) + 3)/(1(-1e^(-1x) + 3) + 2)))^2 - 1) + 1| + 1, x = -0.9, 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": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2(-1|((-1(-2|(2(1cos(2\u03c0x + 3) + 1) + 2)| - 2) + 2)/(3(-2|(2(1cos(2\u03c0x + 3) + 1) + 2)| - 2))) + 2| + 1) + 3 and g(x) = 5(-3cos(1\u03c0(-3(-1(-1x) + 2)^2 - 1(-1(-1x) + 2) - 3) + 1) - 2) + 4 from x = 4.4 to x = 4.5. 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(2|((1(1|(2|x + 3| + 1) + 3| - 1) - 1)/(1(1|(2|x + 3| + 1) + 3| - 1) + 2)) - 2| - 2)^2 + 2(2|((1(1|(2|x + 3| + 1) + 3| - 1) - 1)/(1(1|(2|x + 3| + 1) + 3| - 1) + 2)) - 2| - 2) + 4) + 2| - 1 and g(x) = 3(2|((2(-1|(1|x + 1| - 2) - 1| + 2) - 3)/(1(-1|(1|x + 1| - 2) - 1| + 2) + 3))| - 2) + 4 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": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2sin(2\u03c0(2|(-2((-1(1(5x - 4) + 2) + 3)/(3(1(5x - 4) + 2) - 1)) + 1) + 3| + 1) - 2) + 1 and g(x) = -3(2|(3(1|(1|x - 1| + 1) - 2| - 2) - 4) + 2| - 1)^2 - 1(2|(3(1|(1|x - 1| + 1) - 2| - 2) - 4) + 2| - 1) + 1 between the vertical lines x = -2.9 and x = -2.4. 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) = 3|(2sin(3\u03c0(-5(-3|(5(-2x^2 + 2x - 2)^2 - 2(-2x^2 + 2x - 2)) - 3| - 2)^2 + 1(-3|(5(-2x^2 + 2x - 2)^2 - 2(-2x^2 + 2x - 2)) - 3| - 2) + 2) + 2) - 2) + 2| + 2 and g(x) = 3(1cos(2\u03c0(3((2((1x)/(3x)) - 3)/(-1((1x)/(3x)) + 2)) - 2) - 1) + 1) + 2 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": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2|(3sin(3\u03c0(-3(-3((-2(-3|x| - 1) - 1)/(1(-3|x| - 1) - 3))^2 + 1((-2(-3|x| - 1) - 1)/(1(-3|x| - 1) - 3)) - 1) + 3)) + 1) + 1| + 2, g(x) = 2|(-4(-4(1|(1sin(1\u03c0x - 3)) - 2|) + 3) - 1) - 3| - 2, x = -2.5, 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": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1|((2((1(-1|(1(-1|x - 1|)^2 + 5(-1|x - 1|) - 2) - 2| - 1))/(1(-1|(1(-1|x - 1|)^2 + 5(-1|x - 1|) - 2) - 2| - 1) + 3)) - 2)/(-2((1(-1|(1(-1|x - 1|)^2 + 5(-1|x - 1|) - 2) - 2| - 1))/(1(-1|(1(-1|x - 1|)^2 + 5(-1|x - 1|) - 2) - 2| - 1) + 3)) - 2)) - 3| and g(x) = 4(-1|((-3((-2(2|x + 1| + 2) - 2)/(-1(2|x + 1| + 2) - 1)) + 3)/(2((-2(2|x + 1| + 2) - 2)/(-1(2|x + 1| + 2) - 1)))) + 2| + 2) + 1 from x = -4.7 to x = -4.4. 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) = 1|(-5(2((1(-2(-3x + 2)) + 2)/(-3(-2(-3x + 2)) - 3)) + 4)^2 - 3(2((1(-2(-3x + 2)) + 2)/(-3(-2(-3x + 2)) - 3)) + 4) - 1)|, g(x) = 1|(2|(-1e^(-2((1(3|x + 3| - 1) + 3)/(-1(3|x + 3| - 1) + 3))) - 3) + 1| + 2) - 2| + 3, 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": "40.7", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (1(-4((-2(3((2(1sin(1\u03c0x)))/(2(1sin(1\u03c0x)) - 1))^2 - 2((2(1sin(1\u03c0x)))/(2(1sin(1\u03c0x)) - 1)) - 4) + 2)/(2(3((2(1sin(1\u03c0x)))/(2(1sin(1\u03c0x)) - 1))^2 - 2((2(1sin(1\u03c0x)))/(2(1sin(1\u03c0x)) - 1)) - 4) + 2))^2 - 3((-2(3((2(1sin(1\u03c0x)))/(2(1sin(1\u03c0x)) - 1))^2 - 2((2(1sin(1\u03c0x)))/(2(1sin(1\u03c0x)) - 1)) - 4) + 2)/(2(3((2(1sin(1\u03c0x)))/(2(1sin(1\u03c0x)) - 1))^2 - 2((2(1sin(1\u03c0x)))/(2(1sin(1\u03c0x)) - 1)) - 4) + 2)) + 4) - 1)/(-2(-4((-2(3((2(1sin(1\u03c0x)))/(2(1sin(1\u03c0x)) - 1))^2 - 2((2(1sin(1\u03c0x)))/(2(1sin(1\u03c0x)) - 1)) - 4) + 2)/(2(3((2(1sin(1\u03c0x)))/(2(1sin(1\u03c0x)) - 1))^2 - 2((2(1sin(1\u03c0x)))/(2(1sin(1\u03c0x)) - 1)) - 4) + 2))^2 - 3((-2(3((2(1sin(1\u03c0x)))/(2(1sin(1\u03c0x)) - 1))^2 - 2((2(1sin(1\u03c0x)))/(2(1sin(1\u03c0x)) - 1)) - 4) + 2)/(2(3((2(1sin(1\u03c0x)))/(2(1sin(1\u03c0x)) - 1))^2 - 2((2(1sin(1\u03c0x)))/(2(1sin(1\u03c0x)) - 1)) - 4) + 2)) + 4) + 1), g(x) = -1|(-1(-1|((-3(-3|x - 3| + 2) - 2)/(1(-3|x - 3| + 2))) + 1| - 2) - 5) + 1| + 2, x = 3.4, 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": "29.8", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -5(-5(-2(-2((2((-2x - 2)/(2x - 3)) + 3)/(-1((-2x - 2)/(2x - 3)) + 2)) + 2)) - 4) - 2, g(x) = 3|(3sin(2\u03c0(-4(-2((1x + 3)/(2x)) - 5)^2 + 4(-2((1x + 3)/(2x)) - 5) - 3) + 2) - 1) + 3| + 3, 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": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (1(1cos(1\u03c0(1(-4(3(4x + 3) + 5)^2 + 5(3(4x + 3) + 5) + 3)^2 + 4(-4(3(4x + 3) + 5)^2 + 5(3(4x + 3) + 5) + 3) + 1) - 1) - 1) + 2)/(2(1cos(1\u03c0(1(-4(3(4x + 3) + 5)^2 + 5(3(4x + 3) + 5) + 3)^2 + 4(-4(3(4x + 3) + 5)^2 + 5(3(4x + 3) + 5) + 3) + 1) - 1) - 1) - 1) and g(x) = -5(-2(-2cos(3\u03c0((-3(5x + 3) + 3)/(-2(5x + 3) + 1))) + 2)^2 + 4(-2cos(3\u03c0((-3(5x + 3) + 3)/(-2(5x + 3) + 1))) + 2) + 3)^2 + 4(-2(-2cos(3\u03c0((-3(5x + 3) + 3)/(-2(5x + 3) + 1))) + 2)^2 + 4(-2cos(3\u03c0((-3(5x + 3) + 3)/(-2(5x + 3) + 1))) + 2) + 3) + 4 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": "72.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 3(-2(-1|((3(-5(1x^2 + 4x - 2)^2 - 1(1x^2 + 4x - 2)) - 3)/(-3(-5(1x^2 + 4x - 2)^2 - 1(1x^2 + 4x - 2)) + 2)) - 1| + 2) + 2) - 1 and g(x) = 1(-3|(5(3((-2x - 1)/(-3x + 1)) + 1)^2 + 3(3((-2x - 1)/(-3x + 1)) + 1) + 4) - 3| + 2)^2 - 5(-3|(5(3((-2x - 1)/(-3x + 1)) + 1)^2 + 3(3((-2x - 1)/(-3x + 1)) + 1) + 4) - 3| + 2) + 2 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": "0.7", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 3cos(2\u03c0((-2((2(2((1(5x^2 - 5x - 4) + 1)/(2(5x^2 - 5x - 4) + 2))^2 - 4((1(5x^2 - 5x - 4) + 1)/(2(5x^2 - 5x - 4) + 2)) - 2) + 2)/(1(2((1(5x^2 - 5x - 4) + 1)/(2(5x^2 - 5x - 4) + 2))^2 - 4((1(5x^2 - 5x - 4) + 1)/(2(5x^2 - 5x - 4) + 2)) - 2) - 3)) - 1)/(2((2(2((1(5x^2 - 5x - 4) + 1)/(2(5x^2 - 5x - 4) + 2))^2 - 4((1(5x^2 - 5x - 4) + 1)/(2(5x^2 - 5x - 4) + 2)) - 2) + 2)/(1(2((1(5x^2 - 5x - 4) + 1)/(2(5x^2 - 5x - 4) + 2))^2 - 4((1(5x^2 - 5x - 4) + 1)/(2(5x^2 - 5x - 4) + 2)) - 2) - 3)) + 3)) - 3) + 1 and g(x) = -2(-3|(3|((1((-1x + 1)/(2x - 1)))/(2((-1x + 1)/(2x - 1)) + 1))| - 1)| + 1)^2 + 3(-3|(3|((1((-1x + 1)/(2x - 1)))/(2((-1x + 1)/(2x - 1)) + 1))| - 1)| + 1) + 5 between the vertical lines x = 0.8 and x = 1.2. 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) = 1(-2((3((-2(-1|(-1|x + 2| + 2)|) + 1)/(-2(-1|(-1|x + 2| + 2)|) - 3)) + 2)/(-2((-2(-1|(-1|x + 2| + 2)|) + 1)/(-2(-1|(-1|x + 2| + 2)|) - 3)) + 3)) + 4) - 5 and g(x) = (1(1(3e^(-1((2(-1|x - 2| + 3) - 2)/(2(-1|x - 2| + 3) + 3))))^2 + 2(3e^(-1((2(-1|x - 2| + 3) - 2)/(2(-1|x - 2| + 3) + 3)))) - 2) + 2)/(2(1(3e^(-1((2(-1|x - 2| + 3) - 2)/(2(-1|x - 2| + 3) + 3))))^2 + 2(3e^(-1((2(-1|x - 2| + 3) - 2)/(2(-1|x - 2| + 3) + 3)))) - 2)) between the vertical lines x = -1.0 and x = 1.0. 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": "Find the area of the region bounded by the curves f(x) = -4(-2cos(3\u03c0(-2(1|((2(-4x + 2) - 1)/(-1(-4x + 2))) + 2| - 2) + 3) + 3) - 2) - 3, g(x) = 1((-1(5((-3((-1x + 3)/(-2x + 3)) + 2)/(1((-1x + 3)/(-2x + 3))))^2 - 2((-3((-1x + 3)/(-2x + 3)) + 2)/(1((-1x + 3)/(-2x + 3)))) + 3) + 1)/(-1(5((-3((-1x + 3)/(-2x + 3)) + 2)/(1((-1x + 3)/(-2x + 3))))^2 - 2((-3((-1x + 3)/(-2x + 3)) + 2)/(1((-1x + 3)/(-2x + 3)))) + 3) - 3))^2 + 4((-1(5((-3((-1x + 3)/(-2x + 3)) + 2)/(1((-1x + 3)/(-2x + 3))))^2 - 2((-3((-1x + 3)/(-2x + 3)) + 2)/(1((-1x + 3)/(-2x + 3)))) + 3) + 1)/(-1(5((-3((-1x + 3)/(-2x + 3)) + 2)/(1((-1x + 3)/(-2x + 3))))^2 - 2((-3((-1x + 3)/(-2x + 3)) + 2)/(1((-1x + 3)/(-2x + 3)))) + 3) - 3)) + 3, 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2(2cos(1\u03c0(-1(3|(2|((-1x + 2)/(3x + 3)) - 1| - 1) + 1| + 2) - 3) + 3) - 3)^2 + 5(2cos(1\u03c0(-1(3|(2|((-1x + 2)/(3x + 3)) - 1| - 1) + 1| + 2) - 3) + 3) - 3) + 3, g(x) = 5((2((-3((1(-2|x - 3| + 3) + 1)/(-1(-2|x - 3| + 3) + 3)) + 2)/(-2((1(-2|x - 3| + 3) + 1)/(-1(-2|x - 3| + 3) + 3)))) - 1)/(-2((-3((1(-2|x - 3| + 3) + 1)/(-1(-2|x - 3| + 3) + 3)) + 2)/(-2((1(-2|x - 3| + 3) + 1)/(-1(-2|x - 3| + 3) + 3)))) + 3))^2 + 4((2((-3((1(-2|x - 3| + 3) + 1)/(-1(-2|x - 3| + 3) + 3)) + 2)/(-2((1(-2|x - 3| + 3) + 1)/(-1(-2|x - 3| + 3) + 3)))) - 1)/(-2((-3((1(-2|x - 3| + 3) + 1)/(-1(-2|x - 3| + 3) + 3)) + 2)/(-2((1(-2|x - 3| + 3) + 1)/(-1(-2|x - 3| + 3) + 3)))) + 3)) + 1, 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": "0.9", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1(-3((3(2|(-3(-2|x| + 2) + 2) - 2| - 1) - 3)/(-1(2|(-3(-2|x| + 2) + 2) - 2| - 1) + 2)) - 4) and g(x) = 2((3(2|((-3((2x - 1)/(-1x - 2)) + 1)/(-1((2x - 1)/(-1x - 2)) - 3))| + 1) - 1)/(-2(2|((-3((2x - 1)/(-1x - 2)) + 1)/(-1((2x - 1)/(-1x - 2)) - 3))| + 1) - 3)) - 5 between the vertical lines x = -1.6 and x = -0.1. 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) = (2(-3|((2(2(1(-1e^(1x) - 3)^2 - 1(-1e^(1x) - 3) + 4) + 2) + 1)/(3(2(1(-1e^(1x) - 3)^2 - 1(-1e^(1x) - 3) + 4) + 2) + 1)) + 2| - 2) - 2)/(2(-3|((2(2(1(-1e^(1x) - 3)^2 - 1(-1e^(1x) - 3) + 4) + 2) + 1)/(3(2(1(-1e^(1x) - 3)^2 - 1(-1e^(1x) - 3) + 4) + 2) + 1)) + 2| - 2) + 1), g(x) = 5(1|(5(-3|((3x - 3)/(-3x - 3)) - 3| - 1)^2 + 4(-3|((3x - 3)/(-3x - 3)) - 3| - 1) + 1) - 3| - 2), 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": "5.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 3sin(1\u03c0(3|((2(-3(-2|((1x - 1)/(-1x - 2))|) + 1) - 1)/(-2(-3(-2|((1x - 1)/(-1x - 2))|) + 1))) - 2|) - 1) and g(x) = -3cos(2\u03c0(-2|((1(2|(-3x^2 + 1x - 3) + 3|) + 1)/(-2(2|(-3x^2 + 1x - 3) + 3|) + 1)) - 2| + 2) - 1) + 1 from x = 0.7 to x = 0.7999999999999999. 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(5(-3((1((-2(2|x| - 2) - 1)/(-1(2|x| - 2) + 3)) + 3)/(-3((-2(2|x| - 2) - 1)/(-1(2|x| - 2) + 3)) + 1))) - 3) + 2)/(-2(5(-3((1((-2(2|x| - 2) - 1)/(-1(2|x| - 2) + 3)) + 3)/(-3((-2(2|x| - 2) - 1)/(-1(2|x| - 2) + 3)) + 1))) - 3) + 1) and g(x) = 5(3sin(2\u03c0(-2|(-2(-2|x + 1| + 2)^2 - 3) + 1| + 1)) + 3)^2 - 4(3sin(2\u03c0(-2|(-2(-2|x + 1| + 2)^2 - 3) + 1| + 1)) + 3) - 3 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": "2.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1|(1(-1(-1|((-1((1x + 1)/(-3x - 2)) - 3)/(2((1x + 1)/(-3x - 2)) + 1)) + 1| - 3))^2 + 3(-1(-1|((-1((1x + 1)/(-3x - 2)) - 3)/(2((1x + 1)/(-3x - 2)) + 1)) + 1| - 3)) - 3)| + 2 and g(x) = 3|(2(-2cos(3\u03c0(-3(1|x + 1| - 1)^2 - 3(1|x + 1| - 1) + 3) - 2) - 1) - 3) - 2| + 2 between the vertical lines x = -0.8 and x = -0.6. 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": "Find the area of the region bounded by the curves f(x) = (3(1|(-3(4(4(3cos(1\u03c0x - 1) + 1) - 2) - 1))| - 2) - 2)/(1(1|(-3(4(4(3cos(1\u03c0x - 1) + 1) - 2) - 1))| - 2) - 3), g(x) = 2e^(-1((2((-1((-3(4x^2 - 4))/(-1(4x^2 - 4))) + 2)/(3((-3(4x^2 - 4))/(-1(4x^2 - 4))) + 1)) + 3)/(-2((-1((-3(4x^2 - 4))/(-1(4x^2 - 4))) + 2)/(3((-3(4x^2 - 4))/(-1(4x^2 - 4))) + 1)) + 3))) - 3, x = -2.2, 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": "6.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3|(-3(3|(-1(-2cos(1\u03c0(-1|x + 2| - 3) + 3) + 2)^2 + 4) - 1| + 1)^2 + 2(3|(-1(-2cos(1\u03c0(-1|x + 2| - 3) + 3) + 2)^2 + 4) - 1| + 1) - 1) - 3|, g(x) = -2(-4(1((-1(1|x + 1| - 1) + 3)/(2(1|x + 1| - 1) - 3))^2 + 3((-1(1|x + 1| - 1) + 3)/(2(1|x + 1| - 1) - 3)) + 4)^2 + 2(1((-1(1|x + 1| - 1) + 3)/(2(1|x + 1| - 1) - 3))^2 + 3((-1(1|x + 1| - 1) + 3)/(2(1|x + 1| - 1) - 3)) + 4) + 1) + 4, x = -4.5, 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": "21.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2(1((-2(-1(-4(1x^2 - 1x + 5) - 1)^2 + 3(-4(1x^2 - 1x + 5) - 1) + 2))/(-1(-1(-4(1x^2 - 1x + 5) - 1)^2 + 3(-4(1x^2 - 1x + 5) - 1) + 2) - 3)) - 1)^2 - 1(1((-2(-1(-4(1x^2 - 1x + 5) - 1)^2 + 3(-4(1x^2 - 1x + 5) - 1) + 2))/(-1(-1(-4(1x^2 - 1x + 5) - 1)^2 + 3(-4(1x^2 - 1x + 5) - 1) + 2) - 3)) - 1) and g(x) = -5(1sin(1\u03c0(1(-5(3x - 3)^2 - 3(3x - 3) - 1)^2 - 2(-5(3x - 3)^2 - 3(3x - 3) - 1) - 2) - 2) + 1) - 3 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 3e^(2(-4(1(1((-2(-3|x| + 3) + 2)/(2(-3|x| + 3) - 1)) + 5)^2 - 2(1((-2(-3|x| + 3) + 2)/(2(-3|x| + 3) - 1)) + 5) - 4)^2 + 4(1(1((-2(-3|x| + 3) + 2)/(2(-3|x| + 3) - 1)) + 5)^2 - 2(1((-2(-3|x| + 3) + 2)/(2(-3|x| + 3) - 1)) + 5) - 4) + 2)) - 2 and g(x) = 1(2e^(-1((-1(-1((-3x + 1)/(1x))^2 - 2) - 3)/(1(-1((-3x + 1)/(1x))^2 - 2) + 2))) + 1)^2 + 2(2e^(-1((-1(-1((-3x + 1)/(1x))^2 - 2) - 3)/(1(-1((-3x + 1)/(1x))^2 - 2) + 2))) + 1) + 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": "5.4", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1(-3sin(2\u03c0((1(-3(-1(-3x - 4) + 1)^2 - 5(-1(-3x - 4) + 1) + 4) + 2)/(3(-3(-1(-3x - 4) + 1)^2 - 5(-1(-3x - 4) + 1) + 4) + 1)) + 3))^2 + 1(-3sin(2\u03c0((1(-3(-1(-3x - 4) + 1)^2 - 5(-1(-3x - 4) + 1) + 4) + 2)/(3(-3(-1(-3x - 4) + 1)^2 - 5(-1(-3x - 4) + 1) + 4) + 1)) + 3)) - 1 and g(x) = 2(-1|(3sin(3\u03c0(-3(-2|x - 2| + 3)) + 3) + 2) - 3| + 3)^2 - 3(-1|(3sin(3\u03c0(-3(-2|x - 2| + 3)) + 3) + 2) - 3| + 3) + 3 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": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2(-1((1(-1(2(-4x)^2 + 3(-4x))^2 + 5(2(-4x)^2 + 3(-4x)) - 1))/(1(-1(2(-4x)^2 + 3(-4x))^2 + 5(2(-4x)^2 + 3(-4x)) - 1) - 3))^2 + 4((1(-1(2(-4x)^2 + 3(-4x))^2 + 5(2(-4x)^2 + 3(-4x)) - 1))/(1(-1(2(-4x)^2 + 3(-4x))^2 + 5(2(-4x)^2 + 3(-4x)) - 1) - 3)) + 3) and g(x) = (-3((-2(1|(2e^(1((-1x - 3)/(2x))) - 3) - 1| + 3) - 3)/(3(1|(2e^(1((-1x - 3)/(2x))) - 3) - 1| + 3) + 2)))/(-3((-2(1|(2e^(1((-1x - 3)/(2x))) - 3) - 1| + 3) - 3)/(3(1|(2e^(1((-1x - 3)/(2x))) - 3) - 1| + 3) + 2)) + 2) from x = -0.0 to x = 0.4. 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": "Find the area of the region bounded by the curves f(x) = 1|(2(2cos(3\u03c0(-3|(-1(4x + 3) - 5) + 3| - 1) + 1) - 3)^2 - 1(2cos(3\u03c0(-3|(-1(4x + 3) - 5) + 3| - 1) + 1) - 3) - 1) - 1| - 3, g(x) = 2|(-3|((2(-1e^(2(2x^2 + 5x + 3)) + 3) - 2)/(3(-1e^(2(2x^2 + 5x + 3)) + 3) - 1)) - 2| + 1) - 1| + 3, 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": "2.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2|(5(-5((1(2|(4x^2 + 4x + 4) - 3| + 2) - 3)/(-1(2|(4x^2 + 4x + 4) - 3| + 2) - 2))^2 - 5((1(2|(4x^2 + 4x + 4) - 3| + 2) - 3)/(-1(2|(4x^2 + 4x + 4) - 3| + 2) - 2)) - 1)^2 - 5(-5((1(2|(4x^2 + 4x + 4) - 3| + 2) - 3)/(-1(2|(4x^2 + 4x + 4) - 3| + 2) - 2))^2 - 5((1(2|(4x^2 + 4x + 4) - 3| + 2) - 3)/(-1(2|(4x^2 + 4x + 4) - 3| + 2) - 2)) - 1) + 1) - 3| + 1, g(x) = 1(-1(1(-4(4x)^2 + 3(4x) + 1) - 4)^2 - 5(1(-4(4x)^2 + 3(4x) + 1) - 4) - 2) + 5, 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": "5.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2|(1|((3(-1|((-1(-5x^2 - 2x + 2) - 2)/(-2(-5x^2 - 2x + 2) - 2)) + 1| + 3) + 3)/(2(-1|((-1(-5x^2 - 2x + 2) - 2)/(-2(-5x^2 - 2x + 2) - 2)) + 1| + 3) - 1)) - 1| + 2) + 3| + 1 and g(x) = -2(4((-2(5(1|x + 2| - 2)^2 - 1(1|x + 2| - 2) - 1) + 2)/(1(5(1|x + 2| - 2)^2 - 1(1|x + 2| - 2) - 1) + 2))^2 - 4((-2(5(1|x + 2| - 2)^2 - 1(1|x + 2| - 2) - 1) + 2)/(1(5(1|x + 2| - 2)^2 - 1(1|x + 2| - 2) - 1) + 2))) - 3 from x = -0.2 to x = 0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -3sin(1\u03c0(3(2|((-1(-1(4x^2 - 5) + 3) + 1)/(1(-1(4x^2 - 5) + 3) - 2)) - 3| - 3) - 3)) + 1, g(x) = 2e^(2(-2((-1(1((1x)/(-1x - 1)) - 2))/(2(1((1x)/(-1x - 1)) - 2) + 2))^2 + 2((-1(1((1x)/(-1x - 1)) - 2))/(2(1((1x)/(-1x - 1)) - 2) + 2)) - 3)) - 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": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2((1(3|((1(-2|(2sin(1\u03c0x) - 3) + 2| - 2) + 2)/(-2(-2|(2sin(1\u03c0x) - 3) + 2| - 2) + 3)) + 3|) + 2)/(-2(3|((1(-2|(2sin(1\u03c0x) - 3) + 2| - 2) + 2)/(-2(-2|(2sin(1\u03c0x) - 3) + 2| - 2) + 3)) + 3|) + 3)) + 2, g(x) = (1(-3sin(1\u03c0(-1|(-2|(5x^2 + 3x - 2) + 1| + 2) + 3| - 2) + 2) + 2) - 2)/(-3(-3sin(1\u03c0(-1|(-2|(5x^2 + 3x - 2) + 1| + 2) + 3| - 2) + 2) + 2) + 1), 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) = -3e^(1(2|(-1(2|(1|(-2x^2 + 5x + 4)| - 3) + 1| - 2) + 2) - 2| - 1)) + 3 and g(x) = 5(-1(3(-2sin(3\u03c0(1x^2 - 4x - 2) + 3) - 2)^2 + 2(-2sin(3\u03c0(1x^2 - 4x - 2) + 3) - 2)) - 3) + 3 between the vertical lines x = 2.9 and x = 3.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "50.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 3((-3((1(-1|(-1|((-1x + 1)/(-2x + 3)) + 3| + 2) - 2| + 3) + 3)/(-2(-1|(-1|((-1x + 1)/(-2x + 3)) + 3| + 2) - 2| + 3))))/(-2((1(-1|(-1|((-1x + 1)/(-2x + 3)) + 3| + 2) - 2| + 3) + 3)/(-2(-1|(-1|((-1x + 1)/(-2x + 3)) + 3| + 2) - 2| + 3))) - 1)) and g(x) = (1((2(2|(4(5x + 4) - 5) + 3| + 2) + 1)/(1(2|(4(5x + 4) - 5) + 3| + 2) + 1)) - 2)/(1((2(2|(4(5x + 4) - 5) + 3| + 2) + 1)/(1(2|(4(5x + 4) - 5) + 3| + 2) + 1))) 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": "8.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-1(3|((-2(-1e^(1(-3|(1x^2 + 1x) + 1| - 2))) + 2)/(-3(-1e^(1(-3|(1x^2 + 1x) + 1| - 2)))))| - 3) - 2)/(-3(3|((-2(-1e^(1(-3|(1x^2 + 1x) + 1| - 2))) + 2)/(-3(-1e^(1(-3|(1x^2 + 1x) + 1| - 2)))))| - 3) - 2) and g(x) = -3((1(-3(-5((-2x + 2)/(3x - 2))^2 - 3((-2x + 2)/(3x - 2)) + 2)) - 2)/(-2(-3(-5((-2x + 2)/(3x - 2))^2 - 3((-2x + 2)/(3x - 2)) + 2)))) from x = 0.2 to x = 0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3(2((3(-2|(-1cos(2\u03c0(-1x - 1) + 1) - 1) + 3| + 3) - 3)/(-3(-2|(-1cos(2\u03c0(-1x - 1) + 1) - 1) + 3| + 3) - 3))^2 + 4((3(-2|(-1cos(2\u03c0(-1x - 1) + 1) - 1) + 3| + 3) - 3)/(-3(-2|(-1cos(2\u03c0(-1x - 1) + 1) - 1) + 3| + 3) - 3)) + 4)^2 - 5(2((3(-2|(-1cos(2\u03c0(-1x - 1) + 1) - 1) + 3| + 3) - 3)/(-3(-2|(-1cos(2\u03c0(-1x - 1) + 1) - 1) + 3| + 3) - 3))^2 + 4((3(-2|(-1cos(2\u03c0(-1x - 1) + 1) - 1) + 3| + 3) - 3)/(-3(-2|(-1cos(2\u03c0(-1x - 1) + 1) - 1) + 3| + 3) - 3)) + 4) + 2 and g(x) = -2|(1(-2(-1|((2x - 2)/(1x)) + 2| - 2) + 5)^2 + 2) - 3| - 2 from x = 4.5 to x = 4.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "126.4", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1|(5(1|(3(1(3x + 3)^2) + 4) - 3| - 3)^2 - 2(1|(3(1(3x + 3)^2) + 4) - 3| - 3))| + 2 and g(x) = (-1((-2(1(-2(-1|x + 2| + 2)^2 + 4(-1|x + 2| + 2) + 5)^2 + 3(-2(-1|x + 2| + 2)^2 + 4(-1|x + 2| + 2) + 5) + 3) - 3)/(-3(1(-2(-1|x + 2| + 2)^2 + 4(-1|x + 2| + 2) + 5)^2 + 3(-2(-1|x + 2| + 2)^2 + 4(-1|x + 2| + 2) + 5) + 3) - 2)))/(2((-2(1(-2(-1|x + 2| + 2)^2 + 4(-1|x + 2| + 2) + 5)^2 + 3(-2(-1|x + 2| + 2)^2 + 4(-1|x + 2| + 2) + 5) + 3) - 3)/(-3(1(-2(-1|x + 2| + 2)^2 + 4(-1|x + 2| + 2) + 5)^2 + 3(-2(-1|x + 2| + 2)^2 + 4(-1|x + 2| + 2) + 5) + 3) - 2)) + 2) between the vertical lines x = -0.8 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) = -1|((-3(1sin(1\u03c0((2(-3(-1x - 4)^2 + 1(-1x - 4) + 5) - 3)/(-3(-3(-1x - 4)^2 + 1(-1x - 4) + 5) + 4)) - 3) - 2) - 2)/(1(1sin(1\u03c0((2(-3(-1x - 4)^2 + 1(-1x - 4) + 5) - 3)/(-3(-3(-1x - 4)^2 + 1(-1x - 4) + 5) + 4)) - 3) - 2) - 3)) - 1| + 2 and g(x) = -2(-3|((-1((2(-3x - 3) - 1)/(-3(-3x - 3))) + 1)/(-1((2(-3x - 3) - 1)/(-3(-3x - 3))) + 2)) - 1|) - 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": "Calculate the area enclosed between the functions f(x) = (-1(-3((1(-2e^(1(4(5x + 4) - 4)) + 3) - 3)/(2(-2e^(1(4(5x + 4) - 4)) + 3) - 1)) - 1) - 3)/(-1(-3((1(-2e^(1(4(5x + 4) - 4)) + 3) - 3)/(2(-2e^(1(4(5x + 4) - 4)) + 3) - 1)) - 1) + 3) and g(x) = 5(-1(-2(-1|(3x^2 + 3x - 1) - 3| + 1) - 5)^2 + 1(-2(-1|(3x^2 + 3x - 1) - 3| + 1) - 5) + 4) + 4 from x = 0.3 to x = 1.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "74.6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (1(-5(1(3(-3(-3x^2 - 1x + 4)^2 + 4) + 2)^2 - 1(3(-3(-3x^2 - 1x + 4)^2 + 4) + 2) - 5) + 1))/(-1(-5(1(3(-3(-3x^2 - 1x + 4)^2 + 4) + 2)^2 - 1(3(-3(-3x^2 - 1x + 4)^2 + 4) + 2) - 5) + 1)) and g(x) = -1(-1(-1|(-3sin(1\u03c0(-2x + 2) + 3) + 2) + 3| - 1) - 5)^2 + 2(-1(-1|(-3sin(1\u03c0(-2x + 2) + 3) + 2) + 3| - 1) - 5) + 2 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": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 3|(1|(-4(-5(-3(1x + 1)^2 + 1(1x + 1) + 4) + 4) - 4)| - 2) + 2| - 2 and g(x) = -4(-2|(5(2((1x)/(-2x - 3))^2 - 5((1x)/(-2x - 3)) - 4) + 5) - 3| + 2) + 5 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": "5.6", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -5(-2((2(-4(-1((-2x - 2)/(-2x - 3)) - 3) - 4) + 3)/(-2(-4(-1((-2x - 2)/(-2x - 3)) - 3) - 4) - 1)) - 1)^2 - 1(-2((2(-4(-1((-2x - 2)/(-2x - 3)) - 3) - 4) + 3)/(-2(-4(-1((-2x - 2)/(-2x - 3)) - 3) - 4) - 1)) - 1) - 1 and g(x) = -3|(1|((-1(-4((3x - 3)/(3x - 2)) - 3) + 1)/(2(-4((3x - 3)/(3x - 2)) - 3) + 3))| - 3) + 2| + 1 between the vertical lines x = 0.9 and x = 1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (3(1|(2(1(-2(3|x| - 2) + 4))^2 + 2(1(-2(3|x| - 2) + 4)) + 3) - 3|) + 2)/(2(1|(2(1(-2(3|x| - 2) + 4))^2 + 2(1(-2(3|x| - 2) + 4)) + 3) - 3|) - 3) and g(x) = (-3(4(3cos(1\u03c0(-1|(4x - 3) - 2| + 3) - 3) - 3)^2 + 1(3cos(1\u03c0(-1|(4x - 3) - 2| + 3) - 3) - 3) + 4) - 3)/(3(4(3cos(1\u03c0(-1|(4x - 3) - 2| + 3) - 3) - 3)^2 + 1(3cos(1\u03c0(-1|(4x - 3) - 2| + 3) - 3) - 3) + 4) - 1) between the vertical lines x = -1.5 and x = -1.4. 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) = -3cos(3\u03c0(2|(5((3(-1(-1|x + 3| + 1) - 2) + 2)/(-2(-1(-1|x + 3| + 1) - 2) - 2)) - 3) - 3| - 1) + 1) - 3, g(x) = -3cos(2\u03c0(-1((3(-1|(4x - 5) + 1|) + 1)/(3(-1|(4x - 5) + 1|) + 1)) + 2) + 2) - 2, 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(2(-5((-3(3cos(3\u03c0(1x^2 - 4x - 2) + 3) - 2) - 1)/(2(3cos(3\u03c0(1x^2 - 4x - 2) + 3) - 2))) + 2)^2 + 3(-5((-3(3cos(3\u03c0(1x^2 - 4x - 2) + 3) - 2) - 1)/(2(3cos(3\u03c0(1x^2 - 4x - 2) + 3) - 2))) + 2) - 4) + 3)/(2(2(-5((-3(3cos(3\u03c0(1x^2 - 4x - 2) + 3) - 2) - 1)/(2(3cos(3\u03c0(1x^2 - 4x - 2) + 3) - 2))) + 2)^2 + 3(-5((-3(3cos(3\u03c0(1x^2 - 4x - 2) + 3) - 2) - 1)/(2(3cos(3\u03c0(1x^2 - 4x - 2) + 3) - 2))) + 2) - 4) - 1), g(x) = -1((2((-1((3(2e^(2x) + 3) - 1)/(2(2e^(2x) + 3) + 3)) - 3)/(-1((3(2e^(2x) + 3) - 1)/(2(2e^(2x) + 3) + 3)) - 1)))/(-1((-1((3(2e^(2x) + 3) - 1)/(2(2e^(2x) + 3) + 3)) - 3)/(-1((3(2e^(2x) + 3) - 1)/(2(2e^(2x) + 3) + 3)) - 1)) + 3)) + 5, x = -2.1, 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (2(3(1|(1((3(-4x^2 - 2x - 2) - 1)/(1(-4x^2 - 2x - 2) + 2)) - 3) + 3| - 2)) + 3)/(-3(3(1|(1((3(-4x^2 - 2x - 2) - 1)/(1(-4x^2 - 2x - 2) + 2)) - 3) + 3| - 2)) - 1) and g(x) = -3((-3(4(2|((-3x - 3)/(-3x)) + 2| - 2)^2 - 5(2|((-3x - 3)/(-3x)) + 2| - 2) - 5) - 1)/(2(4(2|((-3x - 3)/(-3x)) + 2| - 2)^2 - 5(2|((-3x - 3)/(-3x)) + 2| - 2) - 5) + 3)) - 4 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": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -5((-1((1(2cos(3\u03c0((-2(-2x^2 - 4x + 2) + 3)/(-1(-2x^2 - 4x + 2) + 2)) + 1) + 2) + 2)/(2(2cos(3\u03c0((-2(-2x^2 - 4x + 2) + 3)/(-1(-2x^2 - 4x + 2) + 2)) + 1) + 2) - 3)) + 2)/(1((1(2cos(3\u03c0((-2(-2x^2 - 4x + 2) + 3)/(-1(-2x^2 - 4x + 2) + 2)) + 1) + 2) + 2)/(2(2cos(3\u03c0((-2(-2x^2 - 4x + 2) + 3)/(-1(-2x^2 - 4x + 2) + 2)) + 1) + 2) - 3))))^2 + 3((-1((1(2cos(3\u03c0((-2(-2x^2 - 4x + 2) + 3)/(-1(-2x^2 - 4x + 2) + 2)) + 1) + 2) + 2)/(2(2cos(3\u03c0((-2(-2x^2 - 4x + 2) + 3)/(-1(-2x^2 - 4x + 2) + 2)) + 1) + 2) - 3)) + 2)/(1((1(2cos(3\u03c0((-2(-2x^2 - 4x + 2) + 3)/(-1(-2x^2 - 4x + 2) + 2)) + 1) + 2) + 2)/(2(2cos(3\u03c0((-2(-2x^2 - 4x + 2) + 3)/(-1(-2x^2 - 4x + 2) + 2)) + 1) + 2) - 3)))) + 2, g(x) = -5(-2e^(-1(1((-1((2x + 2)/(2x)) + 3)/(2((2x + 2)/(2x)) + 2))^2 - 5((-1((2x + 2)/(2x)) + 3)/(2((2x + 2)/(2x)) + 2)))) + 3) + 5, 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": "1.9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2((-1((-3(-1(4(-1x + 5) - 5) + 3) - 1)/(2(-1(4(-1x + 5) - 5) + 3) - 1)))/(-1((-3(-1(4(-1x + 5) - 5) + 3) - 1)/(2(-1(4(-1x + 5) - 5) + 3) - 1)) - 3))^2 - 3((-1((-3(-1(4(-1x + 5) - 5) + 3) - 1)/(2(-1(4(-1x + 5) - 5) + 3) - 1)))/(-1((-3(-1(4(-1x + 5) - 5) + 3) - 1)/(2(-1(4(-1x + 5) - 5) + 3) - 1)) - 3)) - 1 and g(x) = -1sin(3\u03c0(-3(-1|((3(-3|x - 1| + 1) + 2)/(-1(-3|x - 1| + 1) + 2)) - 2| + 2)^2 - 2(-1|((3(-3|x - 1| + 1) + 2)/(-1(-3|x - 1| + 1) + 2)) - 2| + 2) + 5) + 1) + 1 from x = -0.8 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": "Calculate the area enclosed between the functions f(x) = -1|(-1|(1(-2((3((-3x + 1)/(1x + 3)))/(2((-3x + 1)/(1x + 3)) + 2)) + 5))|)| + 2 and g(x) = -1sin(3\u03c0(5((-3((2(-2|x - 1| + 3) + 1)/(-3(-2|x - 1| + 3) + 4)))/(3((2(-2|x - 1| + 3) + 1)/(-3(-2|x - 1| + 3) + 4)) + 3))^2 + 5((-3((2(-2|x - 1| + 3) + 1)/(-3(-2|x - 1| + 3) + 4)))/(3((2(-2|x - 1| + 3) + 1)/(-3(-2|x - 1| + 3) + 4)) + 3)) - 2)) - 1 from x = -2.4 to x = -2.3. 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) = (3(3((1(-2(-3|((3x + 2)/(-1x - 3)) - 1| + 1)^2 + 3(-3|((3x + 2)/(-1x - 3)) - 1| + 1) + 5) - 1)/(1(-2(-3|((3x + 2)/(-1x - 3)) - 1| + 1)^2 + 3(-3|((3x + 2)/(-1x - 3)) - 1| + 1) + 5) + 3)) + 5))/(1(3((1(-2(-3|((3x + 2)/(-1x - 3)) - 1| + 1)^2 + 3(-3|((3x + 2)/(-1x - 3)) - 1| + 1) + 5) - 1)/(1(-2(-3|((3x + 2)/(-1x - 3)) - 1| + 1)^2 + 3(-3|((3x + 2)/(-1x - 3)) - 1| + 1) + 5) + 3)) + 5) + 3) and g(x) = 1((3(-3|(-2cos(3\u03c0(-5x^2 + 1x + 2)) - 1) + 2|) + 1)/(-1(-3|(-2cos(3\u03c0(-5x^2 + 1x + 2)) - 1) + 2|) + 3)) - 3 between the vertical lines x = -1.5 and x = -0.8. 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": "Find the area of the region bounded by the curves f(x) = 1|(3(-3|(-1cos(3\u03c0(-5(-3|x - 1| - 2)^2 - 2(-3|x - 1| - 2) + 3) + 1) + 1) - 3| + 3)^2 + 4(-3|(-1cos(3\u03c0(-5(-3|x - 1| - 2)^2 - 2(-3|x - 1| - 2) + 3) + 1) + 1) - 3| + 3) + 4) - 3| - 2, g(x) = -1(2e^(-1(1|(5(3x^2 - 3x + 1) + 5) + 2| - 3)) - 2)^2 - 4(2e^(-1(1|(5(3x^2 - 3x + 1) + 5) + 2| - 3)) - 2) + 4, x = 3.5, 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": "2.7", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1e^(-2(-1|(-5((-1((-1((-1x - 2)/(3x + 2)) - 1)/(-2((-1x - 2)/(3x + 2)) + 3)) - 2)/(2((-1((-1x - 2)/(3x + 2)) - 1)/(-2((-1x - 2)/(3x + 2)) + 3)) - 3))) - 1| + 2)) - 3 and g(x) = 3sin(1\u03c0(5((-1(-5(-2|x - 3|)^2 - 2(-2|x - 3|) - 1) + 2)/(-3(-5(-2|x - 3|)^2 - 2(-2|x - 3|) - 1) + 1))^2 - 1((-1(-5(-2|x - 3|)^2 - 2(-2|x - 3|) - 1) + 2)/(-3(-5(-2|x - 3|)^2 - 2(-2|x - 3|) - 1) + 1)) - 1) + 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3(4(1|((-1((2((-2x + 2)/(-2x - 3)) + 1)/(3((-2x + 2)/(-2x - 3)) + 1)))/(2((2((-2x + 2)/(-2x - 3)) + 1)/(3((-2x + 2)/(-2x - 3)) + 1)) - 1)) - 1| - 3)^2 + 4(1|((-1((2((-2x + 2)/(-2x - 3)) + 1)/(3((-2x + 2)/(-2x - 3)) + 1)))/(2((2((-2x + 2)/(-2x - 3)) + 1)/(3((-2x + 2)/(-2x - 3)) + 1)) - 1)) - 1| - 3) + 2)^2 + 3(4(1|((-1((2((-2x + 2)/(-2x - 3)) + 1)/(3((-2x + 2)/(-2x - 3)) + 1)))/(2((2((-2x + 2)/(-2x - 3)) + 1)/(3((-2x + 2)/(-2x - 3)) + 1)) - 1)) - 1| - 3)^2 + 4(1|((-1((2((-2x + 2)/(-2x - 3)) + 1)/(3((-2x + 2)/(-2x - 3)) + 1)))/(2((2((-2x + 2)/(-2x - 3)) + 1)/(3((-2x + 2)/(-2x - 3)) + 1)) - 1)) - 1| - 3) + 2) - 2, g(x) = 2|((1((-3((1(2|x + 3|) - 3)/(-2(2|x + 3|))) - 2)/(1((1(2|x + 3|) - 3)/(-2(2|x + 3|))) - 3)) - 2)/(-3((-3((1(2|x + 3|) - 3)/(-2(2|x + 3|))) - 2)/(1((1(2|x + 3|) - 3)/(-2(2|x + 3|))) - 3)) - 1)) + 3| - 2, 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": "83.8", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2sin(1\u03c0((-3(4((2((1(5x^2 + 1) + 1)/(1(5x^2 + 1) + 3)) + 1)/(-3((1(5x^2 + 1) + 1)/(1(5x^2 + 1) + 3)))) + 1) + 1)/(-1(4((2((1(5x^2 + 1) + 1)/(1(5x^2 + 1) + 3)) + 1)/(-3((1(5x^2 + 1) + 1)/(1(5x^2 + 1) + 3)))) + 1) + 3)) - 1) - 2 and g(x) = -2|(-2(-3sin(1\u03c0(2|(5x^2 - 5x - 4) + 2| - 2) + 1) - 2) + 2)| - 3 between the vertical lines x = 2.8 and x = 2.9. 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(-5(3(2|(4(-5x^2 - 3x + 1)^2 + 2(-5x^2 - 3x + 1) - 1) - 3| - 2) + 4) + 1) + 4 and g(x) = 2|(-2|((2(-1(-1cos(1\u03c0x - 3) - 1) + 4) + 2)/(1(-1(-1cos(1\u03c0x - 3) - 1) + 4))) - 3| - 1) + 3| between the vertical lines x = -0.6 and x = 0.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "89.9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1|(-1(4(5(-1|(5x + 2)| + 1)^2 + 1(-1|(5x + 2)| + 1) - 2) + 3)^2 + 5(4(5(-1|(5x + 2)| + 1)^2 + 1(-1|(5x + 2)| + 1) - 2) + 3) - 5) + 1| - 2 and g(x) = 5((2(3|(-4(4x^2 - 2x + 5)^2 - 2(4x^2 - 2x + 5) - 1) + 3| - 2))/(-3(3|(-4(4x^2 - 2x + 5)^2 - 2(4x^2 - 2x + 5) - 1) + 3| - 2))) - 2 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": "6.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2(-2|(-2((2(3(-1sin(2\u03c0x - 1) + 3)^2 - 3(-1sin(2\u03c0x - 1) + 3)) + 2)/(1(3(-1sin(2\u03c0x - 1) + 3)^2 - 3(-1sin(2\u03c0x - 1) + 3)) - 2))^2 + 2((2(3(-1sin(2\u03c0x - 1) + 3)^2 - 3(-1sin(2\u03c0x - 1) + 3)) + 2)/(1(3(-1sin(2\u03c0x - 1) + 3)^2 - 3(-1sin(2\u03c0x - 1) + 3)) - 2)) + 2) + 3| - 1) + 4 and g(x) = (-1(-4(1cos(2\u03c0(4((1x + 2)/(-1x - 3))^2 - 1((1x + 2)/(-1x - 3)) + 1) + 1))^2 - 2(1cos(2\u03c0(4((1x + 2)/(-1x - 3))^2 - 1((1x + 2)/(-1x - 3)) + 1) + 1)) + 4) - 3)/(-2(-4(1cos(2\u03c0(4((1x + 2)/(-1x - 3))^2 - 1((1x + 2)/(-1x - 3)) + 1) + 1))^2 - 2(1cos(2\u03c0(4((1x + 2)/(-1x - 3))^2 - 1((1x + 2)/(-1x - 3)) + 1) + 1)) + 4) + 3) between the vertical lines x = 1.0 and x = 3.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "45.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-3(-1|(1(-1cos(3\u03c0(5(3x - 5) + 4) - 2) - 3) - 2) + 3| + 2) + 1)/(-1(-1|(1(-1cos(3\u03c0(5(3x - 5) + 4) - 2) - 3) - 2) + 3| + 2)) and g(x) = -1|(-1|((1((1(-3|x + 1| - 1) + 3)/(-2(-3|x + 1| - 1) - 2)) - 1)/(2((1(-3|x + 1| - 1) + 3)/(-2(-3|x + 1| - 1) - 2)) - 3)) - 2|) - 3| from x = -4.7 to x = -4.6. 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) = 5(-4(3sin(3\u03c0(-1|((-1(-1|x + 3|) - 1)/(1(-1|x + 3|))) + 1| + 1) + 1) + 1)^2 + 4) and g(x) = (-1(-5(3|(-3e^(2(-1x^2 - 5x - 3))) + 3| - 2)^2 + 1(3|(-3e^(2(-1x^2 - 5x - 3))) + 3| - 2) - 2) + 1)/(-2(-5(3|(-3e^(2(-1x^2 - 5x - 3))) + 3| - 2)^2 + 1(3|(-3e^(2(-1x^2 - 5x - 3))) + 3| - 2) - 2) - 2) 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": "9.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -5(1|((2((2((-2(3x^2 - 4x - 3) + 2)/(2(3x^2 - 4x - 3) + 1)) + 2)/(3((-2(3x^2 - 4x - 3) + 2)/(2(3x^2 - 4x - 3) + 1)) + 2)) - 2)/(1((2((-2(3x^2 - 4x - 3) + 2)/(2(3x^2 - 4x - 3) + 1)) + 2)/(3((-2(3x^2 - 4x - 3) + 2)/(2(3x^2 - 4x - 3) + 1)) + 2))))| - 3) + 3 and g(x) = (-2((3(-2(-5(-1x^2 + 4x + 4) - 2)^2 - 3(-5(-1x^2 + 4x + 4) - 2) + 5) + 3)/(-1(-2(-5(-1x^2 + 4x + 4) - 2)^2 - 3(-5(-1x^2 + 4x + 4) - 2) + 5) - 3)) + 3)/(2((3(-2(-5(-1x^2 + 4x + 4) - 2)^2 - 3(-5(-1x^2 + 4x + 4) - 2) + 5) + 3)/(-1(-2(-5(-1x^2 + 4x + 4) - 2)^2 - 3(-5(-1x^2 + 4x + 4) - 2) + 5) - 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": "2.8", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1|((-1((1(-4(3e^(1(5x + 1)) + 2) - 2) - 3)/(1(-4(3e^(1(5x + 1)) + 2) - 2) + 1)) + 3)/(2((1(-4(3e^(1(5x + 1)) + 2) - 2) - 3)/(1(-4(3e^(1(5x + 1)) + 2) - 2) + 1)) - 3)) + 1| - 1 and g(x) = -3cos(1\u03c0(1|(1(-3((-1x - 3)/(-1x - 1))^2 - 4((-1x - 3)/(-1x - 1)) - 3) - 5)| + 3) + 2) - 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 4(-3|(3cos(3\u03c0(-3(3(2|x + 2| - 1) - 1) + 4) + 2) + 1) + 1| + 1) + 2, g(x) = 2e^(-2(1|(-2|(-3(-2|x| - 3)^2 + 4(-2|x| - 3) - 5) - 2| + 2) + 3| + 3)) - 2, 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": "2.4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1sin(2\u03c0(-2|(-1(2|(-2(-1x + 3) + 2) - 3|) - 3) - 3| + 3) - 1) - 1 and g(x) = 3(-1e^(2(-5((3(2x^2 + 5x) + 2)/(-1(2x^2 + 5x) - 3))^2 + 1((3(2x^2 + 5x) + 2)/(-1(2x^2 + 5x) - 3)) + 2)) - 1) + 3 from x = -1.0 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": "Calculate the area enclosed between the functions f(x) = 1((1(5(-3|(2e^(-1(-5x + 1)) - 3)| + 3)^2 - 3(-3|(2e^(-1(-5x + 1)) - 3)| + 3) - 4) + 3)/(-2(5(-3|(2e^(-1(-5x + 1)) - 3)| + 3)^2 - 3(-3|(2e^(-1(-5x + 1)) - 3)| + 3) - 4) + 3)) and g(x) = (-2(2|((1(-3e^(2(-4x^2 + 3x - 4)) + 1) - 2)/(1(-3e^(2(-4x^2 + 3x - 4)) + 1))) - 3| - 2) - 3)/(3(2|((1(-3e^(2(-4x^2 + 3x - 4)) + 1) - 2)/(1(-3e^(2(-4x^2 + 3x - 4)) + 1))) - 3| - 2) - 1) from x = 0.2 to 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": "Determine the area of the region enclosed by the graphs of f(x) = -2(-4(3(-2|(-2cos(3\u03c0((2x)/(-2x - 2)) + 2) + 1) - 1| + 2) + 4)^2 + 3(3(-2|(-2cos(3\u03c0((2x)/(-2x - 2)) + 2) + 1) - 1| + 2) + 4) + 1) and g(x) = 4(-3|(3sin(1\u03c0(5(2|x + 2| - 3)^2 - 3(2|x + 2| - 3) - 1) - 2) + 2) + 1| - 3)^2 + 4(-3|(3sin(1\u03c0(5(2|x + 2| - 3)^2 - 3(2|x + 2| - 3) - 1) - 2) + 2) + 1| - 3) - 4 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": "56.7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1(1sin(3\u03c0((-2(-1(-4(-4x + 4))^2 - 5(-4(-4x + 4)) - 3) + 3)/(-1(-1(-4(-4x + 4))^2 - 5(-4(-4x + 4)) - 3) + 3)) - 3)) - 3 and g(x) = (3(4(-2cos(2\u03c0(2|(5x^2 - 3x - 5) + 3| + 2) + 1) - 2) + 2) - 3)/(-3(4(-2cos(2\u03c0(2|(5x^2 - 3x - 5) + 3| + 2) + 1) - 2) + 2)) from x = -2.9 to x = -2.8. 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(1|(1|((-2(2e^(2((-1x + 1)/(2x - 1))) - 2) - 3)/(-3(2e^(2((-1x + 1)/(2x - 1))) - 2) + 1)) + 1| - 1) - 3|) - 3)/(-1(1|(1|((-2(2e^(2((-1x + 1)/(2x - 1))) - 2) - 3)/(-3(2e^(2((-1x + 1)/(2x - 1))) - 2) + 1)) + 1| - 1) - 3|) + 3), g(x) = -4(5(2cos(3\u03c0(-1|(-1x^2 + 4x + 1) - 3|) - 3)) + 4) + 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": "5.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2(1cos(1\u03c0(-5((-3(-3|((-2x - 1)/(-1x + 2)) + 2|) - 2)/(-1(-3|((-2x - 1)/(-1x + 2)) + 2|) - 3))) - 3) + 1)^2 + 2 and g(x) = -4((2((2(2|(-1x^2 + 1x + 4) - 3| - 1) + 2)/(-3(2|(-1x^2 + 1x + 4) - 3| - 1))) - 3)/(2((2(2|(-1x^2 + 1x + 4) - 3| - 1) + 2)/(-3(2|(-1x^2 + 1x + 4) - 3| - 1))) - 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": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1(3|(1(-1(2|((-3x + 1)/(-1x + 2)) - 3| + 1) - 2)^2 + 4(-1(2|((-3x + 1)/(-1x + 2)) - 3| + 1) - 2) + 5) + 3| - 2) and g(x) = 2|(5(-1sin(1\u03c0(1|(2x + 5) - 3| + 2) - 2) - 3)^2 - 5(-1sin(1\u03c0(1|(2x + 5) - 3| + 2) - 2) - 3)) - 1| + 2 between the vertical lines x = 3.5 and x = 3.8. 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) = 3|(1sin(1\u03c0(1(1(1(-1x^2 + 5x - 3)^2 + 2(-1x^2 + 5x - 3) - 3) + 4) + 1) + 2) - 1) - 1| + 3 and g(x) = -4(-1(-1((-2((-1x + 1)/(2x + 1)) - 1)/(1((-1x + 1)/(2x + 1)) + 1))^2 - 5((-2((-1x + 1)/(2x + 1)) - 1)/(1((-1x + 1)/(2x + 1)) + 1)) - 2)^2 + 1(-1((-2((-1x + 1)/(2x + 1)) - 1)/(1((-1x + 1)/(2x + 1)) + 1))^2 - 5((-2((-1x + 1)/(2x + 1)) - 1)/(1((-1x + 1)/(2x + 1)) + 1)) - 2) - 3) - 3 from x = -1.3 to x = -1.2. 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) = (2(-5(-4(-3cos(2\u03c0(-3|(-4x - 5) - 3| - 2) - 2) + 1) - 3)^2 - 1(-4(-3cos(2\u03c0(-3|(-4x - 5) - 3| - 2) - 2) + 1) - 3) - 5) + 1)/(-3(-5(-4(-3cos(2\u03c0(-3|(-4x - 5) - 3| - 2) - 2) + 1) - 3)^2 - 1(-4(-3cos(2\u03c0(-3|(-4x - 5) - 3| - 2) - 2) + 1) - 3) - 5)) and g(x) = 2((-2(-3cos(1\u03c0(-5((1x)/(3x + 1))^2 - 1((1x)/(3x + 1))) - 2) + 1) - 3)/(-3(-3cos(1\u03c0(-5((1x)/(3x + 1))^2 - 1((1x)/(3x + 1))) - 2) + 1) - 2)) - 4 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": "Determine the area of the region enclosed by the graphs of f(x) = (-1(3(-1(-1(2sin(1\u03c0(-4x^2 - 3x + 1)) + 1) - 4) - 3) - 3) + 1)/(1(3(-1(-1(2sin(1\u03c0(-4x^2 - 3x + 1)) + 1) - 4) - 3) - 3) - 2) and g(x) = (-1(2|(3(-1cos(1\u03c0(5x^2 + 5x - 5) - 3) + 3) - 5)| + 1) + 1)/(1(2|(3(-1cos(1\u03c0(5x^2 + 5x - 5) - 3) + 3) - 5)| + 1) - 3) 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": "160.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 3|(-3cos(3\u03c0(4(3|(5(-1x^2 - 5x + 3)^2 - 4(-1x^2 - 5x + 3) + 4) - 2| - 2) - 5) - 1) - 1) + 3| - 1 and g(x) = (2((-1((-2(4(4x^2 - 4)^2 + 2(4x^2 - 4)) + 1)/(1(4(4x^2 - 4)^2 + 2(4x^2 - 4)) + 1)) - 1)/(2((-2(4(4x^2 - 4)^2 + 2(4x^2 - 4)) + 1)/(1(4(4x^2 - 4)^2 + 2(4x^2 - 4)) + 1)) + 1)) - 3)/(1((-1((-2(4(4x^2 - 4)^2 + 2(4x^2 - 4)) + 1)/(1(4(4x^2 - 4)^2 + 2(4x^2 - 4)) + 1)) - 1)/(2((-2(4(4x^2 - 4)^2 + 2(4x^2 - 4)) + 1)/(1(4(4x^2 - 4)^2 + 2(4x^2 - 4)) + 1)) + 1))) from x = -3.9 to x = -3.8. 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": "Find the area of the region bounded by the curves f(x) = 4((1(2|(-3|(2(-2x) + 4)| - 2) + 2| - 1) + 3)/(-3(2|(-3|(2(-2x) + 4)| - 2) + 2| - 1) - 2))^2 + 5((1(2|(-3|(2(-2x) + 4)| - 2) + 2| - 1) + 3)/(-3(2|(-3|(2(-2x) + 4)| - 2) + 2| - 1) - 2)) - 3, g(x) = 5(-5((-3(-4(1x^2 - 4) - 1) - 2)/(3(-4(1x^2 - 4) - 1) - 2)) + 2)^2 - 2(-5((-3(-4(1x^2 - 4) - 1) - 2)/(3(-4(1x^2 - 4) - 1) - 2)) + 2) - 4, 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": "19.8", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2|(-4((-1((3(-2(2|x|) + 4) - 3)/(-2(-2(2|x|) + 4) - 3)) + 2)/(-2((3(-2(2|x|) + 4) - 3)/(-2(-2(2|x|) + 4) - 3)) - 1)) - 5)| - 2 and g(x) = (1(2|(-1(2|((-2x - 3)/(2x - 3)) - 2| - 3) + 2) - 3| + 2) + 1)/(-2(2|(-1(2|((-2x - 3)/(2x - 3)) - 2| - 3) + 2) - 3| + 2) - 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": "208.7", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1cos(2\u03c0(2((1(3|(2((2x + 2)/(2x + 1)))| + 2) - 2)/(-2(3|(2((2x + 2)/(2x + 1)))| + 2))) - 5) + 2), g(x) = 4((-3(-2(-3(1x + 2) - 3)^2 - 5(-3(1x + 2) - 3) - 2) + 3)/(1(-2(-3(1x + 2) - 3)^2 - 5(-3(1x + 2) - 3) - 2))) - 2, 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": "0.9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -4((-2(-2((2(-2|(-3x - 5) + 1|) - 2)/(3(-2|(-3x - 5) + 1|) - 2)) - 4) - 2)/(-2(-2((2(-2|(-3x - 5) + 1|) - 2)/(3(-2|(-3x - 5) + 1|) - 2)) - 4) + 1))^2 - 5((-2(-2((2(-2|(-3x - 5) + 1|) - 2)/(3(-2|(-3x - 5) + 1|) - 2)) - 4) - 2)/(-2(-2((2(-2|(-3x - 5) + 1|) - 2)/(3(-2|(-3x - 5) + 1|) - 2)) - 4) + 1)) + 3 and g(x) = -1((2(-2|(2|((-1x + 1)/(2x - 3))|) - 3| + 1) - 2)/(3(-2|(2|((-1x + 1)/(2x - 3))|) - 3| + 1) - 1))^2 + 1((2(-2|(2|((-1x + 1)/(2x - 3))|) - 3| + 1) - 2)/(3(-2|(2|((-1x + 1)/(2x - 3))|) - 3| + 1) - 1)) 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": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (2(-2|(1(2|(-2|(4x) - 3| + 2) + 3|) - 2) - 2| - 2) + 2)/(2(-2|(1(2|(-2|(4x) - 3| + 2) + 3|) - 2) - 2| - 2) - 1), g(x) = 2(-3cos(2\u03c0(2|(-4(1x - 3) - 3) + 2| - 1) + 3) + 3)^2 - 5(-3cos(2\u03c0(2|(-4(1x - 3) - 3) + 2| - 1) + 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": "1.6", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -4(-2sin(2\u03c0((2(-3|(1|(-1x^2 + 3x - 3) - 2| - 1) + 2| + 1))/(1(-3|(1|(-1x^2 + 3x - 3) - 2| - 1) + 2| + 1) + 3)) + 1) + 2) + 5, g(x) = -1(3|((1(2(-2x + 4) - 5) - 3)/(-2(2(-2x + 4) - 5) - 1)) - 3| + 2)^2 + 5(3|((1(2(-2x + 4) - 5) - 3)/(-2(2(-2x + 4) - 5) - 1)) - 3| + 2) + 4, 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": "2.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1(-2e^(1(-4(-4(1(-1x - 3) - 4)^2 + 1(1(-1x - 3) - 4) + 2)^2 - 1(-4(1(-1x - 3) - 4)^2 + 1(1(-1x - 3) - 4) + 2) - 3)) - 1) - 4 and g(x) = -2|((-1(2|(-5(1e^(1x) - 2) + 1) + 3| - 2) + 1)/(-1(2|(-5(1e^(1x) - 2) + 1) + 3| - 2) - 1)) + 1| + 1 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": "1.7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (3(5(-1(1sin(1\u03c0(1|((1x - 1)/(2x + 2)) + 2| + 1) + 1) - 2) - 3) + 5) + 1)/(-3(5(-1(1sin(1\u03c0(1|((1x - 1)/(2x + 2)) + 2| + 1) + 1) - 2) - 3) + 5) - 3) and g(x) = -1(-4(1e^(1((1(3x - 3) + 1)/(2(3x - 3)))) - 2) - 2)^2 - 2(-4(1e^(1((1(3x - 3) + 1)/(2(3x - 3)))) - 2) - 2) from x = -0.7 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) = 3(1|(-3sin(2\u03c0(-2|((1(4x + 2) + 3)/(1(4x + 2))) + 3| - 1) - 1) - 3) - 1| + 1)^2 + 3(1|(-3sin(2\u03c0(-2|((1(4x + 2) + 3)/(1(4x + 2))) + 3| - 1) - 1) - 3) - 1| + 1) + 1, g(x) = 1|((-3((-2((-1(1x + 2))/(2(1x + 2) - 1)) + 2)/(3((-1(1x + 2))/(2(1x + 2) - 1)) + 2)) - 2)/(-1((-2((-1(1x + 2))/(2(1x + 2) - 1)) + 2)/(3((-1(1x + 2))/(2(1x + 2) - 1)) + 2)) + 3)) + 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": "492.4", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1|(-5(2e^(-1((1((-1(2x - 5) + 1)/(-3(2x - 5) - 2)) - 2)/(-1((-1(2x - 5) + 1)/(-3(2x - 5) - 2)) + 3))) + 3) + 1) + 3| + 3 and g(x) = 1|(-4(-4(1cos(1\u03c0(2|x + 2| - 3)) + 1)^2 - 3(1cos(1\u03c0(2|x + 2| - 3)) + 1) - 3) + 3) - 1| - 3 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": "21.6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-2(-2e^(2(4(1(-2(-1|x + 3| + 3) - 5) + 2)^2 - 4(1(-2(-1|x + 3| + 3) - 5) + 2) - 2)) - 1) + 2)/(-1(-2e^(2(4(1(-2(-1|x + 3| + 3) - 5) + 2)^2 - 4(1(-2(-1|x + 3| + 3) - 5) + 2) - 2)) - 1) + 2) and g(x) = -1(-1((2((-1(2|x + 3| - 2) - 3)/(-1(2|x + 3| - 2) + 2)) - 2)/(1((-1(2|x + 3| - 2) - 3)/(-1(2|x + 3| - 2) + 2)) + 2)) - 5) + 2 from x = -3.8 to x = -2.2. 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) = -1|(-3|((3(1|(3sin(2\u03c0(1x - 1)) + 2)| - 1) - 3)/(-2(1|(3sin(2\u03c0(1x - 1)) + 2)| - 1) - 3)) - 3| + 1) + 3| and g(x) = -4((2((-2((2(-1|x - 2| + 1))/(-2(-1|x - 2| + 1) - 1)) + 2)/(3((2(-1|x - 2| + 1))/(-2(-1|x - 2| + 1) - 1)) + 2)))/(1((-2((2(-1|x - 2| + 1))/(-2(-1|x - 2| + 1) - 1)) + 2)/(3((2(-1|x - 2| + 1))/(-2(-1|x - 2| + 1) - 1)) + 2)) + 2)) + 2 from x = 2.0 to x = 2.5. 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": "Calculate the area enclosed between the functions f(x) = (-2(-5(-2(-1(-3(3x - 4) + 3)^2 + 4(-3(3x - 4) + 3) - 1) + 3) - 5) + 3)/(-1(-5(-2(-1(-3(3x - 4) + 3)^2 + 4(-3(3x - 4) + 3) - 1) + 3) - 5) - 3) and g(x) = 3cos(1\u03c0(1|(5(5(-2|x + 1| + 2)^2 + 3(-2|x + 1| + 2))^2 + 4(5(-2|x + 1| + 2)^2 + 3(-2|x + 1| + 2))) - 3| - 3) - 2) - 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": "1.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-1(-5((-2(-4((3(1cos(1\u03c0x - 2)) - 3)/(-1(1cos(1\u03c0x - 2)) - 2)) + 2) - 1)/(2(-4((3(1cos(1\u03c0x - 2)) - 3)/(-1(1cos(1\u03c0x - 2)) - 2)) + 2) - 1)) - 4) + 1)/(3(-5((-2(-4((3(1cos(1\u03c0x - 2)) - 3)/(-1(1cos(1\u03c0x - 2)) - 2)) + 2) - 1)/(2(-4((3(1cos(1\u03c0x - 2)) - 3)/(-1(1cos(1\u03c0x - 2)) - 2)) + 2) - 1)) - 4) + 3) and g(x) = 2(-4((-2(4(-2|x - 2| + 2)^2 - 5(-2|x - 2| + 2)))/(-2(4(-2|x - 2| + 2)^2 - 5(-2|x - 2| + 2)))) + 2) - 4 from x = -1.8 to x = -1.0. Round 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(1(-3cos(3\u03c0(-2(1(2x^2 + 4x - 1)^2 + 1(2x^2 + 4x - 1) - 4)^2 - 5(1(2x^2 + 4x - 1)^2 + 1(2x^2 + 4x - 1) - 4) - 2) - 2) + 3) - 3) - 3 and g(x) = 5(-3sin(3\u03c0(1(5((-1x + 2)/(-3x + 2)) + 4) + 1) - 3) + 2)^2 - 3(-3sin(3\u03c0(1(5((-1x + 2)/(-3x + 2)) + 4) + 1) - 3) + 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": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1|(1((-2(-1|(-1sin(3\u03c0((3x - 1)/(-3x + 1)) - 2) - 2) + 1| - 3) + 3)/(-2(-1|(-1sin(3\u03c0((3x - 1)/(-3x + 1)) - 2) - 2) + 1| - 3) + 1)) - 2) - 1| and g(x) = (-3(-2(2((-1(-2x^2 + 3x) - 3)/(-2(-2x^2 + 3x) - 1)) - 2) - 1) + 3)/(-1(-2(2((-1(-2x^2 + 3x) - 3)/(-2(-2x^2 + 3x) - 1)) - 2) - 1) - 2) between the vertical lines x = -0.4 and x = 1.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "45.9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2|(5((-3(-3(1cos(2\u03c0(-1|x| - 1) - 1) - 3) - 2) - 1)/(3(-3(1cos(2\u03c0(-1|x| - 1) - 1) - 3) - 2) - 1)) - 1) + 3| - 2 and g(x) = (-3(-4(-5(-3sin(1\u03c0(1x + 1) + 2)) + 5) - 1) - 2)/(-2(-4(-5(-3sin(1\u03c0(1x + 1) + 2)) + 5) - 1)) from x = 2.2 to x = 3.5. 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) = -5(1(4(1(2sin(1\u03c0(3|x + 3| - 3) - 2) - 3)^2 + 2(2sin(1\u03c0(3|x + 3| - 3) - 2) - 3)) - 5) - 3)^2 + 2(1(4(1(2sin(1\u03c0(3|x + 3| - 3) - 2) - 3)^2 + 2(2sin(1\u03c0(3|x + 3| - 3) - 2) - 3)) - 5) - 3) - 5 and g(x) = -4(-1((3(1((-2x + 2)/(-3x))^2 + 2) + 2)/(1(1((-2x + 2)/(-3x))^2 + 2))) + 3)^2 + 5(-1((3(1((-2x + 2)/(-3x))^2 + 2) + 2)/(1(1((-2x + 2)/(-3x))^2 + 2))) + 3) + 1 between the vertical lines x = -4.5 and x = -4.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "155.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3((-3(2(-1e^(2(-2(1x - 4)^2 - 4(1x - 4) + 1)) + 2)^2 - 4(-1e^(2(-2(1x - 4)^2 - 4(1x - 4) + 1)) + 2) - 3) - 1)/(-3(2(-1e^(2(-2(1x - 4)^2 - 4(1x - 4) + 1)) + 2)^2 - 4(-1e^(2(-2(1x - 4)^2 - 4(1x - 4) + 1)) + 2) - 3) - 3))^2 - 3((-3(2(-1e^(2(-2(1x - 4)^2 - 4(1x - 4) + 1)) + 2)^2 - 4(-1e^(2(-2(1x - 4)^2 - 4(1x - 4) + 1)) + 2) - 3) - 1)/(-3(2(-1e^(2(-2(1x - 4)^2 - 4(1x - 4) + 1)) + 2)^2 - 4(-1e^(2(-2(1x - 4)^2 - 4(1x - 4) + 1)) + 2) - 3) - 3)) + 5 and g(x) = (-1(2sin(1\u03c0(1(-5(-2|x + 3| + 1) - 1) + 1) - 2) + 1) - 3)/(3(2sin(1\u03c0(1(-5(-2|x + 3| + 1) - 1) + 1) - 2) + 1) - 2) 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": "1.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1(-2|(2(-2(3|(-3|x + 3| + 2) - 1|) + 2) - 1) - 2| - 1) - 2, g(x) = 4(-5((-1(1|(2x + 3) + 1| - 3))/(1(1|(2x + 3) + 1| - 3) - 2))^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": "2.8", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1(-2(-2((-2(1(-3x^2 - 3x - 1)^2 - 1(-3x^2 - 3x - 1) - 1) + 1)/(-1(1(-3x^2 - 3x - 1)^2 - 1(-3x^2 - 3x - 1) - 1) - 2))^2 - 4((-2(1(-3x^2 - 3x - 1)^2 - 1(-3x^2 - 3x - 1) - 1) + 1)/(-1(1(-3x^2 - 3x - 1)^2 - 1(-3x^2 - 3x - 1) - 1) - 2)) + 5) - 5)^2 - 5(-2(-2((-2(1(-3x^2 - 3x - 1)^2 - 1(-3x^2 - 3x - 1) - 1) + 1)/(-1(1(-3x^2 - 3x - 1)^2 - 1(-3x^2 - 3x - 1) - 1) - 2))^2 - 4((-2(1(-3x^2 - 3x - 1)^2 - 1(-3x^2 - 3x - 1) - 1) + 1)/(-1(1(-3x^2 - 3x - 1)^2 - 1(-3x^2 - 3x - 1) - 1) - 2)) + 5) - 5) - 5, g(x) = (-1(-2|(-1|(-1|((1x)/(1x - 2)) - 3| - 3) - 1| - 1)| + 2) - 3)/(-2(-2|(-1|(-1|((1x)/(1x - 2)) - 3| - 3) - 1| - 1)| + 2) + 3), 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": "225.9", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2|(-2|(1sin(1\u03c0((2(5(-1|x - 2| - 1)^2 - 4(-1|x - 2| - 1) - 1) - 3)/(2(5(-1|x - 2| - 1)^2 - 4(-1|x - 2| - 1) - 1) + 3)) - 1) - 3) - 1| + 3)| and g(x) = (2((-3(-1((-3(3x^2 + 5x) - 1)/(-2(3x^2 + 5x)))^2 - 1((-3(3x^2 + 5x) - 1)/(-2(3x^2 + 5x))) - 2) + 2)/(1(-1((-3(3x^2 + 5x) - 1)/(-2(3x^2 + 5x)))^2 - 1((-3(3x^2 + 5x) - 1)/(-2(3x^2 + 5x))) - 2))) - 1)/(-1((-3(-1((-3(3x^2 + 5x) - 1)/(-2(3x^2 + 5x)))^2 - 1((-3(3x^2 + 5x) - 1)/(-2(3x^2 + 5x))) - 2) + 2)/(1(-1((-3(3x^2 + 5x) - 1)/(-2(3x^2 + 5x)))^2 - 1((-3(3x^2 + 5x) - 1)/(-2(3x^2 + 5x))) - 2))) - 2) between the vertical lines x = -1.7 and 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) = -3|(-3((2(4(3|((2x + 2)/(-1x - 3)) + 2| - 2) - 1) + 1)/(-2(4(3|((2x + 2)/(-1x - 3)) + 2| - 2) - 1) - 3))^2 + 5((2(4(3|((2x + 2)/(-1x - 3)) + 2| - 2) - 1) + 1)/(-2(4(3|((2x + 2)/(-1x - 3)) + 2| - 2) - 1) - 3)) - 3) - 2| - 1 and g(x) = -2(-3(-1|(-1|(5x + 4) + 2| + 2) - 1|) - 4) + 5 between the vertical lines x = -3.2 and x = 0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "106.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3((-3(1((1(3(-3|x - 2|) - 5) + 1)/(1(3(-3|x - 2|) - 5))) - 1))/(3(1((1(3(-3|x - 2|) - 5) + 1)/(1(3(-3|x - 2|) - 5))) - 1) - 2)) - 2 and g(x) = -1|(5((-1(1((1x + 3)/(-2x)) + 1) - 3)/(-1(1((1x + 3)/(-2x)) + 1) + 2)) + 4) + 2| between the vertical lines x = 1.3 and x = 3.2. 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) = (-1(-2|((-2(4(-1sin(3\u03c0(1|x - 2| + 2)) + 3)^2 + 2(-1sin(3\u03c0(1|x - 2| + 2)) + 3) + 3) - 2)/(1(4(-1sin(3\u03c0(1|x - 2| + 2)) + 3)^2 + 2(-1sin(3\u03c0(1|x - 2| + 2)) + 3) + 3) + 3)) + 3| - 2) - 2)/(2(-2|((-2(4(-1sin(3\u03c0(1|x - 2| + 2)) + 3)^2 + 2(-1sin(3\u03c0(1|x - 2| + 2)) + 3) + 3) - 2)/(1(4(-1sin(3\u03c0(1|x - 2| + 2)) + 3)^2 + 2(-1sin(3\u03c0(1|x - 2| + 2)) + 3) + 3) + 3)) + 3| - 2) - 1) and g(x) = -4((-2(1(-1(2cos(3\u03c0x))^2 + 1(2cos(3\u03c0x)) + 1)^2 - 2(-1(2cos(3\u03c0x))^2 + 1(2cos(3\u03c0x)) + 1) - 5) - 3)/(-1(1(-1(2cos(3\u03c0x))^2 + 1(2cos(3\u03c0x)) + 1)^2 - 2(-1(2cos(3\u03c0x))^2 + 1(2cos(3\u03c0x)) + 1) - 5) - 3)) + 1 between the vertical lines x = -3.1 and x = -2.9. 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) = -2((2(-1((-2(-4((2x + 2)/(1x))^2 + 5((2x + 2)/(1x)) + 2) - 3)/(-3(-4((2x + 2)/(1x))^2 + 5((2x + 2)/(1x)) + 2) + 2)) - 5) + 1)/(2(-1((-2(-4((2x + 2)/(1x))^2 + 5((2x + 2)/(1x)) + 2) - 3)/(-3(-4((2x + 2)/(1x))^2 + 5((2x + 2)/(1x)) + 2) + 2)) - 5) + 3))^2 + 4((2(-1((-2(-4((2x + 2)/(1x))^2 + 5((2x + 2)/(1x)) + 2) - 3)/(-3(-4((2x + 2)/(1x))^2 + 5((2x + 2)/(1x)) + 2) + 2)) - 5) + 1)/(2(-1((-2(-4((2x + 2)/(1x))^2 + 5((2x + 2)/(1x)) + 2) - 3)/(-3(-4((2x + 2)/(1x))^2 + 5((2x + 2)/(1x)) + 2) + 2)) - 5) + 3)) - 2 and g(x) = (-2(-2(1(-5(-3x + 1)^2 + 3(-3x + 1) + 4)^2 + 3(-5(-3x + 1)^2 + 3(-3x + 1) + 4) + 3) + 5) + 3)/(-3(-2(1(-5(-3x + 1)^2 + 3(-3x + 1) + 4)^2 + 3(-5(-3x + 1)^2 + 3(-3x + 1) + 4) + 3) + 5) - 2) between the vertical lines x = -0.1 and x = 0.6. 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(2(-3|(-1((-1(2|x + 1| + 2) + 1)/(1(2|x + 1| + 2) + 2))^2 - 5((-1(2|x + 1| + 2) + 1)/(1(2|x + 1| + 2) + 2)) + 2) - 3| + 2)^2 - 3) + 2 and g(x) = -1((-2(3|(-5(-5x - 3) - 5) - 3| - 1) + 1)/(-1(3|(-5(-5x - 3) - 5) - 3| - 1))) - 3 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": "1.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-2(1(-1(1(-2|(2x^2 - 3)|) - 4) - 2)) + 2)/(1(1(-1(1(-2|(2x^2 - 3)|) - 4) - 2)) - 2) and g(x) = -1(1(-1((2((-2x + 1)/(1x)) - 3)/(-1((-2x + 1)/(1x)) + 3)) + 1)^2 + 4)^2 + 3(1(-1((2((-2x + 1)/(1x)) - 3)/(-1((-2x + 1)/(1x)) + 3)) + 1)^2 + 4) + 5 from x = -1.2 to x = 0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "153.9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2((1(-4((-1(5(-2x) + 4) + 1)/(-2(5(-2x) + 4)))^2 + 5((-1(5(-2x) + 4) + 1)/(-2(5(-2x) + 4))) + 1) + 3)/(-2(-4((-1(5(-2x) + 4) + 1)/(-2(5(-2x) + 4)))^2 + 5((-1(5(-2x) + 4) + 1)/(-2(5(-2x) + 4))) + 1) - 3)) - 2 and g(x) = 2((-3(3(-1(3|x + 3| + 1) + 4)^2 - 2(-1(3|x + 3| + 1) + 4) - 1) - 2)/(-1(3(-1(3|x + 3| + 1) + 4)^2 - 2(-1(3|x + 3| + 1) + 4) - 1) - 1))^2 - 5((-3(3(-1(3|x + 3| + 1) + 4)^2 - 2(-1(3|x + 3| + 1) + 4) - 1) - 2)/(-1(3(-1(3|x + 3| + 1) + 4)^2 - 2(-1(3|x + 3| + 1) + 4) - 1) - 1)) + 3 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) = (3(5((-1(2(1|((-2x)/(-2x - 2))|)^2 - 5) + 2)/(2(2(1|((-2x)/(-2x - 2))|)^2 - 5)))^2 + 4((-1(2(1|((-2x)/(-2x - 2))|)^2 - 5) + 2)/(2(2(1|((-2x)/(-2x - 2))|)^2 - 5))) - 2) - 2)/(2(5((-1(2(1|((-2x)/(-2x - 2))|)^2 - 5) + 2)/(2(2(1|((-2x)/(-2x - 2))|)^2 - 5)))^2 + 4((-1(2(1|((-2x)/(-2x - 2))|)^2 - 5) + 2)/(2(2(1|((-2x)/(-2x - 2))|)^2 - 5))) - 2) + 2) and g(x) = 4((-2(1(2|((-1x - 3)/(2x + 3)) - 1| - 1) - 3) + 1)/(-3(1(2|((-1x - 3)/(2x + 3)) - 1| - 1) - 3) - 2)) + 1 from x = -0.6 to x = -0.5. 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": "Determine the area of the region enclosed by the graphs of f(x) = (3(-1((-2(-1(4(1|x + 2| - 3) + 2)^2 - 2(4(1|x + 2| - 3) + 2) + 1))/(3(-1(4(1|x + 2| - 3) + 2)^2 - 2(4(1|x + 2| - 3) + 2) + 1) - 2))^2 - 4((-2(-1(4(1|x + 2| - 3) + 2)^2 - 2(4(1|x + 2| - 3) + 2) + 1))/(3(-1(4(1|x + 2| - 3) + 2)^2 - 2(4(1|x + 2| - 3) + 2) + 1) - 2)) + 5) + 2)/(-1(-1((-2(-1(4(1|x + 2| - 3) + 2)^2 - 2(4(1|x + 2| - 3) + 2) + 1))/(3(-1(4(1|x + 2| - 3) + 2)^2 - 2(4(1|x + 2| - 3) + 2) + 1) - 2))^2 - 4((-2(-1(4(1|x + 2| - 3) + 2)^2 - 2(4(1|x + 2| - 3) + 2) + 1))/(3(-1(4(1|x + 2| - 3) + 2)^2 - 2(4(1|x + 2| - 3) + 2) + 1) - 2)) + 5) - 2) and g(x) = 2|(1e^(-1(-2|(1|(2x^2 + 3x - 3) - 1| - 1)| + 2)) + 1) - 3| - 3 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": "Find the area of the region bounded by the curves f(x) = 3|(5(-1(1((-1(1|x| + 1) + 3)/(-1(1|x| + 1) - 2))^2 - 5((-1(1|x| + 1) + 3)/(-1(1|x| + 1) - 2)) + 1)^2 + 4(1((-1(1|x| + 1) + 3)/(-1(1|x| + 1) - 2))^2 - 5((-1(1|x| + 1) + 3)/(-1(1|x| + 1) - 2)) + 1) + 1)^2 - 3(-1(1((-1(1|x| + 1) + 3)/(-1(1|x| + 1) - 2))^2 - 5((-1(1|x| + 1) + 3)/(-1(1|x| + 1) - 2)) + 1)^2 + 4(1((-1(1|x| + 1) + 3)/(-1(1|x| + 1) - 2))^2 - 5((-1(1|x| + 1) + 3)/(-1(1|x| + 1) - 2)) + 1) + 1) - 4) - 1|, g(x) = (1(-2(-1(3|((2x + 1)/(-3x + 2)) - 3| - 2)^2 + 5(3|((2x + 1)/(-3x + 2)) - 3| - 2) - 4) - 2) + 1)/(1(-2(-1(3|((2x + 1)/(-3x + 2)) - 3| - 2)^2 + 5(3|((2x + 1)/(-3x + 2)) - 3| - 2) - 4) - 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2cos(2\u03c0(5(-2(1(-5((-1x - 3)/(-1x + 2)) + 5) - 2)^2 - 4(1(-5((-1x - 3)/(-1x + 2)) + 5) - 2))^2 - 5(-2(1(-5((-1x - 3)/(-1x + 2)) + 5) - 2)^2 - 4(1(-5((-1x - 3)/(-1x + 2)) + 5) - 2)) + 1) + 1) - 2, g(x) = 2((-3(3|(-2((-3x - 2)/(-3x - 3)) + 5) - 1|) + 3)/(-2(3|(-2((-3x - 2)/(-3x - 3)) + 5) - 1|) + 3)) - 5, 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) = 5(1|(-2(-3|(-2(3x^2 + 2x - 4)^2 - 1(3x^2 + 2x - 4) + 5) - 2| + 1) + 4) - 2|) - 4 and g(x) = (-3(-1|(2|(3e^(1(-2|x - 3| - 1))) - 3| + 2) + 3| + 3) + 3)/(2(-1|(2|(3e^(1(-2|x - 3| - 1))) - 3| + 2) + 3| + 3)) from x = -1.3 to x = -1.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 4(-4((-3(-2(-2|(1|x + 2| - 3) + 3| + 2) - 2) + 2)/(-1(-2(-2|(1|x + 2| - 3) + 3| + 2) - 2) - 1)) - 2) - 2 and g(x) = -1(2(-3|(-1(-5x^2 - 2x) + 4) - 3| - 1)^2 - 4) - 5 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) = -1cos(3\u03c0((-1(2|(2|(-4(2x - 1) + 3) - 3| - 3) - 2| + 3) + 1)/(-1(2|(2|(-4(2x - 1) + 3) - 3| - 3) - 2| + 3) - 3)) + 3) + 3 and g(x) = 2(5(2|((-2((1x)/(3x - 1)) - 3)/(3((1x)/(3x - 1)) - 1)) + 2| - 3) - 4)^2 - 4(5(2|((-2((1x)/(3x - 1)) - 3)/(3((1x)/(3x - 1)) - 1)) + 2| - 3) - 4) - 4 from x = 0.2 to x = 0.3. 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": "Find the area of the region bounded by the curves f(x) = -4(2cos(2\u03c0(-4(-4((-2(1|x - 2| - 2) + 3)/(3(1|x - 2| - 2) + 2)) - 1)^2 - 5(-4((-2(1|x - 2| - 2) + 3)/(3(1|x - 2| - 2) + 2)) - 1) - 1) + 1))^2 + 1, g(x) = 2(-3sin(2\u03c0(1(-1|((2x)/(-3x - 1)) - 2| - 1)) + 2))^2 + 1(-3sin(2\u03c0(1(-1|((2x)/(-3x - 1)) - 2| - 1)) + 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": "1.6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1(1((-2((1(1|(-3x - 2)| - 1) - 2)/(-3(1|(-3x - 2)| - 1) + 1)) + 1)/(-3((1(1|(-3x - 2)| - 1) - 2)/(-3(1|(-3x - 2)| - 1) + 1))))^2 + 2((-2((1(1|(-3x - 2)| - 1) - 2)/(-3(1|(-3x - 2)| - 1) + 1)) + 1)/(-3((1(1|(-3x - 2)| - 1) - 2)/(-3(1|(-3x - 2)| - 1) + 1)))) - 4) + 1 and g(x) = -1|(1sin(1\u03c0(3(-3(5x - 3)^2 - 1(5x - 3) + 3)^2 - 1(-3(5x - 3)^2 - 1(5x - 3) + 3)) + 1) + 3) - 2| + 3 from x = -0.8 to x = -0.7000000000000001. 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(-1(-2|((2(-4x + 2) + 1)/(1(-4x + 2) - 2)) - 3| - 1) - 2)^2 - 3(-1(-2|((2(-4x + 2) + 1)/(1(-4x + 2) - 2)) - 3| - 1) - 2) + 2) + 1)/(-2(-1(-1(-2|((2(-4x + 2) + 1)/(1(-4x + 2) - 2)) - 3| - 1) - 2)^2 - 3(-1(-2|((2(-4x + 2) + 1)/(1(-4x + 2) - 2)) - 3| - 1) - 2) + 2) - 2), g(x) = -1(-1(-1|((2((1x - 3)/(1x + 3)) + 2)/(2((1x - 3)/(1x + 3)) + 1)) + 3| + 2) + 5)^2 + 5(-1(-1|((2((1x - 3)/(1x + 3)) + 2)/(2((1x - 3)/(1x + 3)) + 1)) + 3| + 2) + 5) + 3, x = 0.3, 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": "2.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 4((-2(4(1(1(-3e^(2x) + 1) - 2) + 2)^2 - 1(1(1(-3e^(2x) + 1) - 2) + 2) - 2) + 1)/(-1(4(1(1(-3e^(2x) + 1) - 2) + 2)^2 - 1(1(1(-3e^(2x) + 1) - 2) + 2) - 2) + 2))^2 + 1 and g(x) = -2((3((-3(-5(-1|x + 1| + 1) + 3))/(-2(-5(-1|x + 1| + 1) + 3) - 2)) - 1)/(1((-3(-5(-1|x + 1| + 1) + 3))/(-2(-5(-1|x + 1| + 1) + 3) - 2)) - 3))^2 + 4((3((-3(-5(-1|x + 1| + 1) + 3))/(-2(-5(-1|x + 1| + 1) + 3) - 2)) - 1)/(1((-3(-5(-1|x + 1| + 1) + 3))/(-2(-5(-1|x + 1| + 1) + 3) - 2)) - 3)) + 2 from x = -1.4 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) = 5((2(3(5(4(2x - 1) + 4) - 2) - 2) + 1)/(-1(3(5(4(2x - 1) + 4) - 2) - 2))) - 5, g(x) = -1((1(-1(-1(2x^2 - 5x - 5) - 3)^2 + 2(-1(2x^2 - 5x - 5) - 3) + 1) - 1)/(1(-1(-1(2x^2 - 5x - 5) - 3)^2 + 2(-1(2x^2 - 5x - 5) - 3) + 1) + 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": "11.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-2(-5(-3|(-1e^(-1(-3(1x^2 - 2x - 1) + 1))) - 2| - 1) + 3) + 3)/(1(-5(-3|(-1e^(-1(-3(1x^2 - 2x - 1) + 1))) - 2| - 1) + 3) + 2) and g(x) = -1(-1|(-5(-3(1|x - 3| + 1) + 4) - 4) - 3| - 1) - 5 between the vertical lines x = 2.1 and x = 2.3. 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": "Find the area of the region bounded by the curves f(x) = -1((-2((-2(-1sin(2\u03c0(3|(3|x + 3|) + 3| - 2) + 1) - 3) + 1)/(1(-1sin(2\u03c0(3|(3|x + 3|) + 3| - 2) + 1) - 3) + 1)) - 3)/(1((-2(-1sin(2\u03c0(3|(3|x + 3|) + 3| - 2) + 1) - 3) + 1)/(1(-1sin(2\u03c0(3|(3|x + 3|) + 3| - 2) + 1) - 3) + 1))))^2 - 5((-2((-2(-1sin(2\u03c0(3|(3|x + 3|) + 3| - 2) + 1) - 3) + 1)/(1(-1sin(2\u03c0(3|(3|x + 3|) + 3| - 2) + 1) - 3) + 1)) - 3)/(1((-2(-1sin(2\u03c0(3|(3|x + 3|) + 3| - 2) + 1) - 3) + 1)/(1(-1sin(2\u03c0(3|(3|x + 3|) + 3| - 2) + 1) - 3) + 1)))) + 2, g(x) = -3(-4((-2((-2(-5x^2 - 1x + 5) + 1)/(-1(-5x^2 - 1x + 5) + 2)) + 1)/(-2((-2(-5x^2 - 1x + 5) + 1)/(-1(-5x^2 - 1x + 5) + 2)) - 1)) - 2) + 5, x = -1.1, 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": "36.8", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 4(-1|(4(5(-4(-1e^(1x) + 2)^2 + 5(-1e^(1x) + 2) - 1)^2 + 4(-4(-1e^(1x) + 2)^2 + 5(-1e^(1x) + 2) - 1) - 1) + 2) - 3|) - 3, g(x) = -5(-2cos(2\u03c0(3|(-2(4x - 1) - 1) + 2| + 3) + 1) + 2)^2 - 1(-2cos(2\u03c0(3|(-2(4x - 1) - 1) + 2| + 3) + 1) + 2) + 3, 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": "2.6", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1(-1|(-1((-2((-1(-2|x - 1| + 3) - 1)/(-3(-2|x - 1| + 3) + 4)) + 3)/(-3((-1(-2|x - 1| + 3) - 1)/(-3(-2|x - 1| + 3) + 4)) + 2))^2 + 5((-2((-1(-2|x - 1| + 3) - 1)/(-3(-2|x - 1| + 3) + 4)) + 3)/(-3((-1(-2|x - 1| + 3) - 1)/(-3(-2|x - 1| + 3) + 4)) + 2)) - 3)| - 2) - 1 and g(x) = -5(3sin(2\u03c0(-1|(4(2|x - 1| - 3) - 5) - 1| + 2) + 1) + 2) + 1 between the vertical lines x = 4.4 and x = 4.5. 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": "Find the area of the region bounded by the curves f(x) = -1sin(2\u03c0((2(-1(3((2(-2x + 2) + 1)/(-2(-2x + 2) - 1)) + 4) - 1) - 3)/(-1(-1(3((2(-2x + 2) + 1)/(-2(-2x + 2) - 1)) + 4) - 1) - 2)) + 1) + 1, g(x) = (1(-1(3((3(4x^2 - 3x - 3) + 1)/(1(4x^2 - 3x - 3) - 2)) + 5) - 3) + 2)/(2(-1(3((3(4x^2 - 3x - 3) + 1)/(1(4x^2 - 3x - 3) - 2)) + 5) - 3) + 1), x = -0.6, 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (1(-3sin(1\u03c0((3(5(-3|(4x - 5) - 3| + 1)^2 + 4(-3|(4x - 5) - 3| + 1) - 3))/(3(5(-3|(4x - 5) - 3| + 1)^2 + 4(-3|(4x - 5) - 3| + 1) - 3) - 1)) - 2) + 1) + 3)/(-3(-3sin(1\u03c0((3(5(-3|(4x - 5) - 3| + 1)^2 + 4(-3|(4x - 5) - 3| + 1) - 3))/(3(5(-3|(4x - 5) - 3| + 1)^2 + 4(-3|(4x - 5) - 3| + 1) - 3) - 1)) - 2) + 1) - 1) and g(x) = (3(4(2|((2((-1x)/(-3x + 4)) - 3)/(-2((-1x)/(-3x + 4)) - 1)) + 3| - 2)) + 2)/(1(4(2|((2((-1x)/(-3x + 4)) - 3)/(-2((-1x)/(-3x + 4)) - 1)) + 3| - 2)) - 2) between the vertical lines x = 2.0 and x = 2.1. 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": "Calculate the area enclosed between the functions f(x) = 2((-2(1((-2(3|((-3x - 2)/(-1x)) + 3| - 1) + 3)/(-1(3|((-3x - 2)/(-1x)) + 3| - 1) - 3)) + 4) + 3)/(-1(1((-2(3|((-3x - 2)/(-1x)) + 3| - 1) + 3)/(-1(3|((-3x - 2)/(-1x)) + 3| - 1) - 3)) + 4) + 3)) - 4 and g(x) = 4(3|(3sin(1\u03c0(4(-2x)^2 + 2) - 1) + 3) + 1| + 3) - 2 from x = -0.4 to x = -0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -4(5(2sin(2\u03c0(4(-5(5x^2 + 1)^2 - 1(5x^2 + 1) + 4) - 4) - 1) + 2)^2 + 4(2sin(2\u03c0(4(-5(5x^2 + 1)^2 - 1(5x^2 + 1) + 4) - 4) - 1) + 2) - 1) + 2 and g(x) = -5(-3(-1(1|(-2x - 4) - 1|)^2 + 2(1|(-2x - 4) - 1|) - 5) + 1) - 4 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": "14.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1(-2|(5(-1|(-5(3cos(3\u03c0x) + 1)) - 3| + 2) + 1) + 1| + 2) - 4 and g(x) = 3|((-2(-3(-1|(5x + 3)|)) + 2)/(1(-3(-1|(5x + 3)|)) + 2)) + 2| + 2 between the vertical lines x = 3.7 and x = 3.8. 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) = -1(3((3(1|((2(-3x^2 - 1x + 4) - 2)/(2(-3x^2 - 1x + 4) - 3)) - 2| - 3) - 2)/(-2(1|((2(-3x^2 - 1x + 4) - 2)/(2(-3x^2 - 1x + 4) - 3)) - 2| - 3) + 3)) - 5) + 3, g(x) = -2(-3sin(1\u03c0((1(-1((-1x + 1)/(3x + 2))^2 + 5((-1x + 1)/(3x + 2)) + 5) + 2)/(-1(-1((-1x + 1)/(3x + 2))^2 + 5((-1x + 1)/(3x + 2)) + 5) - 1)) + 1) - 3)^2 + 5(-3sin(1\u03c0((1(-1((-1x + 1)/(3x + 2))^2 + 5((-1x + 1)/(3x + 2)) + 5) + 2)/(-1(-1((-1x + 1)/(3x + 2))^2 + 5((-1x + 1)/(3x + 2)) + 5) - 1)) + 1) - 3), 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": "2.4", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (2((3((-1(4((-2(1x^2 + 3x) + 2)/(-3(1x^2 + 3x) + 4))^2 - 2((-2(1x^2 + 3x) + 2)/(-3(1x^2 + 3x) + 4))) + 2)/(1(4((-2(1x^2 + 3x) + 2)/(-3(1x^2 + 3x) + 4))^2 - 2((-2(1x^2 + 3x) + 2)/(-3(1x^2 + 3x) + 4))) + 2)) - 2)/(1((-1(4((-2(1x^2 + 3x) + 2)/(-3(1x^2 + 3x) + 4))^2 - 2((-2(1x^2 + 3x) + 2)/(-3(1x^2 + 3x) + 4))) + 2)/(1(4((-2(1x^2 + 3x) + 2)/(-3(1x^2 + 3x) + 4))^2 - 2((-2(1x^2 + 3x) + 2)/(-3(1x^2 + 3x) + 4))) + 2)) - 2)) + 1)/(-2((3((-1(4((-2(1x^2 + 3x) + 2)/(-3(1x^2 + 3x) + 4))^2 - 2((-2(1x^2 + 3x) + 2)/(-3(1x^2 + 3x) + 4))) + 2)/(1(4((-2(1x^2 + 3x) + 2)/(-3(1x^2 + 3x) + 4))^2 - 2((-2(1x^2 + 3x) + 2)/(-3(1x^2 + 3x) + 4))) + 2)) - 2)/(1((-1(4((-2(1x^2 + 3x) + 2)/(-3(1x^2 + 3x) + 4))^2 - 2((-2(1x^2 + 3x) + 2)/(-3(1x^2 + 3x) + 4))) + 2)/(1(4((-2(1x^2 + 3x) + 2)/(-3(1x^2 + 3x) + 4))^2 - 2((-2(1x^2 + 3x) + 2)/(-3(1x^2 + 3x) + 4))) + 2)) - 2)) - 2) and g(x) = 2(-2(3|(-3|((-1x - 2)/(-1x - 2)) + 1| - 2) + 1| + 1) + 4) + 1 between the vertical lines x = -3.0 and x = 0.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "243.6", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 5(1(5((2(2|(5x^2 - 1x + 4) - 2| - 2) - 2)/(1(2|(5x^2 - 1x + 4) - 2| - 2) + 2))^2 - 2((2(2|(5x^2 - 1x + 4) - 2| - 2) - 2)/(1(2|(5x^2 - 1x + 4) - 2| - 2) + 2)) - 3) + 2)^2 - 1(1(5((2(2|(5x^2 - 1x + 4) - 2| - 2) - 2)/(1(2|(5x^2 - 1x + 4) - 2| - 2) + 2))^2 - 2((2(2|(5x^2 - 1x + 4) - 2| - 2) - 2)/(1(2|(5x^2 - 1x + 4) - 2| - 2) + 2)) - 3) + 2) - 1, g(x) = 2|((1((-2(-4(-1x^2 - 1)^2 - 5(-1x^2 - 1) - 2) + 2)/(2(-4(-1x^2 - 1)^2 - 5(-1x^2 - 1) - 2) + 1)) + 3)/(2((-2(-4(-1x^2 - 1)^2 - 5(-1x^2 - 1) - 2) + 2)/(2(-4(-1x^2 - 1)^2 - 5(-1x^2 - 1) - 2) + 1)) + 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": "13.4", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -3|((2((-3(1(-2sin(2\u03c0((-3x - 1)/(1x + 2)) - 2)) + 1) + 2)/(-1(1(-2sin(2\u03c0((-3x - 1)/(1x + 2)) - 2)) + 1) - 1)) + 3)/(1((-3(1(-2sin(2\u03c0((-3x - 1)/(1x + 2)) - 2)) + 1) + 2)/(-1(1(-2sin(2\u03c0((-3x - 1)/(1x + 2)) - 2)) + 1) - 1)) + 1))| - 1, g(x) = (2(-4(-1cos(3\u03c0(2|(-2|x - 3| + 2) + 3| - 3) + 3))^2 + 1(-1cos(3\u03c0(2|(-2|x - 3| + 2) + 3| - 3) + 3)) + 4) + 1)/(-1(-4(-1cos(3\u03c0(2|(-2|x - 3| + 2) + 3| - 3) + 3))^2 + 1(-1cos(3\u03c0(2|(-2|x - 3| + 2) + 3| - 3) + 3)) + 4) - 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1(4(-2|(1(-1((-1x + 2)/(-1x - 2))^2 - 4((-1x + 2)/(-1x - 2)) + 1)^2 - 5(-1((-1x + 2)/(-1x - 2))^2 - 4((-1x + 2)/(-1x - 2)) + 1) + 2) - 1| + 3)^2 + 3(-2|(1(-1((-1x + 2)/(-1x - 2))^2 - 4((-1x + 2)/(-1x - 2)) + 1)^2 - 5(-1((-1x + 2)/(-1x - 2))^2 - 4((-1x + 2)/(-1x - 2)) + 1) + 2) - 1| + 3) + 4) - 2 and g(x) = (3(-2|(-3((-2(1|x - 3| + 3) - 1)/(3(1|x - 3| + 3) + 1)) + 5)|) + 1)/(1(-2|(-3((-2(1|x - 3| + 3) - 1)/(3(1|x - 3| + 3) + 1)) + 5)|) - 2) 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": "12.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2|((2(3|(4(-5(1sin(1\u03c0x + 3) + 1)^2 + 5(1sin(1\u03c0x + 3) + 1) - 3) + 4) - 1| - 3) + 3)/(3(3|(4(-5(1sin(1\u03c0x + 3) + 1)^2 + 5(1sin(1\u03c0x + 3) + 1) - 3) + 4) - 1| - 3) + 2)) - 2| - 3 and g(x) = -2e^(1((-1(-4(1(-3x + 5)^2 - 1(-3x + 5) - 5)^2 - 4(1(-3x + 5)^2 - 1(-3x + 5) - 5) + 1) + 1)/(1(-4(1(-3x + 5)^2 - 1(-3x + 5) - 5)^2 - 4(1(-3x + 5)^2 - 1(-3x + 5) - 5) + 1) + 3))) + 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -4(-1(-3cos(2\u03c0(3|(1|((-1x + 2)/(1x - 3)) + 2| - 2) - 3| + 1) - 2) + 3)^2 + 5(-3cos(2\u03c0(3|(1|((-1x + 2)/(1x - 3)) + 2| - 2) - 3| + 1) - 2) + 3) + 1)^2 + 4(-1(-3cos(2\u03c0(3|(1|((-1x + 2)/(1x - 3)) + 2| - 2) - 3| + 1) - 2) + 3)^2 + 5(-3cos(2\u03c0(3|(1|((-1x + 2)/(1x - 3)) + 2| - 2) - 3| + 1) - 2) + 3) + 1) - 4, g(x) = -4((-3((-2(1(3|x| - 2) - 3) - 2)/(-2(1(3|x| - 2) - 3) - 3)) - 2)/(-2((-2(1(3|x| - 2) - 3) - 2)/(-2(1(3|x| - 2) - 3) - 3)) - 2))^2 - 1((-3((-2(1(3|x| - 2) - 3) - 2)/(-2(1(3|x| - 2) - 3) - 3)) - 2)/(-2((-2(1(3|x| - 2) - 3) - 2)/(-2(1(3|x| - 2) - 3) - 3)) - 2)) - 1, x = 3.5, 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": "6.8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1(2cos(1\u03c0(1(2(3((-1x + 2)/(2x - 1)) - 2) + 4)^2 + 2(2(3((-1x + 2)/(2x - 1)) - 2) + 4)) + 2)) - 2 and g(x) = 3((2((1(-5(2x^2 - 3x - 1)^2 - 4(2x^2 - 3x - 1) + 3) - 3)/(-1(-5(2x^2 - 3x - 1)^2 - 4(2x^2 - 3x - 1) + 3) + 2)) + 1)/(-3((1(-5(2x^2 - 3x - 1)^2 - 4(2x^2 - 3x - 1) + 3) - 3)/(-1(-5(2x^2 - 3x - 1)^2 - 4(2x^2 - 3x - 1) + 3) + 2)) - 3)) + 5 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 4(3((2(-5(5(-1x^2 - 2x)^2 + 4(-1x^2 - 2x) - 3)^2 + 2(5(-1x^2 - 2x)^2 + 4(-1x^2 - 2x) - 3) + 1) + 1)/(1(-5(5(-1x^2 - 2x)^2 + 4(-1x^2 - 2x) - 3)^2 + 2(5(-1x^2 - 2x)^2 + 4(-1x^2 - 2x) - 3) + 1) + 2)) + 4) + 1 and g(x) = -2|((1(-2|((3(2|x - 2|))/(2(2|x - 2|) - 1)) + 1| - 1))/(3(-2|((3(2|x - 2|))/(2(2|x - 2|) - 1)) + 1| - 1) - 2))| + 1 from x = -1.7 to x = -0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "59.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1|(-3((3(-3|(1(-3e^(-1x))^2 + 4(-3e^(-1x)) + 5) - 3| + 1) - 3)/(-1(-3|(1(-3e^(-1x))^2 + 4(-3e^(-1x)) + 5) - 3| + 1))) + 1) + 2| + 2 and g(x) = -1(3(1(1e^(-1(2|x + 1| - 2)) + 3) + 5) + 5)^2 - 5(3(1(1e^(-1(2|x + 1| - 2)) + 3) + 5) + 5) - 5 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": "395.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -4(1sin(2\u03c0(3|(-2|(-5(-3x - 4)) - 3| - 3)| - 3) - 1) - 1) - 4 and g(x) = 2cos(1\u03c0(3(3|((1(-4x + 5) - 3)/(2(-4x + 5) - 1)) + 2|) - 2) - 3) from x = 0.9 to x = 1.0. 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(3|((2(3|(1sin(1\u03c0(5x^2 - 3x - 5) - 2) - 2) + 1| - 3) - 3)/(-1(3|(1sin(1\u03c0(5x^2 - 3x - 5) - 2) - 2) + 1| - 3) + 2)) - 2| - 3)^2 - 4(3|((2(3|(1sin(1\u03c0(5x^2 - 3x - 5) - 2) - 2) + 1| - 3) - 3)/(-1(3|(1sin(1\u03c0(5x^2 - 3x - 5) - 2) - 2) + 1| - 3) + 2)) - 2| - 3) + 3 and g(x) = (-1((-1(3|(-5(2x^2 - 5x - 3) + 4) + 1| - 1))/(-1(3|(-5(2x^2 - 5x - 3) + 4) + 1| - 1) + 2)) + 1)/(1((-1(3|(-5(2x^2 - 5x - 3) + 4) + 1| - 1))/(-1(3|(-5(2x^2 - 5x - 3) + 4) + 1| - 1) + 2)) + 3) from x = -4.7 to x = -4.6000000000000005. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "254.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-3((-3(-3(1|(-1(5x + 1) - 2) + 3| - 2) + 1) - 1)/(-1(-3(1|(-1(5x + 1) - 2) + 3| - 2) + 1) - 1)) + 1)/(-2((-3(-3(1|(-1(5x + 1) - 2) + 3| - 2) + 1) - 1)/(-1(-3(1|(-1(5x + 1) - 2) + 3| - 2) + 1) - 1)) - 1) and g(x) = (-2((1(1((1(-4x - 3) - 3)/(2(-4x - 3) + 1)) - 5) - 1)/(-2(1((1(-4x - 3) - 3)/(2(-4x - 3) + 1)) - 5))))/(3((1(1((1(-4x - 3) - 3)/(2(-4x - 3) + 1)) - 5) - 1)/(-2(1((1(-4x - 3) - 3)/(2(-4x - 3) + 1)) - 5))) + 2) from x = -0.6 to x = -0.5. 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": "Calculate the area enclosed between the functions f(x) = (1(2(4((-2(-2|((-2x + 3)/(-3x + 2)) + 3| - 1) - 3)/(-2(-2|((-2x + 3)/(-3x + 2)) + 3| - 1) + 3))^2 + 4((-2(-2|((-2x + 3)/(-3x + 2)) + 3| - 1) - 3)/(-2(-2|((-2x + 3)/(-3x + 2)) + 3| - 1) + 3)) - 1)^2 + 1(4((-2(-2|((-2x + 3)/(-3x + 2)) + 3| - 1) - 3)/(-2(-2|((-2x + 3)/(-3x + 2)) + 3| - 1) + 3))^2 + 4((-2(-2|((-2x + 3)/(-3x + 2)) + 3| - 1) - 3)/(-2(-2|((-2x + 3)/(-3x + 2)) + 3| - 1) + 3)) - 1)) + 1)/(-1(2(4((-2(-2|((-2x + 3)/(-3x + 2)) + 3| - 1) - 3)/(-2(-2|((-2x + 3)/(-3x + 2)) + 3| - 1) + 3))^2 + 4((-2(-2|((-2x + 3)/(-3x + 2)) + 3| - 1) - 3)/(-2(-2|((-2x + 3)/(-3x + 2)) + 3| - 1) + 3)) - 1)^2 + 1(4((-2(-2|((-2x + 3)/(-3x + 2)) + 3| - 1) - 3)/(-2(-2|((-2x + 3)/(-3x + 2)) + 3| - 1) + 3))^2 + 4((-2(-2|((-2x + 3)/(-3x + 2)) + 3| - 1) - 3)/(-2(-2|((-2x + 3)/(-3x + 2)) + 3| - 1) + 3)) - 1)) - 1) and g(x) = 1(1(3(-3(5x)^2 - 5(5x) + 1)^2 - 4(-3(5x)^2 - 5(5x) + 1) - 5) + 4)^2 - 4(1(3(-3(5x)^2 - 5(5x) + 1)^2 - 4(-3(5x)^2 - 5(5x) + 1) - 5) + 4) - 2 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": "5.7", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2|(-1e^(1(3|((-3(-2|((-1x - 2)/(2x - 1)) - 1| + 1) + 3)/(2(-2|((-1x - 2)/(2x - 1)) - 1| + 1) + 3)) + 3| + 1)) + 3) - 2| - 2 and g(x) = 3sin(2\u03c0(3(1((-2(-2|x - 2| + 1) + 2)/(3(-2|x - 2| + 1) - 2)) - 1)^2 + 3(1((-2(-2|x - 2| + 1) + 2)/(3(-2|x - 2| + 1) - 2)) - 1) + 5) + 1) + 2 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3|(-3e^(2(1(-2|((-1(-3x - 2) + 3)/(-3(-3x - 2) - 2)) + 2|) - 1)) + 3)| - 2 and g(x) = -1(1|(3|(-3sin(3\u03c0((2x + 1)/(1x - 3)) - 3) + 1)| - 2) - 3| - 2)^2 - 3(1|(3|(-3sin(3\u03c0((2x + 1)/(1x - 3)) - 3) + 1)| - 2) - 3| - 2) + 4 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": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3|(-1|(2e^(-1((1(5(3x^2 - 3x - 2) + 2))/(-3(5(3x^2 - 3x - 2) + 2) + 4))) - 1)| + 2) - 2| + 3 and g(x) = 4(4(2sin(3\u03c0(1|(-4x + 1)|) + 1) + 2) - 5) - 1 between the vertical lines x = 4.2 and x = 4.3. 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) = -5(-1(-4(-2|(-1((-2x + 3)/(-1x + 2)) - 2) + 3| + 1)^2 - 3(-2|(-1((-2x + 3)/(-1x + 2)) - 2) + 3| + 1) + 1)^2 - 4(-4(-2|(-1((-2x + 3)/(-1x + 2)) - 2) + 3| + 1)^2 - 3(-2|(-1((-2x + 3)/(-1x + 2)) - 2) + 3| + 1) + 1)) + 2 and g(x) = -3((1((-3(-3(-2|x - 3| + 2) - 5) - 2)/(3(-3(-2|x - 3| + 2) - 5) - 1)) - 2)/(-1((-3(-3(-2|x - 3| + 2) - 5) - 2)/(3(-3(-2|x - 3| + 2) - 5) - 1)) - 2))^2 + 4((1((-3(-3(-2|x - 3| + 2) - 5) - 2)/(3(-3(-2|x - 3| + 2) - 5) - 1)) - 2)/(-1((-3(-3(-2|x - 3| + 2) - 5) - 2)/(3(-3(-2|x - 3| + 2) - 5) - 1)) - 2)) + 3 from x = 1.1 to x = 1.3. 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) = -4(-2sin(3\u03c0(2|(-1|(-2(-2|x - 2| - 1) + 3) + 1| - 2) + 1| + 3) - 3) - 1) - 5 and g(x) = (-2(1cos(2\u03c0(-1(1((3x - 3)/(2x)) + 4) - 5) - 2) + 2) - 2)/(3(1cos(2\u03c0(-1(1((3x - 3)/(2x)) + 4) - 5) - 2) + 2) + 2) 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -3(1(1cos(3\u03c0(3(-3((-1x + 3)/(-2x - 3))^2 - 3((-1x + 3)/(-2x - 3)) - 3)^2 + 3(-3((-1x + 3)/(-2x - 3))^2 - 3((-1x + 3)/(-2x - 3)) - 3) - 4) - 2) + 3) - 1), g(x) = -4(1(2(2|(-2cos(3\u03c0x + 2) + 1) - 2|)^2 - 4(2|(-2cos(3\u03c0x + 2) + 1) - 2|))) - 5, x = -4.6, 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": "1.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (3(1|(3|(-3(1cos(1\u03c0(2x^2 - 5x - 5) - 1) - 3)^2 - 2(1cos(1\u03c0(2x^2 - 5x - 5) - 1) - 3) + 3) + 3| + 2)| - 2))/(2(1|(3|(-3(1cos(1\u03c0(2x^2 - 5x - 5) - 1) - 3)^2 - 2(1cos(1\u03c0(2x^2 - 5x - 5) - 1) - 3) + 3) + 3| + 2)| - 2) - 1) and g(x) = 3((-1(-1((2(2cos(2\u03c0x - 2) - 2))/(-2(2cos(2\u03c0x - 2) - 2) - 2))^2 - 3((2(2cos(2\u03c0x - 2) - 2))/(-2(2cos(2\u03c0x - 2) - 2) - 2)) + 5) + 2)/(3(-1((2(2cos(2\u03c0x - 2) - 2))/(-2(2cos(2\u03c0x - 2) - 2) - 2))^2 - 3((2(2cos(2\u03c0x - 2) - 2))/(-2(2cos(2\u03c0x - 2) - 2) - 2)) + 5) - 2))^2 + 4((-1(-1((2(2cos(2\u03c0x - 2) - 2))/(-2(2cos(2\u03c0x - 2) - 2) - 2))^2 - 3((2(2cos(2\u03c0x - 2) - 2))/(-2(2cos(2\u03c0x - 2) - 2) - 2)) + 5) + 2)/(3(-1((2(2cos(2\u03c0x - 2) - 2))/(-2(2cos(2\u03c0x - 2) - 2) - 2))^2 - 3((2(2cos(2\u03c0x - 2) - 2))/(-2(2cos(2\u03c0x - 2) - 2) - 2)) + 5) - 2)) + 1 between the vertical lines x = 3.2 and x = 3.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8.5", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -3(1(1|(-1cos(1\u03c0(-2|(1x + 2) - 1| - 2) + 3)) - 2| - 2))^2 + 3(1(1|(-1cos(1\u03c0(-2|(1x + 2) - 1| - 2) + 3)) - 2| - 2)) + 4, g(x) = -4((3(-5((2(2|x + 3|) - 2)/(-2(2|x + 3|)))^2 + 1((2(2|x + 3|) - 2)/(-2(2|x + 3|))) + 5))/(1(-5((2(2|x + 3|) - 2)/(-2(2|x + 3|)))^2 + 1((2(2|x + 3|) - 2)/(-2(2|x + 3|))) + 5) + 3)) - 5, 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": "7.6", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -3cos(1\u03c0(3(-1(1|((3(-2x - 5) + 1)/(2(-2x - 5) - 1)) + 2| + 2) + 4)^2 - 3(-1(1|((3(-2x - 5) + 1)/(2(-2x - 5) - 1)) + 2| + 2) + 4) + 3) - 2) + 1, g(x) = 3cos(2\u03c0((3(1|((1(-2|x - 3| - 2) - 1)/(2(-2|x - 3| - 2) - 3)) + 1|) - 3)/(2(1|((1(-2|x - 3| - 2) - 1)/(2(-2|x - 3| - 2) - 3)) + 1|) - 3)) + 1) + 2, 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (1(-2((-3(3(1e^(-1((-3x + 2)/(-2x - 3))) + 1)^2 + 5(1e^(-1((-3x + 2)/(-2x - 3))) + 1) + 5) - 3)/(3(3(1e^(-1((-3x + 2)/(-2x - 3))) + 1)^2 + 5(1e^(-1((-3x + 2)/(-2x - 3))) + 1) + 5) + 2))) - 3)/(-2(-2((-3(3(1e^(-1((-3x + 2)/(-2x - 3))) + 1)^2 + 5(1e^(-1((-3x + 2)/(-2x - 3))) + 1) + 5) - 3)/(3(3(1e^(-1((-3x + 2)/(-2x - 3))) + 1)^2 + 5(1e^(-1((-3x + 2)/(-2x - 3))) + 1) + 5) + 2))) - 2), g(x) = (1(2|(1cos(1\u03c0(-5(-2x - 2)^2 - 4(-2x - 2) + 5) + 1)) - 2| - 2) - 3)/(-2(2|(1cos(1\u03c0(-5(-2x - 2)^2 - 4(-2x - 2) + 5) + 1)) - 2| - 2) - 3), x = -3, and x = 3. 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) = 3|(2|(-2sin(2\u03c0(5(-1|(2|x + 3| + 1) + 3| + 2)^2 + 4(-1|(2|x + 3| + 1) + 3| + 2) + 5) + 3) - 1) + 1| + 1) - 3| + 1, g(x) = 4((-3(1|(1|(3|x + 3|) - 1| - 1)| + 2) + 2)/(2(1|(1|(3|x + 3|) - 1| - 1)| + 2) + 1))^2 - 2((-3(1|(1|(3|x + 3|) - 1| - 1)| + 2) + 2)/(2(1|(1|(3|x + 3|) - 1| - 1)| + 2) + 1)) - 4, 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 3cos(1\u03c0(-3|((1((-2(-1(4x - 2) + 4) - 2)/(-3(-1(4x - 2) + 4))))/(-1((-2(-1(4x - 2) + 4) - 2)/(-3(-1(4x - 2) + 4))) - 2))|) + 2) + 1 and g(x) = (-2(5((-2(-2|(-2|x - 2| + 1) - 3|) + 1)/(1(-2|(-2|x - 2| + 1) - 3|) - 3)) + 3) + 2)/(1(5((-2(-2|(-2|x - 2| + 1) - 3|) + 1)/(1(-2|(-2|x - 2| + 1) - 3|) - 3)) + 3) - 2) 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": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1cos(1\u03c0((-3(-4((-2(2(-3x^2 - 2x + 1)^2 - 5(-3x^2 - 2x + 1)))/(2(2(-3x^2 - 2x + 1)^2 - 5(-3x^2 - 2x + 1)) + 2))^2 - 5((-2(2(-3x^2 - 2x + 1)^2 - 5(-3x^2 - 2x + 1)))/(2(2(-3x^2 - 2x + 1)^2 - 5(-3x^2 - 2x + 1)) + 2))) + 2)/(3(-4((-2(2(-3x^2 - 2x + 1)^2 - 5(-3x^2 - 2x + 1)))/(2(2(-3x^2 - 2x + 1)^2 - 5(-3x^2 - 2x + 1)) + 2))^2 - 5((-2(2(-3x^2 - 2x + 1)^2 - 5(-3x^2 - 2x + 1)))/(2(2(-3x^2 - 2x + 1)^2 - 5(-3x^2 - 2x + 1)) + 2))) + 2)) + 2) - 2, g(x) = (2(-4((-2(-1(3x^2 - 3x) - 1) + 2)/(3(-1(3x^2 - 3x) - 1)))) + 3)/(-2(-4((-2(-1(3x^2 - 3x) - 1) + 2)/(3(-1(3x^2 - 3x) - 1)))) - 2), x = 0.1, and x = 0.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "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(1|(1cos(1\u03c0(5(1|x + 1| + 3)^2 + 1(1|x + 1| + 3) - 5) + 3) + 2) - 1| - 1) - 2)/(-3(1|(1cos(1\u03c0(5(1|x + 1| + 3)^2 + 1(1|x + 1| + 3) - 5) + 3) + 2) - 1| - 1))) + 2| + 2 and g(x) = -3(-1|(2|(1(4x^2 - 2x - 5) + 2) + 1| - 3) - 2|)^2 + 1(-1|(2|(1(4x^2 - 2x - 5) + 2) + 1| - 3) - 2|) + 5 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": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2(2|(-2sin(2\u03c0(5(-2(1|x - 2| - 2) - 5)^2 + 5(-2(1|x - 2| - 2) - 5) + 3) - 1) + 2) + 2|) - 3 and g(x) = 4((3(2(-4(-4x - 1) - 3)^2 - 5(-4(-4x - 1) - 3) - 3) + 3)/(2(2(-4(-4x - 1) - 3)^2 - 5(-4(-4x - 1) - 3) - 3) - 1)) + 5 between the vertical lines x = -1.4 and x = -1.2999999999999998. 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((2((-1(3cos(1\u03c0(1|((1x + 2)/(1x - 3)) - 3|)) + 1) + 2)/(2(3cos(1\u03c0(1|((1x + 2)/(1x - 3)) - 3|)) + 1) - 1)))/(-1((-1(3cos(1\u03c0(1|((1x + 2)/(1x - 3)) - 3|)) + 1) + 2)/(2(3cos(1\u03c0(1|((1x + 2)/(1x - 3)) - 3|)) + 1) - 1)) - 2)))/(1((2((-1(3cos(1\u03c0(1|((1x + 2)/(1x - 3)) - 3|)) + 1) + 2)/(2(3cos(1\u03c0(1|((1x + 2)/(1x - 3)) - 3|)) + 1) - 1)))/(-1((-1(3cos(1\u03c0(1|((1x + 2)/(1x - 3)) - 3|)) + 1) + 2)/(2(3cos(1\u03c0(1|((1x + 2)/(1x - 3)) - 3|)) + 1) - 1)) - 2)) - 2) and g(x) = (-2((3(1cos(2\u03c0(-1(-1x - 2)^2 + 5(-1x - 2) + 1) - 1)) + 3)/(3(1cos(2\u03c0(-1(-1x - 2)^2 + 5(-1x - 2) + 1) - 1)) + 1)) + 3)/(2((3(1cos(2\u03c0(-1(-1x - 2)^2 + 5(-1x - 2) + 1) - 1)) + 3)/(3(1cos(2\u03c0(-1(-1x - 2)^2 + 5(-1x - 2) + 1) - 1)) + 1)) + 2) 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": "1.9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1((3((-3(1cos(3\u03c0(2(5x - 2) - 5) + 2) + 3) - 1)/(3(1cos(3\u03c0(2(5x - 2) - 5) + 2) + 3) + 2)) - 3)/(-1((-3(1cos(3\u03c0(2(5x - 2) - 5) + 2) + 3) - 1)/(3(1cos(3\u03c0(2(5x - 2) - 5) + 2) + 3) + 2)) + 3))^2 + 1((3((-3(1cos(3\u03c0(2(5x - 2) - 5) + 2) + 3) - 1)/(3(1cos(3\u03c0(2(5x - 2) - 5) + 2) + 3) + 2)) - 3)/(-1((-3(1cos(3\u03c0(2(5x - 2) - 5) + 2) + 3) - 1)/(3(1cos(3\u03c0(2(5x - 2) - 5) + 2) + 3) + 2)) + 3)) + 5 and g(x) = -4((-1(1(-5(5x^2 - 1x - 3)^2 - 2(5x^2 - 1x - 3) + 1)^2 + 2(-5(5x^2 - 1x - 3)^2 - 2(5x^2 - 1x - 3) + 1) - 4) + 1)/(-2(1(-5(5x^2 - 1x - 3)^2 - 2(5x^2 - 1x - 3) + 1)^2 + 2(-5(5x^2 - 1x - 3)^2 - 2(5x^2 - 1x - 3) + 1) - 4) - 3)) + 1 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": "4.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-1(-2|(1(-1(-4(2x^2 - 2x + 3)^2 + 5(2x^2 - 2x + 3) - 2) - 4)^2 - 1(-1(-4(2x^2 - 2x + 3)^2 + 5(2x^2 - 2x + 3) - 2) - 4) - 3)| + 3) + 2)/(-2(-2|(1(-1(-4(2x^2 - 2x + 3)^2 + 5(2x^2 - 2x + 3) - 2) - 4)^2 - 1(-1(-4(2x^2 - 2x + 3)^2 + 5(2x^2 - 2x + 3) - 2) - 4) - 3)| + 3) + 1) and g(x) = 1|(-3|(3(3e^(2((1x - 2)/(1x + 2)))) - 2)| - 1) + 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": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 3(-1(-1|((-3(3|(-1|x|) - 3|))/(2(3|(-1|x|) - 3|) - 1)) - 3| + 1)^2 + 4(-1|((-3(3|(-1|x|) - 3|))/(2(3|(-1|x|) - 3|) - 1)) - 3| + 1) - 2) + 5 and g(x) = (-1((-1(4(3|(-3|x - 1| + 1)| + 2)^2 - 4(3|(-3|x - 1| + 1)| + 2) + 2) - 2)/(-3(4(3|(-3|x - 1| + 1)| + 2)^2 - 4(3|(-3|x - 1| + 1)| + 2) + 2))) - 2)/(3((-1(4(3|(-3|x - 1| + 1)| + 2)^2 - 4(3|(-3|x - 1| + 1)| + 2) + 2) - 2)/(-3(4(3|(-3|x - 1| + 1)| + 2)^2 - 4(3|(-3|x - 1| + 1)| + 2) + 2))) - 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": "0.9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 4(-4((-2(3(1(2|x - 2| - 2)^2 + 5(2|x - 2| - 2) - 5)^2 - 3(1(2|x - 2| - 2)^2 + 5(2|x - 2| - 2) - 5) - 4) + 2)/(-1(3(1(2|x - 2| - 2)^2 + 5(2|x - 2| - 2) - 5)^2 - 3(1(2|x - 2| - 2)^2 + 5(2|x - 2| - 2) - 5) - 4) + 2)) - 3) - 3 and g(x) = -1sin(3\u03c0(-3(-4(1((2x + 2)/(1x + 2))^2 - 4((2x + 2)/(1x + 2)) + 2) + 3)^2 - 2(-4(1((2x + 2)/(1x + 2))^2 - 4((2x + 2)/(1x + 2)) + 2) + 3) - 3) + 1) - 2 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": "14.7", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1(5(4(-5((-1((1x - 1)/(-2x - 3)) + 1)/(-3((1x - 1)/(-2x - 3)) + 1))^2 + 4((-1((1x - 1)/(-2x - 3)) + 1)/(-3((1x - 1)/(-2x - 3)) + 1))) - 1) - 1) - 1 and g(x) = (-2(-3(-4((3(3cos(1\u03c0x + 1)) - 3)/(3(3cos(1\u03c0x + 1)))) + 3)^2 - 2(-4((3(3cos(1\u03c0x + 1)) - 3)/(3(3cos(1\u03c0x + 1)))) + 3) - 4) + 2)/(-3(-3(-4((3(3cos(1\u03c0x + 1)) - 3)/(3(3cos(1\u03c0x + 1)))) + 3)^2 - 2(-4((3(3cos(1\u03c0x + 1)) - 3)/(3(3cos(1\u03c0x + 1)))) + 3) - 4) - 3) between the vertical lines x = -0.7 and x = 2.8. 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": "Find the area of the region bounded by the curves f(x) = -1cos(1\u03c0(1(-2|(-2(2|(1|x - 3| - 2) - 1| - 2) + 3) - 3| + 3)^2 + 1(-2|(-2(2|(1|x - 3| - 2) - 1| - 2) + 3) - 3| + 3) - 1) + 3) - 2, g(x) = (-3((2(-5(5(2|x - 1| - 1) + 4) - 3) + 1)/(1(-5(5(2|x - 1| - 1) + 4) - 3) + 1)))/(-2((2(-5(5(2|x - 1| - 1) + 4) - 3) + 1)/(1(-5(5(2|x - 1| - 1) + 4) - 3) + 1)) + 3), 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": "8.5", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -3(-1((-3(1|(-1sin(1\u03c0(3x^2 + 5x + 1) - 3) + 2) - 1| - 1) - 1)/(-2(1|(-1sin(1\u03c0(3x^2 + 5x + 1) - 3) + 2) - 1| - 1) - 1))), g(x) = (1((3(-3|(-2(3x^2 - 5x + 4)^2 + 2(3x^2 - 5x + 4)) + 1| - 3) - 3)/(-1(-3|(-2(3x^2 - 5x + 4)^2 + 2(3x^2 - 5x + 4)) + 1| - 3) + 2)) + 2)/(2((3(-3|(-2(3x^2 - 5x + 4)^2 + 2(3x^2 - 5x + 4)) + 1| - 3) - 3)/(-1(-3|(-2(3x^2 - 5x + 4)^2 + 2(3x^2 - 5x + 4)) + 1| - 3) + 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": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1((-1(-3cos(3\u03c0((3(-2|(5x - 3)|) + 1)/(2(-2|(5x - 3)|) + 2)) + 3) + 1) + 3)/(1(-3cos(3\u03c0((3(-2|(5x - 3)|) + 1)/(2(-2|(5x - 3)|) + 2)) + 3) + 1) - 3))^2 + 3((-1(-3cos(3\u03c0((3(-2|(5x - 3)|) + 1)/(2(-2|(5x - 3)|) + 2)) + 3) + 1) + 3)/(1(-3cos(3\u03c0((3(-2|(5x - 3)|) + 1)/(2(-2|(5x - 3)|) + 2)) + 3) + 1) - 3)) - 3, g(x) = -1|(2(3|(-2(5x + 4)^2 - 1(5x + 4) + 3) - 1| - 2)^2 - 4(3|(-2(5x + 4)^2 - 1(5x + 4) + 3) - 1| - 2) + 3)| + 2, 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": "1.8", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1|(-5(-4(5(-4((-1x + 2)/(-1x - 3)) - 3)^2 - 4(-4((-1x + 2)/(-1x - 3)) - 3) + 1)^2 - 5(5(-4((-1x + 2)/(-1x - 3)) - 3)^2 - 4(-4((-1x + 2)/(-1x - 3)) - 3) + 1) + 1)^2 + 5(-4(5(-4((-1x + 2)/(-1x - 3)) - 3)^2 - 4(-4((-1x + 2)/(-1x - 3)) - 3) + 1)^2 - 5(5(-4((-1x + 2)/(-1x - 3)) - 3)^2 - 4(-4((-1x + 2)/(-1x - 3)) - 3) + 1) + 1) + 1) + 1| + 1, g(x) = (-2(-5((-3(-4(-3x - 3) + 3) - 2)/(-1(-4(-3x - 3) + 3) - 3))^2 + 4) + 1)/(1(-5((-3(-4(-3x - 3) + 3) - 2)/(-1(-4(-3x - 3) + 3) - 3))^2 + 4) - 3), 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": "1.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1(-1|((2((2((2(1e^(1x) + 2) - 1)/(3(1e^(1x) + 2) - 2)) - 1)/(2((2(1e^(1x) + 2) - 1)/(3(1e^(1x) + 2) - 2)) - 1)) - 2)/(2((2((2(1e^(1x) + 2) - 1)/(3(1e^(1x) + 2) - 2)) - 1)/(2((2(1e^(1x) + 2) - 1)/(3(1e^(1x) + 2) - 2)) - 1)) + 1)) + 2|)^2 - 5 and g(x) = (3(-2|(-3cos(2\u03c0(-1|((-1x - 2)/(1x))| - 3) + 3) - 2) - 2| + 3) - 2)/(1(-2|(-3cos(2\u03c0(-1|((-1x - 2)/(1x))| - 3) + 3) - 2) - 2| + 3)) 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": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3(-1(-1(-2sin(3\u03c0((-3(-2|x - 1| - 2) - 3)/(-2(-2|x - 1| - 2))) - 2) + 1) - 4) + 1) + 2 and g(x) = (1(2((3(-5(5x^2 - 1x - 2)^2 + 1(5x^2 - 1x - 2) + 1) - 2)/(1(-5(5x^2 - 1x - 2)^2 + 1(5x^2 - 1x - 2) + 1) - 3)) + 2) - 3)/(-2(2((3(-5(5x^2 - 1x - 2)^2 + 1(5x^2 - 1x - 2) + 1) - 2)/(1(-5(5x^2 - 1x - 2)^2 + 1(5x^2 - 1x - 2) + 1) - 3)) + 2) + 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": "2.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -3(-2cos(3\u03c0(-2|(-3((2(2x^2 + 5x + 4) - 3)/(2(2x^2 + 5x + 4) - 1))^2 + 1) - 3| + 1) + 1) + 1) - 2, g(x) = (1((1(-3(2|((-2x + 1)/(2x + 3)) + 1| + 1)) - 2)/(3(-3(2|((-2x + 1)/(2x + 3)) + 1| + 1)) + 3)) - 3)/(1((1(-3(2|((-2x + 1)/(2x + 3)) + 1| + 1)) - 2)/(3(-3(2|((-2x + 1)/(2x + 3)) + 1| + 1)) + 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": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-1(-3(-3sin(2\u03c0(5(1|(-3|x + 1| + 1) - 2| - 1)^2 + 1(1|(-3|x + 1| + 1) - 2| - 1) + 1) - 3) + 3)^2 - 1(-3sin(2\u03c0(5(1|(-3|x + 1| + 1) - 2| - 1)^2 + 1(1|(-3|x + 1| + 1) - 2| - 1) + 1) - 3) + 3) - 5))/(1(-3(-3sin(2\u03c0(5(1|(-3|x + 1| + 1) - 2| - 1)^2 + 1(1|(-3|x + 1| + 1) - 2| - 1) + 1) - 3) + 3)^2 - 1(-3sin(2\u03c0(5(1|(-3|x + 1| + 1) - 2| - 1)^2 + 1(1|(-3|x + 1| + 1) - 2| - 1) + 1) - 3) + 3) - 5)), g(x) = -2(5(-1|(2|(-3x - 2) + 3|) + 1| + 3)^2 + 5(-1|(2|(-3x - 2) + 3|) + 1| + 3) + 1) + 4, 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": "13.7", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2((-2(2sin(2\u03c0(-3|(1((2x)/(-3x + 1))^2 + 3((2x)/(-3x + 1)) + 1)|) - 3) - 1) + 1)/(2(2sin(2\u03c0(-3|(1((2x)/(-3x + 1))^2 + 3((2x)/(-3x + 1)) + 1)|) - 3) - 1) - 3))^2 - 3((-2(2sin(2\u03c0(-3|(1((2x)/(-3x + 1))^2 + 3((2x)/(-3x + 1)) + 1)|) - 3) - 1) + 1)/(2(2sin(2\u03c0(-3|(1((2x)/(-3x + 1))^2 + 3((2x)/(-3x + 1)) + 1)|) - 3) - 1) - 3)) - 1, g(x) = (1(-1|((1(-1(2x^2 + 4x + 4) + 3) + 1)/(-1(-1(2x^2 + 4x + 4) + 3) - 1)) - 2| - 1) + 3)/(-1(-1|((1(-1(2x^2 + 4x + 4) + 3) + 1)/(-1(-1(2x^2 + 4x + 4) + 3) - 1)) - 2| - 1) + 2), 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 3((1(2(1(1(2x - 5)^2 - 3(2x - 5) - 3)^2 + 2(1(2x - 5)^2 - 3(2x - 5) - 3) - 5)^2 + 5(1(1(2x - 5)^2 - 3(2x - 5) - 3)^2 + 2(1(2x - 5)^2 - 3(2x - 5) - 3) - 5)) + 2)/(3(2(1(1(2x - 5)^2 - 3(2x - 5) - 3)^2 + 2(1(2x - 5)^2 - 3(2x - 5) - 3) - 5)^2 + 5(1(1(2x - 5)^2 - 3(2x - 5) - 3)^2 + 2(1(2x - 5)^2 - 3(2x - 5) - 3) - 5)) + 2))^2 - 2((1(2(1(1(2x - 5)^2 - 3(2x - 5) - 3)^2 + 2(1(2x - 5)^2 - 3(2x - 5) - 3) - 5)^2 + 5(1(1(2x - 5)^2 - 3(2x - 5) - 3)^2 + 2(1(2x - 5)^2 - 3(2x - 5) - 3) - 5)) + 2)/(3(2(1(1(2x - 5)^2 - 3(2x - 5) - 3)^2 + 2(1(2x - 5)^2 - 3(2x - 5) - 3) - 5)^2 + 5(1(1(2x - 5)^2 - 3(2x - 5) - 3)^2 + 2(1(2x - 5)^2 - 3(2x - 5) - 3) - 5)) + 2)) and g(x) = 3|(3cos(3\u03c0(3(4(5x^2 - 3x)^2 + 5(5x^2 - 3x)) - 3) - 3) + 3) + 1| - 2 between the vertical lines x = 2.0 and x = 2.1. 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": "Find the area of the region bounded by the curves f(x) = -2sin(1\u03c0(1(-4(-1|(2(-5x - 5) - 4) + 3| - 2)^2 - 4(-1|(2(-5x - 5) - 4) + 3| - 2) - 2)^2 + 2(-4(-1|(2(-5x - 5) - 4) + 3| - 2)^2 - 4(-1|(2(-5x - 5) - 4) + 3| - 2) - 2) + 2) + 2) - 2, g(x) = -2(3e^(1(1(-2(3x^2 + 2x - 5) + 4) + 5)) - 2)^2 - 3(3e^(1(1(-2(3x^2 + 2x - 5) + 4) + 5)) - 2) + 1, x = 1.6, 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": "2.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1|((-3((1((2(3(-2|x| - 1) - 1))/(-3(3(-2|x| - 1) - 1) - 3)) + 3)/(-2((2(3(-2|x| - 1) - 1))/(-3(3(-2|x| - 1) - 1) - 3)) - 3)) + 1)/(-3((1((2(3(-2|x| - 1) - 1))/(-3(3(-2|x| - 1) - 1) - 3)) + 3)/(-2((2(3(-2|x| - 1) - 1))/(-3(3(-2|x| - 1) - 1) - 3)) - 3)) + 2)) + 3| + 3 and g(x) = (2(3(3(4(1x - 4) + 2)^2 + 2(4(1x - 4) + 2) - 3) - 3) - 3)/(1(3(3(4(1x - 4) + 2)^2 + 2(4(1x - 4) + 2) - 3) - 3)) between the vertical lines x = 3.1 and x = 3.7. 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": "Find the area of the region bounded by the curves f(x) = (-2(-2(-3|(3|(1(2|x + 3| - 2)^2 - 4(2|x + 3| - 2) - 2)|) + 3| + 3)) - 2)/(2(-2(-3|(3|(1(2|x + 3| - 2)^2 - 4(2|x + 3| - 2) - 2)|) + 3| + 3)) - 1), g(x) = 1e^(-1(-2(-2(-4(4x^2 + 2x - 5) - 5) + 5) + 3)) - 2, x = -1.2, 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": "1.8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1|(4(-4(-5(-2|((-3x + 1)/(2x)) + 2|)^2 + 5(-2|((-3x + 1)/(2x)) + 2|) + 3)^2 + 4(-5(-2|((-3x + 1)/(2x)) + 2|)^2 + 5(-2|((-3x + 1)/(2x)) + 2|) + 3)) + 3) + 3| + 1 and g(x) = (3((-1(4((-1(-1x^2 + 4x + 5) - 3)/(-2(-1x^2 + 4x + 5) - 1)) + 3) + 3)/(1(4((-1(-1x^2 + 4x + 5) - 3)/(-2(-1x^2 + 4x + 5) - 1)) + 3) + 1)) - 2)/(-1((-1(4((-1(-1x^2 + 4x + 5) - 3)/(-2(-1x^2 + 4x + 5) - 1)) + 3) + 3)/(1(4((-1(-1x^2 + 4x + 5) - 3)/(-2(-1x^2 + 4x + 5) - 1)) + 3) + 1)) - 2) 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": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1(1(-2(3(-2|((-1x)/(-3x + 1)) - 3| + 1) + 4) - 5)) + 5, g(x) = -3sin(2\u03c0(-5(1(-3((3x + 2)/(1x + 1))^2 - 5((3x + 2)/(1x + 1)) - 3) - 3)^2 - 5(1(-3((3x + 2)/(1x + 1))^2 - 5((3x + 2)/(1x + 1)) - 3) - 3) - 2) - 3), 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": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-3((-2(1(4(-3|(1x^2 - 1) - 2| + 3)^2 - 4(-3|(1x^2 - 1) - 2| + 3) - 2)^2 - 1) - 2)/(-1(1(4(-3|(1x^2 - 1) - 2| + 3)^2 - 4(-3|(1x^2 - 1) - 2| + 3) - 2)^2 - 1))) + 1)/(3((-2(1(4(-3|(1x^2 - 1) - 2| + 3)^2 - 4(-3|(1x^2 - 1) - 2| + 3) - 2)^2 - 1) - 2)/(-1(1(4(-3|(1x^2 - 1) - 2| + 3)^2 - 4(-3|(1x^2 - 1) - 2| + 3) - 2)^2 - 1))) - 2) and g(x) = (-1(2((-3(-3|(-3e^(-2x) + 3)|) - 3)/(-1(-3|(-3e^(-2x) + 3)|)))^2 - 3((-3(-3|(-3e^(-2x) + 3)|) - 3)/(-1(-3|(-3e^(-2x) + 3)|))) + 1) + 2)/(-1(2((-3(-3|(-3e^(-2x) + 3)|) - 3)/(-1(-3|(-3e^(-2x) + 3)|)))^2 - 3((-3(-3|(-3e^(-2x) + 3)|) - 3)/(-1(-3|(-3e^(-2x) + 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": "2.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1|(-2e^(-1(-1(-1(-1(2|x - 2|)^2 + 4(2|x - 2|) + 4))^2 + 2(-1(-1(2|x - 2|)^2 + 4(2|x - 2|) + 4)))) + 3) + 2| + 2 and g(x) = (-3(1|(4((1(-4x^2 + 4x + 4) + 2)/(-2(-4x^2 + 4x + 4)))) - 2| - 1))/(3(1|(4((1(-4x^2 + 4x + 4) + 2)/(-2(-4x^2 + 4x + 4)))) - 2| - 1) - 2) between the vertical lines x = -0.4 and x = -0.30000000000000004. 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(4((2(3|((-1(-4x + 1) - 1)/(1(-4x + 1) - 3))| + 2) + 1)/(-1(3|((-1(-4x + 1) - 1)/(1(-4x + 1) - 3))| + 2) - 2)) - 1) - 3)/(-1(4((2(3|((-1(-4x + 1) - 1)/(1(-4x + 1) - 3))| + 2) + 1)/(-1(3|((-1(-4x + 1) - 1)/(1(-4x + 1) - 3))| + 2) - 2)) - 1) - 3) and g(x) = -2|(-2(-3|(2|(2|x + 3| - 1) + 2| - 1) - 3| + 2) - 5) - 1| + 1 from x = -2.8 to x = -2.2. 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": "Calculate the area enclosed between the functions f(x) = (1(-4(2|(-2sin(1\u03c0((-1(2x) - 3)/(-1(2x) - 3)) - 1) - 1) + 1| + 3) - 4))/(-2(-4(2|(-2sin(1\u03c0((-1(2x) - 3)/(-1(2x) - 3)) - 1) - 1) + 1| + 3) - 4)) and g(x) = 3(2((3(1(-2sin(1\u03c0x) + 3)^2 - 4(-2sin(1\u03c0x) + 3) + 4) - 1)/(1(1(-2sin(1\u03c0x) + 3)^2 - 4(-2sin(1\u03c0x) + 3) + 4) + 3)) - 2) + 1 from x = -2.0 to x = -1.0. 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": "Calculate the area enclosed between the functions f(x) = (1((1(5(-2((1(-2sin(3\u03c0x) - 1) + 1)/(1(-2sin(3\u03c0x) - 1))) - 3)^2 + 5(-2((1(-2sin(3\u03c0x) - 1) + 1)/(1(-2sin(3\u03c0x) - 1))) - 3) - 5))/(1(5(-2((1(-2sin(3\u03c0x) - 1) + 1)/(1(-2sin(3\u03c0x) - 1))) - 3)^2 + 5(-2((1(-2sin(3\u03c0x) - 1) + 1)/(1(-2sin(3\u03c0x) - 1))) - 3) - 5) - 3)) + 2)/(-1((1(5(-2((1(-2sin(3\u03c0x) - 1) + 1)/(1(-2sin(3\u03c0x) - 1))) - 3)^2 + 5(-2((1(-2sin(3\u03c0x) - 1) + 1)/(1(-2sin(3\u03c0x) - 1))) - 3) - 5))/(1(5(-2((1(-2sin(3\u03c0x) - 1) + 1)/(1(-2sin(3\u03c0x) - 1))) - 3)^2 + 5(-2((1(-2sin(3\u03c0x) - 1) + 1)/(1(-2sin(3\u03c0x) - 1))) - 3) - 5) - 3)) + 3) and g(x) = -1((-3(-5(-1cos(3\u03c0(1|x - 2| + 2) - 3) - 2)^2 + 5(-1cos(3\u03c0(1|x - 2| + 2) - 3) - 2) - 3) - 3)/(1(-5(-1cos(3\u03c0(1|x - 2| + 2) - 3) - 2)^2 + 5(-1cos(3\u03c0(1|x - 2| + 2) - 3) - 2) - 3) - 3)) + 4 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-3(4((-3(-5((-1(3x - 2) + 2)/(3(3x - 2))) + 3) - 1)/(3(-5((-1(3x - 2) + 2)/(3(3x - 2))) + 3) - 2))^2 + 3((-3(-5((-1(3x - 2) + 2)/(3(3x - 2))) + 3) - 1)/(3(-5((-1(3x - 2) + 2)/(3(3x - 2))) + 3) - 2)) + 1) - 2)/(-3(4((-3(-5((-1(3x - 2) + 2)/(3(3x - 2))) + 3) - 1)/(3(-5((-1(3x - 2) + 2)/(3(3x - 2))) + 3) - 2))^2 + 3((-3(-5((-1(3x - 2) + 2)/(3(3x - 2))) + 3) - 1)/(3(-5((-1(3x - 2) + 2)/(3(3x - 2))) + 3) - 2)) + 1) + 4), g(x) = -3|(-3|(1|(-3cos(2\u03c0((-2x + 2)/(2x - 1)) + 2)) - 2| - 2) - 2| + 2) + 3| + 3, 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": "5.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2(4((-2(-1|((-2((-2x - 3)/(2x + 1)) + 2)/(2((-2x - 3)/(2x + 1)) - 1)) + 1| + 2) + 2)/(-3(-1|((-2((-2x - 3)/(2x + 1)) + 2)/(2((-2x - 3)/(2x + 1)) - 1)) + 1| + 2) + 1)) + 5)^2 - 3(4((-2(-1|((-2((-2x - 3)/(2x + 1)) + 2)/(2((-2x - 3)/(2x + 1)) - 1)) + 1| + 2) + 2)/(-3(-1|((-2((-2x - 3)/(2x + 1)) + 2)/(2((-2x - 3)/(2x + 1)) - 1)) + 1| + 2) + 1)) + 5) - 2, g(x) = 4(-4((3((-1((2x + 1)/(-2x - 2)) - 3)/(1((2x + 1)/(-2x - 2)) + 2)) - 2)/(-2((-1((2x + 1)/(-2x - 2)) - 3)/(1((2x + 1)/(-2x - 2)) + 2)) - 1)) - 5)^2 - 5(-4((3((-1((2x + 1)/(-2x - 2)) - 3)/(1((2x + 1)/(-2x - 2)) + 2)) - 2)/(-2((-1((2x + 1)/(-2x - 2)) - 3)/(1((2x + 1)/(-2x - 2)) + 2)) - 1)) - 5) - 3, x = -2.5, 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": "20.7", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1((1(1(2(-1(-2x^2 + 2x + 4) - 4) - 1) - 2) - 2)/(2(1(2(-1(-2x^2 + 2x + 4) - 4) - 1) - 2) - 1)) - 1, g(x) = 2(-1(-1sin(2\u03c0((-3((2x)/(-2x + 1)) - 2)/(-2((2x)/(-2x + 1)))) + 1)) + 3) + 1, 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": "40.7", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -5(2|(2sin(1\u03c0(1|(3(1x - 4) + 5) - 1| - 2) - 3)) + 1| - 3)^2 + 5(2|(2sin(1\u03c0(1|(3(1x - 4) + 5) - 1| - 2) - 3)) + 1| - 3) + 5, g(x) = 2((2(-3(1(1x^2 - 5x + 3) - 3) + 1))/(1(-3(1(1x^2 - 5x + 3) - 3) + 1) + 1))^2 - 5((2(-3(1(1x^2 - 5x + 3) - 3) + 1))/(1(-3(1(1x^2 - 5x + 3) - 3) + 1) + 1)) + 4, x = -4.6, 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": "3.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-3(-5(-5(-3|((-2(5x^2 + 3x - 3) - 2)/(-2(5x^2 + 3x - 3))) + 2| + 1)^2 + 4(-3|((-2(5x^2 + 3x - 3) - 2)/(-2(5x^2 + 3x - 3))) + 2| + 1)) + 3) + 3)/(2(-5(-5(-3|((-2(5x^2 + 3x - 3) - 2)/(-2(5x^2 + 3x - 3))) + 2| + 1)^2 + 4(-3|((-2(5x^2 + 3x - 3) - 2)/(-2(5x^2 + 3x - 3))) + 2| + 1)) + 3)) and g(x) = 2e^(-1((-2(-2|((1(-1x + 4) + 3)/(-1(-1x + 4) + 2)) - 2| + 3))/(-2(-2|((1(-1x + 4) + 3)/(-1(-1x + 4) + 2)) - 2| + 3) - 3))) + 1 between the vertical lines x = -1.1 and x = 0.5. 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) = 3|(5((2(2(2|(-2x^2 + 5x) + 3|) + 3))/(-1(2(2|(-2x^2 + 5x) + 3|) + 3) + 2))^2 - 3((2(2(2|(-2x^2 + 5x) + 3|) + 3))/(-1(2(2|(-2x^2 + 5x) + 3|) + 3) + 2)) - 2) - 3| - 1 and g(x) = (-1(2(-2(4(-2sin(2\u03c0x - 2)) + 2) - 5) - 4))/(-1(2(-2(4(-2sin(2\u03c0x - 2)) + 2) - 5) - 4) - 2) between the vertical lines x = -0.3 and x = 3.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "338.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (1(1(2|(-3((2(2x^2 - 1x - 4) - 1)/(-3(2x^2 - 1x - 4)))^2 - 2((2(2x^2 - 1x - 4) - 1)/(-3(2x^2 - 1x - 4))) + 3) - 2| + 1) - 3))/(-1(1(2|(-3((2(2x^2 - 1x - 4) - 1)/(-3(2x^2 - 1x - 4)))^2 - 2((2(2x^2 - 1x - 4) - 1)/(-3(2x^2 - 1x - 4))) + 3) - 2| + 1) - 3) + 2), g(x) = -1(-3e^(-1(2(5(2|x + 2| + 3) - 5) - 4)) - 3) - 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1(-4((1(-3|(-5(1x + 1) - 4) - 2| - 3) - 1)/(-2(-3|(-5(1x + 1) - 4) - 2| - 3) + 1)) + 4)^2 + 1(-4((1(-3|(-5(1x + 1) - 4) - 2| - 3) - 1)/(-2(-3|(-5(1x + 1) - 4) - 2| - 3) + 1)) + 4) + 5 and g(x) = -3((3(5(-4(-4x + 1) - 1)^2 - 2(-4(-4x + 1) - 1) + 2) - 3)/(1(5(-4(-4x + 1) - 1)^2 - 2(-4(-4x + 1) - 1) + 2) - 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": "4.7", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2(-5((3((2(1|(2x^2 + 5x + 2) - 3| - 3) - 1)/(3(1|(2x^2 + 5x + 2) - 3| - 3))) + 2)/(1((2(1|(2x^2 + 5x + 2) - 3| - 3) - 1)/(3(1|(2x^2 + 5x + 2) - 3| - 3))) + 2))^2 - 3((3((2(1|(2x^2 + 5x + 2) - 3| - 3) - 1)/(3(1|(2x^2 + 5x + 2) - 3| - 3))) + 2)/(1((2(1|(2x^2 + 5x + 2) - 3| - 3) - 1)/(3(1|(2x^2 + 5x + 2) - 3| - 3))) + 2)) - 2) - 5 and g(x) = 2|(2((-3(2|(5x^2 + 3x - 2) + 2| - 2))/(2(2|(5x^2 + 3x - 2) + 2| - 2) + 3)) + 2) + 1| + 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": "91.7", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3(1|(2(2|(3sin(2\u03c0(-3x + 1) + 1) - 3) - 2| - 3)^2 - 1(2|(3sin(2\u03c0(-3x + 1) + 1) - 3) - 2| - 3) + 5)| - 2) + 2, g(x) = 4(3(1|(-1((3x + 1)/(-2x + 3))^2 + 3((3x + 1)/(-2x + 3)) - 4)|)^2 - 1(1|(-1((3x + 1)/(-2x + 3))^2 + 3((3x + 1)/(-2x + 3)) - 4)|) - 3)^2 - 3(3(1|(-1((3x + 1)/(-2x + 3))^2 + 3((3x + 1)/(-2x + 3)) - 4)|)^2 - 1(1|(-1((3x + 1)/(-2x + 3))^2 + 3((3x + 1)/(-2x + 3)) - 4)|) - 3) - 2, 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": "22.6", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2(2(1|(-5(-2e^(1(-3x - 5)))^2 - 2(-2e^(1(-3x - 5))) - 3) + 1| - 3) - 5) + 5, g(x) = -1|((-1(-4(2|((2x - 3)/(-1x + 2)) + 2| - 2)^2 + 5) - 2)/(2(-4(2|((2x - 3)/(-1x + 2)) + 2| - 2)^2 + 5) - 1)) - 2| + 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": "4.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1(5(3(5(-4((-1x)/(3x - 2)) - 5) + 1) - 4)^2 - 1) + 5, g(x) = (1(-1|(5(5((2x - 2)/(2x + 2))^2 - 2((2x - 2)/(2x + 2)) + 2)^2 + 1(5((2x - 2)/(2x + 2))^2 - 2((2x - 2)/(2x + 2)) + 2) - 1) + 3| + 1))/(-3(-1|(5(5((2x - 2)/(2x + 2))^2 - 2((2x - 2)/(2x + 2)) + 2)^2 + 1(5((2x - 2)/(2x + 2))^2 - 2((2x - 2)/(2x + 2)) + 2) - 1) + 3| + 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": "47.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-2(-2|(-5(3|(-4((1x + 3)/(1x + 3)) - 2) + 3| - 3)^2 - 5(3|(-4((1x + 3)/(1x + 3)) - 2) + 3| - 3) + 3) + 3| + 1) - 2)/(-1(-2|(-5(3|(-4((1x + 3)/(1x + 3)) - 2) + 3| - 3)^2 - 5(3|(-4((1x + 3)/(1x + 3)) - 2) + 3| - 3) + 3) + 3| + 1) + 2) and g(x) = 5(-2|(2|((-2((3x - 3)/(-1x - 2)) - 1)/(1((3x - 3)/(-1x - 2)) - 2)) + 2| + 1) - 1| + 1) + 5 from x = -3.2 to x = -1.5. 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) = (1(-3|(2((2(-4(2cos(3\u03c0x + 2)) - 4) - 3)/(-1(-4(2cos(3\u03c0x + 2)) - 4))) - 2) - 2| + 3) + 2)/(-1(-3|(2((2(-4(2cos(3\u03c0x + 2)) - 4) - 3)/(-1(-4(2cos(3\u03c0x + 2)) - 4))) - 2) - 2| + 3) + 2), g(x) = 4(-2cos(2\u03c0(-2|((1((2x + 3)/(1x - 3)))/(-2((2x + 3)/(1x - 3)) + 1)) + 1| - 1) + 3) - 1)^2 + 2(-2cos(2\u03c0(-2|((1((2x + 3)/(1x - 3)))/(-2((2x + 3)/(1x - 3)) + 1)) + 1| - 1) + 3) - 1), x = -3.1, 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": "47.9", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -3cos(3\u03c0((-1(3|(1(-2|(-1|x| + 1) - 1| + 2) + 3)|) - 1)/(-3(3|(1(-2|(-1|x| + 1) - 1| + 2) + 3)|))) - 3) + 2, g(x) = 2|(1((-1(-2sin(1\u03c0(1|x + 1| + 3) - 2) - 1) + 1)/(-1(-2sin(1\u03c0(1|x + 1| + 3) - 2) - 1)))) - 3| + 2, x = 2.6, 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2(-2cos(1\u03c0(1|(5(1(-1|x| + 1)^2 - 4(-1|x| + 1) - 5)) - 1| - 3))) + 2 and g(x) = 2cos(3\u03c0(1|((-1(3|((-1x - 1)/(3x + 2)) + 2| - 3) - 1)/(1(3|((-1x - 1)/(3x + 2)) + 2| - 3) - 2))| + 1) - 3) 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": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (1(-2cos(1\u03c0(1((-1((3(3|x| - 2) - 3)/(2(3|x| - 2) + 1)) + 3)/(-2((3(3|x| - 2) - 3)/(2(3|x| - 2) + 1)) + 3))^2 + 3((-1((3(3|x| - 2) - 3)/(2(3|x| - 2) + 1)) + 3)/(-2((3(3|x| - 2) - 3)/(2(3|x| - 2) + 1)) + 3)) + 4) - 2) + 1) + 2)/(1(-2cos(1\u03c0(1((-1((3(3|x| - 2) - 3)/(2(3|x| - 2) + 1)) + 3)/(-2((3(3|x| - 2) - 3)/(2(3|x| - 2) + 1)) + 3))^2 + 3((-1((3(3|x| - 2) - 3)/(2(3|x| - 2) + 1)) + 3)/(-2((3(3|x| - 2) - 3)/(2(3|x| - 2) + 1)) + 3)) + 4) - 2) + 1)) and g(x) = -5((1(-2sin(2\u03c0(1|((3x)/(1x + 2)) - 1| - 3) - 2) + 3) + 2)/(-1(-2sin(2\u03c0(1|((3x)/(1x + 2)) - 1| - 3) - 2) + 3) + 2)) + 2 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": "1.9", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-2(-1|((-2((3((1(-2|x - 1| + 2) - 1)/(2(-2|x - 1| + 2) + 1)))/(-3((1(-2|x - 1| + 2) - 1)/(2(-2|x - 1| + 2) + 1)) - 1)) + 2)/(-2((3((1(-2|x - 1| + 2) - 1)/(2(-2|x - 1| + 2) + 1)))/(-3((1(-2|x - 1| + 2) - 1)/(2(-2|x - 1| + 2) + 1)) - 1)) + 3)) + 3| - 1) + 2)/(1(-1|((-2((3((1(-2|x - 1| + 2) - 1)/(2(-2|x - 1| + 2) + 1)))/(-3((1(-2|x - 1| + 2) - 1)/(2(-2|x - 1| + 2) + 1)) - 1)) + 2)/(-2((3((1(-2|x - 1| + 2) - 1)/(2(-2|x - 1| + 2) + 1)))/(-3((1(-2|x - 1| + 2) - 1)/(2(-2|x - 1| + 2) + 1)) - 1)) + 3)) + 3| - 1) + 3), g(x) = -2|((2((1((-2(1|x - 3| + 1) + 1)/(-2(1|x - 3| + 1) + 3)) + 3)/(3((-2(1|x - 3| + 1) + 1)/(-2(1|x - 3| + 1) + 3)) - 2)) + 2)/(-3((1((-2(1|x - 3| + 1) + 1)/(-2(1|x - 3| + 1) + 3)) + 3)/(3((-2(1|x - 3| + 1) + 1)/(-2(1|x - 3| + 1) + 3)) - 2)) + 4)) - 1| + 3, x = 1.7, 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": "0.9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2|((1(3((2(2(-1x + 3)^2 + 3(-1x + 3) - 3) - 2)/(-1(2(-1x + 3)^2 + 3(-1x + 3) - 3) + 3)) + 5) + 2)/(1(3((2(2(-1x + 3)^2 + 3(-1x + 3) - 3) - 2)/(-1(2(-1x + 3)^2 + 3(-1x + 3) - 3) + 3)) + 5) - 2)) - 2| and g(x) = -2(-1|(1|(1|(-1sin(3\u03c0x - 2) + 1) + 3| - 2) - 1| + 3)| - 2)^2 - 4(-1|(1|(1|(-1sin(3\u03c0x - 2) + 1) + 3| - 2) - 1| + 3)| - 2) - 4 from x = 2.6 to x = 4.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "101.6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2|(5(-1|(-2cos(1\u03c0(2|(5x + 3) - 2| + 1)) + 3) + 2| - 2)^2 + 1(-1|(-2cos(1\u03c0(2|(5x + 3) - 2| + 1)) + 3) + 2| - 2) - 3) + 2| - 3 and g(x) = -1(-1((-2(2|(1x - 1) - 2|) + 3)/(2(2|(1x - 1) - 2|) - 1)))^2 + 3(-1((-2(2|(1x - 1) - 2|) + 3)/(2(2|(1x - 1) - 2|) - 1))) - 1 from x = 2.8 to x = 3.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "192.8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 5(2cos(2\u03c0(-1|(-1(5(5x + 2)) + 2) + 3| - 3) - 3) - 1) + 5 and g(x) = (-2((1(-2cos(2\u03c0(-5(-2x) + 4) - 2)) - 3)/(3(-2cos(2\u03c0(-5(-2x) + 4) - 2)) - 2)) + 3)/(2((1(-2cos(2\u03c0(-5(-2x) + 4) - 2)) - 3)/(3(-2cos(2\u03c0(-5(-2x) + 4) - 2)) - 2)) + 3) from x = 2.7 to x = 2.8. 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) = (-3((-2(-1(-3(-2sin(3\u03c0(1|x - 2| - 1) + 2) - 2) + 2) + 5) + 1)/(3(-1(-3(-2sin(3\u03c0(1|x - 2| - 1) + 2) - 2) + 2) + 5))) - 1)/(-1((-2(-1(-3(-2sin(3\u03c0(1|x - 2| - 1) + 2) - 2) + 2) + 5) + 1)/(3(-1(-3(-2sin(3\u03c0(1|x - 2| - 1) + 2) - 2) + 2) + 5))) - 2), g(x) = 1(-1|(3|(2|(1x - 4) + 3|) + 2| + 1) - 2| + 2) + 5, 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": "1.4", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -5(-3(3|(3cos(2\u03c0(-4((-3x + 3)/(1x)) - 5) + 2) + 2)|) + 3) + 4 and g(x) = (-1(1(-3(-4(2x - 4) + 5)^2 + 4(-4(2x - 4) + 5) - 5)^2 - 2(-3(-4(2x - 4) + 5)^2 + 4(-4(2x - 4) + 5) - 5) - 4) + 2)/(-2(1(-3(-4(2x - 4) + 5)^2 + 4(-4(2x - 4) + 5) - 5)^2 - 2(-3(-4(2x - 4) + 5)^2 + 4(-4(2x - 4) + 5) - 5) - 4) - 1) between the vertical lines x = -0.4 and x = -0.30000000000000004. 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) = -4(-2((-3((-2(-2|((-2x - 2)/(2x - 3)) - 1| - 1) + 2)/(-1(-2|((-2x - 2)/(2x - 3)) - 1| - 1) - 1)) + 1)/(1((-2(-2|((-2x - 2)/(2x - 3)) - 1| - 1) + 2)/(-1(-2|((-2x - 2)/(2x - 3)) - 1| - 1) - 1)) + 3))^2 - 1((-3((-2(-2|((-2x - 2)/(2x - 3)) - 1| - 1) + 2)/(-1(-2|((-2x - 2)/(2x - 3)) - 1| - 1) - 1)) + 1)/(1((-2(-2|((-2x - 2)/(2x - 3)) - 1| - 1) + 2)/(-1(-2|((-2x - 2)/(2x - 3)) - 1| - 1) - 1)) + 3)) - 1)^2 + 2(-2((-3((-2(-2|((-2x - 2)/(2x - 3)) - 1| - 1) + 2)/(-1(-2|((-2x - 2)/(2x - 3)) - 1| - 1) - 1)) + 1)/(1((-2(-2|((-2x - 2)/(2x - 3)) - 1| - 1) + 2)/(-1(-2|((-2x - 2)/(2x - 3)) - 1| - 1) - 1)) + 3))^2 - 1((-3((-2(-2|((-2x - 2)/(2x - 3)) - 1| - 1) + 2)/(-1(-2|((-2x - 2)/(2x - 3)) - 1| - 1) - 1)) + 1)/(1((-2(-2|((-2x - 2)/(2x - 3)) - 1| - 1) + 2)/(-1(-2|((-2x - 2)/(2x - 3)) - 1| - 1) - 1)) + 3)) - 1) + 3 and g(x) = -2(3sin(3\u03c0((-1(2(-4x - 5) - 4) + 3)/(1(2(-4x - 5) - 4) - 3)) + 1) - 2)^2 + 3(3sin(3\u03c0((-1(2(-4x - 5) - 4) + 3)/(1(2(-4x - 5) - 4) - 3)) + 1) - 2) + 1 between the vertical lines x = -4.8 and x = 0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "312.4", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2sin(2\u03c0(1(2(-4(4((-2x)/(-1x - 3)) - 1) + 4)^2 - 1(-4(4((-2x)/(-1x - 3)) - 1) + 4) - 2) + 5) + 3) - 3, g(x) = -3|(-1|(-2sin(2\u03c0(4((-1x + 1)/(2x - 3))^2 - 2((-1x + 1)/(2x - 3)) - 3) + 1) + 1) - 1| - 1)|, x = 2.8, 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": "2.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -5(-5((-2(-4(-3cos(3\u03c0((-2x)/(1x - 3)) - 3) - 1)^2 + 2(-3cos(3\u03c0((-2x)/(1x - 3)) - 3) - 1) + 1) - 1)/(-1(-4(-3cos(3\u03c0((-2x)/(1x - 3)) - 3) - 1)^2 + 2(-3cos(3\u03c0((-2x)/(1x - 3)) - 3) - 1) + 1) - 2))^2 - 4((-2(-4(-3cos(3\u03c0((-2x)/(1x - 3)) - 3) - 1)^2 + 2(-3cos(3\u03c0((-2x)/(1x - 3)) - 3) - 1) + 1) - 1)/(-1(-4(-3cos(3\u03c0((-2x)/(1x - 3)) - 3) - 1)^2 + 2(-3cos(3\u03c0((-2x)/(1x - 3)) - 3) - 1) + 1) - 2)) + 4) - 4 and g(x) = 2|(1((-2(1(2e^(-1x) + 1) + 1) - 1)/(2(1(2e^(-1x) + 1) + 1) + 1))^2 - 2((-2(1(2e^(-1x) + 1) + 1) - 1)/(2(1(2e^(-1x) + 1) + 1) + 1)) + 4) - 1| - 1 from x = 2.8 to x = 2.9. 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) = (-3(-2|((3((-1(-2cos(3\u03c0(4x^2 + 2x + 1) - 2) + 1) - 3)/(2(-2cos(3\u03c0(4x^2 + 2x + 1) - 2) + 1) - 3)) - 3)/(-1((-1(-2cos(3\u03c0(4x^2 + 2x + 1) - 2) + 1) - 3)/(2(-2cos(3\u03c0(4x^2 + 2x + 1) - 2) + 1) - 3)) - 3)) + 2| + 1) + 1)/(-1(-2|((3((-1(-2cos(3\u03c0(4x^2 + 2x + 1) - 2) + 1) - 3)/(2(-2cos(3\u03c0(4x^2 + 2x + 1) - 2) + 1) - 3)) - 3)/(-1((-1(-2cos(3\u03c0(4x^2 + 2x + 1) - 2) + 1) - 3)/(2(-2cos(3\u03c0(4x^2 + 2x + 1) - 2) + 1) - 3)) - 3)) + 2| + 1) - 1) and g(x) = (-3((-2((3(-1|(-1x - 5) + 1| - 3) - 3)/(3(-1|(-1x - 5) + 1| - 3) - 2)) + 2)/(1((3(-1|(-1x - 5) + 1| - 3) - 3)/(3(-1|(-1x - 5) + 1| - 3) - 2)))))/(3((-2((3(-1|(-1x - 5) + 1| - 3) - 3)/(3(-1|(-1x - 5) + 1| - 3) - 2)) + 2)/(1((3(-1|(-1x - 5) + 1| - 3) - 3)/(3(-1|(-1x - 5) + 1| - 3) - 2)))) + 1) 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-3((1(-3cos(2\u03c0(2|(5(5x^2 + 4x - 3) + 3) + 1|) + 1) + 2) + 3)/(-3(-3cos(2\u03c0(2|(5(5x^2 + 4x - 3) + 3) + 1|) + 1) + 2) - 1)) - 2)/(3((1(-3cos(2\u03c0(2|(5(5x^2 + 4x - 3) + 3) + 1|) + 1) + 2) + 3)/(-3(-3cos(2\u03c0(2|(5(5x^2 + 4x - 3) + 3) + 1|) + 1) + 2) - 1)) - 2) and g(x) = 1|(-1(1(-1(-2x^2)^2 + 4(-2x^2) + 5)^2 - 1(-1(-2x^2)^2 + 4(-2x^2) + 5)) + 4) + 1| - 2 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-1(1(-3sin(1\u03c0((-1(-1|(-4x - 4) + 2| + 1) + 3)/(-2(-1|(-4x - 4) + 2| + 1))) + 1) - 1) + 2) + 2)/(3(1(-3sin(1\u03c0((-1(-1|(-4x - 4) + 2| + 1) + 3)/(-2(-1|(-4x - 4) + 2| + 1))) + 1) - 1) + 2)), g(x) = 1|(-3((-2((-3(1x^2 - 4x) + 1)/(-3(1x^2 - 4x) - 2)) + 2)/(2((-3(1x^2 - 4x) + 1)/(-3(1x^2 - 4x) - 2)) - 1))^2 + 4((-2((-3(1x^2 - 4x) + 1)/(-3(1x^2 - 4x) - 2)) + 2)/(2((-3(1x^2 - 4x) + 1)/(-3(1x^2 - 4x) - 2)) - 1)) - 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": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1|(-1|(5(-2((-2(-3|x - 3| + 2) + 2)/(-1(-3|x - 3| + 2) - 1)) + 3) + 2)| - 3) + 1| + 1, g(x) = -2|(-1cos(1\u03c0(3|(2(-1x - 3)^2 + 5(-1x - 3) - 4) - 1|) - 1) - 1) - 3|, 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) = -1((-1(-2(-2((3(3x + 5) - 2)/(-1(3x + 5) - 3))^2 + 3((3(3x + 5) - 2)/(-1(3x + 5) - 3)) - 4)^2 + 4(-2((3(3x + 5) - 2)/(-1(3x + 5) - 3))^2 + 3((3(3x + 5) - 2)/(-1(3x + 5) - 3)) - 4) - 4) - 3)/(-1(-2(-2((3(3x + 5) - 2)/(-1(3x + 5) - 3))^2 + 3((3(3x + 5) - 2)/(-1(3x + 5) - 3)) - 4)^2 + 4(-2((3(3x + 5) - 2)/(-1(3x + 5) - 3))^2 + 3((3(3x + 5) - 2)/(-1(3x + 5) - 3)) - 4) - 4) + 3))^2 + 1 and g(x) = 3(3(1sin(1\u03c0(2|(3x^2 + 4x + 5) - 2| + 3) - 1) - 2) + 5) - 3 from x = 4.9 to x = 5.0. 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": "Determine the area of the region enclosed by the graphs of f(x) = 2|((-3(-2(-1(1(1|x - 2| - 3) + 3)^2 + 5(1(1|x - 2| - 3) + 3) - 5) - 4) + 1)/(-2(-2(-1(1(1|x - 2| - 3) + 3)^2 + 5(1(1|x - 2| - 3) + 3) - 5) - 4)))| - 2 and g(x) = 3(-3cos(3\u03c0(-3|((-2((-1x - 1)/(3x)) - 1)/(-3((-1x - 1)/(3x)) - 3)) + 2| - 1) - 1) + 1) - 1 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": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -4(-2|(3|((-2(3((1x + 1)/(3x))^2 - 2) + 1)/(-1(3((1x + 1)/(3x))^2 - 2))) - 1| - 2)| - 3)^2 + 5(-2|(3|((-2(3((1x + 1)/(3x))^2 - 2) + 1)/(-1(3((1x + 1)/(3x))^2 - 2))) - 1| - 2)| - 3) + 2 and g(x) = -1(-3(-1(2|(-2|x - 2| - 2) + 3| - 3)^2 - 2(2|(-2|x - 2| - 2) + 3| - 3) - 5) + 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": "2.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1|(-3cos(2\u03c0((-3(-1(-1|(3x) + 1| - 3) + 3) + 1)/(3(-1(-1|(3x) + 1| - 3) + 3) + 3))) + 2) + 2| + 2 and g(x) = (-3(-3sin(3\u03c0(2|(-5(4x^2 - 5x - 5) - 2) + 2| + 2)) - 3) - 1)/(-3(-3sin(3\u03c0(2|(-5(4x^2 - 5x - 5) - 2) + 2| + 2)) - 3) - 2) 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": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-2((-3(-1(-2(1|(2e^(2x) - 1)| - 2)^2 + 2(1|(2e^(2x) - 1)| - 2)) - 3) - 1)/(-2(-1(-2(1|(2e^(2x) - 1)| - 2)^2 + 2(1|(2e^(2x) - 1)| - 2)) - 3) - 1)))/(-1((-3(-1(-2(1|(2e^(2x) - 1)| - 2)^2 + 2(1|(2e^(2x) - 1)| - 2)) - 3) - 1)/(-2(-1(-2(1|(2e^(2x) - 1)| - 2)^2 + 2(1|(2e^(2x) - 1)| - 2)) - 3) - 1)) + 2), g(x) = (-2(2(2sin(1\u03c0((-2(4x + 5) - 3)/(-1(4x + 5) + 3)) + 3) + 2)^2 - 2(2sin(1\u03c0((-2(4x + 5) - 3)/(-1(4x + 5) + 3)) + 3) + 2) - 1) + 1)/(1(2(2sin(1\u03c0((-2(4x + 5) - 3)/(-1(4x + 5) + 3)) + 3) + 2)^2 - 2(2sin(1\u03c0((-2(4x + 5) - 3)/(-1(4x + 5) + 3)) + 3) + 2) - 1) - 3), 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1|(-1|(-5((1(3|(2x^2 - 5x + 2) - 2| + 3) - 1)/(-2(3|(2x^2 - 5x + 2) - 2| + 3) + 3)) + 3) + 1| - 1) + 3| + 2 and g(x) = 3cos(1\u03c0(-4((3(1(2x^2 + 4x + 5)^2 - 4(2x^2 + 4x + 5) + 5) - 2)/(1(1(2x^2 + 4x + 5)^2 - 4(2x^2 + 4x + 5) + 5) - 2)) + 2) + 3) - 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": "Determine the area of the region enclosed by the graphs of f(x) = -2(1(1|(-4(2(1x^2 + 4x - 3)^2 - 5(1x^2 + 4x - 3) + 3) - 5) + 2| + 1)^2 - 4(1|(-4(2(1x^2 + 4x - 3)^2 - 5(1x^2 + 4x - 3) + 3) - 5) + 2| + 1) - 3) + 1 and g(x) = (3((2(2((1((-3x - 1)/(-3x + 2)) - 1)/(1((-3x - 1)/(-3x + 2)) + 2))^2 - 4((1((-3x - 1)/(-3x + 2)) - 1)/(1((-3x - 1)/(-3x + 2)) + 2))) + 1)/(2(2((1((-3x - 1)/(-3x + 2)) - 1)/(1((-3x - 1)/(-3x + 2)) + 2))^2 - 4((1((-3x - 1)/(-3x + 2)) - 1)/(1((-3x - 1)/(-3x + 2)) + 2))))))/(-3((2(2((1((-3x - 1)/(-3x + 2)) - 1)/(1((-3x - 1)/(-3x + 2)) + 2))^2 - 4((1((-3x - 1)/(-3x + 2)) - 1)/(1((-3x - 1)/(-3x + 2)) + 2))) + 1)/(2(2((1((-3x - 1)/(-3x + 2)) - 1)/(1((-3x - 1)/(-3x + 2)) + 2))^2 - 4((1((-3x - 1)/(-3x + 2)) - 1)/(1((-3x - 1)/(-3x + 2)) + 2))))) + 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": "0.7", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (2((-3(-5(-1(3cos(1\u03c0((-1x - 2)/(3x + 3)) + 2)) - 1) + 5) + 3)/(2(-5(-1(3cos(1\u03c0((-1x - 2)/(3x + 3)) + 2)) - 1) + 5) + 3)) - 2)/(1((-3(-5(-1(3cos(1\u03c0((-1x - 2)/(3x + 3)) + 2)) - 1) + 5) + 3)/(2(-5(-1(3cos(1\u03c0((-1x - 2)/(3x + 3)) + 2)) - 1) + 5) + 3)) - 3), g(x) = (-2(-3(2(-3|(-3x^2 - 5x) - 2|)^2 + 3(-3|(-3x^2 - 5x) - 2|)) + 1))/(-2(-3(2(-3|(-3x^2 - 5x) - 2|)^2 + 3(-3|(-3x^2 - 5x) - 2|)) + 1) - 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": "Determine the area of the region enclosed by the graphs of f(x) = 4(-1(-1sin(3\u03c0(4(-4((3x + 3)/(3x + 1)) - 3) + 3) - 1) - 1) - 1)^2 - 2(-1(-1sin(3\u03c0(4(-4((3x + 3)/(3x + 1)) - 3) + 3) - 1) - 1) - 1) - 4 and g(x) = -1|(1|(-2((-2(-4x^2 + 5x + 5) - 1)/(-1(-4x^2 + 5x + 5) - 1)) - 2) + 2| + 1) + 1| - 1 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": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1(-1(1(5(1(4x + 4) + 1) - 1) + 5) - 2)^2 + 5(-1(1(5(1(4x + 4) + 1) - 1) + 5) - 2) + 2, g(x) = -1|(2|(-2sin(2\u03c0((1(2|x + 3| - 3) - 3)/(2(2|x + 3| - 3) - 1)) + 2) - 1)|) - 1| + 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": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1(1(2e^(1(2(4(1x^2 + 2x - 1) - 4) - 1)) - 1)^2 + 3(2e^(1(2(4(1x^2 + 2x - 1) - 4) - 1)) - 1) - 4)^2 + 2(1(2e^(1(2(4(1x^2 + 2x - 1) - 4) - 1)) - 1)^2 + 3(2e^(1(2(4(1x^2 + 2x - 1) - 4) - 1)) - 1) - 4) + 1, g(x) = (1(5(4(-2(1x^2 + 5x + 1)^2 - 5(1x^2 + 5x + 1) - 1) + 1)^2 + 1(4(-2(1x^2 + 5x + 1)^2 - 5(1x^2 + 5x + 1) - 1) + 1) - 4) + 2)/(3(5(4(-2(1x^2 + 5x + 1)^2 - 5(1x^2 + 5x + 1) - 1) + 1)^2 + 1(4(-2(1x^2 + 5x + 1)^2 - 5(1x^2 + 5x + 1) - 1) + 1) - 4) - 2), 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": "5.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3|(-2sin(3\u03c0((1(-4(3|((1x + 3)/(1x - 3)) + 2| + 3) + 3) + 3)/(-2(-4(3|((1x + 3)/(1x - 3)) + 2| + 3) + 3) - 1)) + 1) - 3) + 2| + 1, g(x) = 5((-3(1cos(1\u03c0((-3(-4x^2 + 4x - 4))/(3(-4x^2 + 4x - 4))) - 3) + 3) - 3)/(-2(1cos(1\u03c0((-3(-4x^2 + 4x - 4))/(3(-4x^2 + 4x - 4))) - 3) + 3) - 3)) - 5, 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-1(3|(-1(2(2(1cos(2\u03c0x - 2))^2 - 3(1cos(2\u03c0x - 2)) - 3) - 1) + 5)|) - 3)/(-1(3|(-1(2(2(1cos(2\u03c0x - 2))^2 - 3(1cos(2\u03c0x - 2)) - 3) - 1) + 5)|) + 2), g(x) = 1(3(-3sin(2\u03c0(2|(-1x^2 - 4x - 3) + 2| - 2) + 2) - 2)^2 + 5(-3sin(2\u03c0(2|(-1x^2 - 4x - 3) + 2| - 2) + 2) - 2) - 2) + 5, 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": "1.9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2(1(-2|(-1(2(-5x - 1)^2 - 3(-5x - 1) + 5)) + 2| + 2) + 2) - 3 and g(x) = -1(3cos(3\u03c0(3(-1(-4x)^2 + 1(-4x) + 1)^2 - 5(-1(-4x)^2 + 1(-4x) + 1) + 2)) + 1) - 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -5((1((3((2(-3|(3e^(-1x) - 1) - 1| + 3) - 2)/(1(-3|(3e^(-1x) - 1) - 1| + 3))) + 3)/(2((2(-3|(3e^(-1x) - 1) - 1| + 3) - 2)/(1(-3|(3e^(-1x) - 1) - 1| + 3))) - 3)) + 2)/(3((3((2(-3|(3e^(-1x) - 1) - 1| + 3) - 2)/(1(-3|(3e^(-1x) - 1) - 1| + 3))) + 3)/(2((2(-3|(3e^(-1x) - 1) - 1| + 3) - 2)/(1(-3|(3e^(-1x) - 1) - 1| + 3))) - 3)) - 2)) - 2 and g(x) = (1(-1(-2|(-3e^(-2((1x - 3)/(1x))) + 2) - 3| + 2)^2 - 4) + 1)/(-3(-1(-2|(-3e^(-2((1x - 3)/(1x))) + 2) - 3| + 2)^2 - 4)) 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": "1.7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2|(-3|((-2(3(-3(2sin(2\u03c0x + 3) + 2)^2 + 2(2sin(2\u03c0x + 3) + 2) + 4)^2 + 3(-3(2sin(2\u03c0x + 3) + 2)^2 + 2(2sin(2\u03c0x + 3) + 2) + 4) + 2) + 3)/(1(3(-3(2sin(2\u03c0x + 3) + 2)^2 + 2(2sin(2\u03c0x + 3) + 2) + 4)^2 + 3(-3(2sin(2\u03c0x + 3) + 2)^2 + 2(2sin(2\u03c0x + 3) + 2) + 4) + 2) + 3)) - 2| + 1) + 2| + 3 and g(x) = 1|(1|((-2((-2(1x^2 - 2) + 3)/(-1(1x^2 - 2) + 2)) + 3)/(-3((-2(1x^2 - 2) + 3)/(-1(1x^2 - 2) + 2)) - 3)) - 2| + 1)| - 2 from x = -1.9 to x = 1.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "71.6", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 3((-2(-3|(-2|(2(-5x^2 - 5x + 4)^2 - 2(-5x^2 - 5x + 4)) + 3| - 3)| - 2) - 2)/(1(-3|(-2|(2(-5x^2 - 5x + 4)^2 - 2(-5x^2 - 5x + 4)) + 3| - 3)| - 2) + 2))^2 + 2((-2(-3|(-2|(2(-5x^2 - 5x + 4)^2 - 2(-5x^2 - 5x + 4)) + 3| - 3)| - 2) - 2)/(1(-3|(-2|(2(-5x^2 - 5x + 4)^2 - 2(-5x^2 - 5x + 4)) + 3| - 3)| - 2) + 2)) - 5 and g(x) = (2(3sin(1\u03c0((-3(-1|(-4x^2 + 4x + 3) - 3| + 3) - 1)/(-1(-1|(-4x^2 + 4x + 3) - 3| + 3) - 2)) + 3) - 1) + 2)/(-2(3sin(1\u03c0((-3(-1|(-4x^2 + 4x + 3) - 3| + 3) - 1)/(-1(-1|(-4x^2 + 4x + 3) - 3| + 3) - 2)) + 3) - 1) + 1) between the vertical lines x = 0.1 and x = 0.9. 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) = -1(-3|(1|(-5((3(1sin(2\u03c0x - 2) - 2) - 1)/(2(1sin(2\u03c0x - 2) - 2)))^2 - 4((3(1sin(2\u03c0x - 2) - 2) - 1)/(2(1sin(2\u03c0x - 2) - 2))) + 5) + 2| + 3) - 1| - 1) + 5, g(x) = 2|(2|(3|(-1(3|x + 2| + 3) + 1) + 3| + 2) - 2| - 1) - 3| + 1, x = -4.0, 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": "159.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (1(-1sin(3\u03c0((-1(5(4((-1x)/(-1x)) - 4)^2 - 4(4((-1x)/(-1x)) - 4) + 5) + 3)/(3(5(4((-1x)/(-1x)) - 4)^2 - 4(4((-1x)/(-1x)) - 4) + 5) - 2))) - 1) - 3)/(-3(-1sin(3\u03c0((-1(5(4((-1x)/(-1x)) - 4)^2 - 4(4((-1x)/(-1x)) - 4) + 5) + 3)/(3(5(4((-1x)/(-1x)) - 4)^2 - 4(4((-1x)/(-1x)) - 4) + 5) - 2))) - 1) + 2) and g(x) = -5(3cos(3\u03c0(3(1(3x - 1) - 1)^2 + 2(1(3x - 1) - 1) - 5)) + 2) + 2 between the vertical lines x = 1.4 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) = 1(2|((1(4(-3(3|x + 1| - 2)^2 - 1(3|x + 1| - 2) - 1)^2 + 4(-3(3|x + 1| - 2)^2 - 1(3|x + 1| - 2) - 1)))/(3(4(-3(3|x + 1| - 2)^2 - 1(3|x + 1| - 2) - 1)^2 + 4(-3(3|x + 1| - 2)^2 - 1(3|x + 1| - 2) - 1)) + 3)) - 2| + 2) - 4 and g(x) = 3|(-3((-3((-1(-4x + 5) + 2)/(-2(-4x + 5) + 3)) + 3)/(1((-1(-4x + 5) + 2)/(-2(-4x + 5) + 3)))) - 1) + 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) = -5(-1((3(-2|(2(2x - 4)^2 + 1(2x - 4) + 4) + 2| - 2) + 3)/(1(-2|(2(2x - 4)^2 + 1(2x - 4) + 4) + 2| - 2)))^2 - 1) - 3 and g(x) = 1|(-1(-3|(-3|(-2cos(3\u03c0x + 1) - 2) - 2| + 1) + 3| + 1)^2 - 3(-3|(-3|(-2cos(3\u03c0x + 1) - 2) - 2| + 1) + 3| + 1) + 3) - 3| between the vertical lines x = 4.2 and x = 4.3. 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": "Find the area of the region bounded by the curves f(x) = -3((1(-1|((-2(-4(3|x - 1| - 2)^2 + 3(3|x - 1| - 2) - 4) - 3)/(-1(-4(3|x - 1| - 2)^2 + 3(3|x - 1| - 2) - 4) - 3)) + 3| + 3) - 1)/(1(-1|((-2(-4(3|x - 1| - 2)^2 + 3(3|x - 1| - 2) - 4) - 3)/(-1(-4(3|x - 1| - 2)^2 + 3(3|x - 1| - 2) - 4) - 3)) + 3| + 3) + 2)) + 3, g(x) = 3sin(1\u03c0(2(5((-2((1x + 2)/(1x + 3)) - 3)/(-3((1x + 2)/(1x + 3)) - 2)) + 2) + 1) - 2) - 2, 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": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2sin(3\u03c0(2|(2(-2(-5((-2x - 3)/(3x - 2)) + 2) - 3)^2 - 3(-2(-5((-2x - 3)/(3x - 2)) + 2) - 3) - 2) + 1| - 2) - 3) - 2 and g(x) = 1(-1e^(-1(-1((2(2x^2 - 1x - 4) - 2)/(1(2x^2 - 1x - 4) + 2))^2 - 2((2(2x^2 - 1x - 4) - 2)/(1(2x^2 - 1x - 4) + 2)) + 1)) + 3) + 4 between the vertical lines x = 2.3 and 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": "Determine the area of the region enclosed by the graphs of f(x) = -5(-1(-1(-3|((2(5x + 5))/(1(5x + 5))) - 1| - 2) + 2)^2 - 5(-1(-3|((2(5x + 5))/(1(5x + 5))) - 1| - 2) + 2) - 4) - 5 and g(x) = -1(-1((3(-2((-3x - 1)/(1x))^2 + 1((-3x - 1)/(1x))) - 1)/(-1(-2((-3x - 1)/(1x))^2 + 1((-3x - 1)/(1x))) - 2))^2 + 4((3(-2((-3x - 1)/(1x))^2 + 1((-3x - 1)/(1x))) - 1)/(-1(-2((-3x - 1)/(1x))^2 + 1((-3x - 1)/(1x))) - 2)) + 1) + 4 between the vertical lines x = -0.4 and x = -0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "275.6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2((-1(-1|((-2(-3(2|x + 1| - 1)^2 - 3(2|x + 1| - 1) + 5) - 2)/(1(-3(2|x + 1| - 1)^2 - 3(2|x + 1| - 1) + 5) - 2)) + 2| - 2) - 2)/(2(-1|((-2(-3(2|x + 1| - 1)^2 - 3(2|x + 1| - 1) + 5) - 2)/(1(-3(2|x + 1| - 1)^2 - 3(2|x + 1| - 1) + 5) - 2)) + 2| - 2) - 1)) - 3 and g(x) = (2(-3cos(3\u03c0(-2(-1((3x - 3)/(-3x + 1))^2 + 4((3x - 3)/(-3x + 1)) - 5)^2 + 5(-1((3x - 3)/(-3x + 1))^2 + 4((3x - 3)/(-3x + 1)) - 5) - 5) + 3)) - 2)/(-3(-3cos(3\u03c0(-2(-1((3x - 3)/(-3x + 1))^2 + 4((3x - 3)/(-3x + 1)) - 5)^2 + 5(-1((3x - 3)/(-3x + 1))^2 + 4((3x - 3)/(-3x + 1)) - 5) - 5) + 3)) - 2) from x = 3.2 to x = 3.3. 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(2|((-3(-5(4x + 5)^2 + 1(4x + 5) + 4))/(3(-5(4x + 5)^2 + 1(4x + 5) + 4) - 2)) + 3| - 2) + 2)/(-2(2|((-3(-5(4x + 5)^2 + 1(4x + 5) + 4))/(3(-5(4x + 5)^2 + 1(4x + 5) + 4) - 2)) + 3| - 2) + 3)) and g(x) = -2(-2((-1(5(-2x - 4)^2 + 3) + 1)/(-1(5(-2x - 4)^2 + 3) + 2))^2 - 3((-1(5(-2x - 4)^2 + 3) + 1)/(-1(5(-2x - 4)^2 + 3) + 2)) - 2) - 4 from x = -1.3 to x = -1.1. 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": "Calculate the area enclosed between the functions f(x) = -1|(-2(-3sin(3\u03c0(1((-3(-1x^2 - 2) + 1)/(1(-1x^2 - 2))) - 2)) - 1) - 5) - 2| and g(x) = -2((3((-3((-1(-5x^2 + 2x - 2) + 2)/(3(-5x^2 + 2x - 2) + 1)) - 3)/(1((-1(-5x^2 + 2x - 2) + 2)/(3(-5x^2 + 2x - 2) + 1)) - 3)) - 3)/(2((-3((-1(-5x^2 + 2x - 2) + 2)/(3(-5x^2 + 2x - 2) + 1)) - 3)/(1((-1(-5x^2 + 2x - 2) + 2)/(3(-5x^2 + 2x - 2) + 1)) - 3)) - 1)) + 1 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": "3.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (1(-1|(2cos(2\u03c0(2(2|(-1x^2 + 5x - 1) + 1| - 2)^2 + 1(2|(-1x^2 + 5x - 1) + 1| - 2) - 5) - 1) + 3) + 2| + 3) - 2)/(-2(-1|(2cos(2\u03c0(2(2|(-1x^2 + 5x - 1) + 1| - 2)^2 + 1(2|(-1x^2 + 5x - 1) + 1| - 2) - 5) - 1) + 3) + 2| + 3)) and g(x) = 5(-3((-3((1(1x - 5) + 3)/(-1(1x - 5) + 2)) + 2)/(2((1(1x - 5) + 3)/(-1(1x - 5) + 2)) - 1)) - 5)^2 - 3(-3((-3((1(1x - 5) + 3)/(-1(1x - 5) + 2)) + 2)/(2((1(1x - 5) + 3)/(-1(1x - 5) + 2)) - 1)) - 5) - 2 between the vertical lines x = -1.2 and x = -1.0999999999999999. 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(3cos(3\u03c0((-2(-5(-5(2|x + 1| - 2) - 4) - 1) - 3)/(1(-5(-5(2|x + 1| - 2) - 4) - 1) + 2)) + 2) - 3) - 5 and g(x) = 1e^(-2(2(-1|(1((3x + 1)/(-2x - 2)) - 2) - 2| - 2)^2 - 4(-1|(1((3x + 1)/(-2x - 2)) - 2) - 2| - 2) + 2)) - 3 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": "0.7", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2((1(2((-2((-3(5x^2 + 2x - 1) - 3)/(1(5x^2 + 2x - 1))) + 2)/(1((-3(5x^2 + 2x - 1) - 3)/(1(5x^2 + 2x - 1))) + 3))^2 + 2((-2((-3(5x^2 + 2x - 1) - 3)/(1(5x^2 + 2x - 1))) + 2)/(1((-3(5x^2 + 2x - 1) - 3)/(1(5x^2 + 2x - 1))) + 3)) - 2) - 2)/(-1(2((-2((-3(5x^2 + 2x - 1) - 3)/(1(5x^2 + 2x - 1))) + 2)/(1((-3(5x^2 + 2x - 1) - 3)/(1(5x^2 + 2x - 1))) + 3))^2 + 2((-2((-3(5x^2 + 2x - 1) - 3)/(1(5x^2 + 2x - 1))) + 2)/(1((-3(5x^2 + 2x - 1) - 3)/(1(5x^2 + 2x - 1))) + 3)) - 2) + 2))^2 + 2((1(2((-2((-3(5x^2 + 2x - 1) - 3)/(1(5x^2 + 2x - 1))) + 2)/(1((-3(5x^2 + 2x - 1) - 3)/(1(5x^2 + 2x - 1))) + 3))^2 + 2((-2((-3(5x^2 + 2x - 1) - 3)/(1(5x^2 + 2x - 1))) + 2)/(1((-3(5x^2 + 2x - 1) - 3)/(1(5x^2 + 2x - 1))) + 3)) - 2) - 2)/(-1(2((-2((-3(5x^2 + 2x - 1) - 3)/(1(5x^2 + 2x - 1))) + 2)/(1((-3(5x^2 + 2x - 1) - 3)/(1(5x^2 + 2x - 1))) + 3))^2 + 2((-2((-3(5x^2 + 2x - 1) - 3)/(1(5x^2 + 2x - 1))) + 2)/(1((-3(5x^2 + 2x - 1) - 3)/(1(5x^2 + 2x - 1))) + 3)) - 2) + 2)), g(x) = 3sin(2\u03c0(2|(-1|(3(-3|x - 1|)^2 - 4(-3|x - 1|) + 5)| - 3) - 1| + 2) - 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3(1(3(-1sin(2\u03c0(-1(1|x + 3| - 2) + 5) + 2) + 2) - 3)^2 + 5(3(-1sin(2\u03c0(-1(1|x + 3| - 2) + 5) + 2) + 2) - 3) - 2) + 3 and g(x) = 4(3sin(3\u03c0(-2|((-3((-2x - 3)/(2x - 3)))/(1((-2x - 3)/(2x - 3)) - 3)) + 3| + 2) - 3) + 2)^2 + 5(3sin(3\u03c0(-2|((-3((-2x - 3)/(2x - 3)))/(1((-2x - 3)/(2x - 3)) - 3)) + 3| + 2) - 3) + 2) - 1 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": "4.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (2(-1|((-3(1e^(-1(-4(-2|x + 2| + 2))) + 2) - 1)/(1(1e^(-1(-4(-2|x + 2| + 2))) + 2) + 3)) - 1| - 2) - 2)/(1(-1|((-3(1e^(-1(-4(-2|x + 2| + 2))) + 2) - 1)/(1(1e^(-1(-4(-2|x + 2| + 2))) + 2) + 3)) - 1| - 2) + 1) and g(x) = (3(-1(-2(3|(-2x^2 - 3x + 3) + 2| + 2)^2 + 4(3|(-2x^2 - 3x + 3) + 2| + 2) - 3)^2 - 5(-2(3|(-2x^2 - 3x + 3) + 2| + 2)^2 + 4(3|(-2x^2 - 3x + 3) + 2| + 2) - 3) + 4) + 1)/(-1(-1(-2(3|(-2x^2 - 3x + 3) + 2| + 2)^2 + 4(3|(-2x^2 - 3x + 3) + 2| + 2) - 3)^2 - 5(-2(3|(-2x^2 - 3x + 3) + 2| + 2)^2 + 4(3|(-2x^2 - 3x + 3) + 2| + 2) - 3) + 4) + 2) from x = -2.5 to x = -2.4. 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) = (2(5((2(-4(-1|((-1x - 2)/(-1x - 2)) - 3|)^2 - 2(-1|((-1x - 2)/(-1x - 2)) - 3|) + 2) + 3)/(1(-4(-1|((-1x - 2)/(-1x - 2)) - 3|)^2 - 2(-1|((-1x - 2)/(-1x - 2)) - 3|) + 2) - 3))^2 - 4) - 3)/(-2(5((2(-4(-1|((-1x - 2)/(-1x - 2)) - 3|)^2 - 2(-1|((-1x - 2)/(-1x - 2)) - 3|) + 2) + 3)/(1(-4(-1|((-1x - 2)/(-1x - 2)) - 3|)^2 - 2(-1|((-1x - 2)/(-1x - 2)) - 3|) + 2) - 3))^2 - 4) - 1), g(x) = 3(-2((2((-2((-3x - 1)/(2x + 2)) + 2)/(-1((-3x - 1)/(2x + 2)) - 2)) - 1)/(1((-2((-3x - 1)/(2x + 2)) + 2)/(-1((-3x - 1)/(2x + 2)) - 2)) + 1))^2 - 4((2((-2((-3x - 1)/(2x + 2)) + 2)/(-1((-3x - 1)/(2x + 2)) - 2)) - 1)/(1((-2((-3x - 1)/(2x + 2)) + 2)/(-1((-3x - 1)/(2x + 2)) - 2)) + 1)) + 2)^2 - 5(-2((2((-2((-3x - 1)/(2x + 2)) + 2)/(-1((-3x - 1)/(2x + 2)) - 2)) - 1)/(1((-2((-3x - 1)/(2x + 2)) + 2)/(-1((-3x - 1)/(2x + 2)) - 2)) + 1))^2 - 4((2((-2((-3x - 1)/(2x + 2)) + 2)/(-1((-3x - 1)/(2x + 2)) - 2)) - 1)/(1((-2((-3x - 1)/(2x + 2)) + 2)/(-1((-3x - 1)/(2x + 2)) - 2)) + 1)) + 2) - 5, 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2e^(1(-2|((-2(-2|(1|((1x - 1)/(2x + 3)) + 3| - 3)| + 3) - 3)/(-2(-2|(1|((1x - 1)/(2x + 3)) + 3| - 3)| + 3) + 1))| + 3)) - 3, g(x) = -1|(-2cos(2\u03c0((1((2(-3x^2 - 5x + 2) + 1)/(-3(-3x^2 - 5x + 2) - 2)) - 2)/(3((2(-3x^2 - 5x + 2) + 1)/(-3(-3x^2 - 5x + 2) - 2)) + 3))) - 3) + 3| + 1, x = -1.2, 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": "5.4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-1(1((-2(-3sin(3\u03c0(-4((-3x + 1)/(-3x - 2))^2 + 3((-3x + 1)/(-3x - 2)) - 3) - 3) + 3) + 1)/(2(-3sin(3\u03c0(-4((-3x + 1)/(-3x - 2))^2 + 3((-3x + 1)/(-3x - 2)) - 3) - 3) + 3) - 3))^2 + 1((-2(-3sin(3\u03c0(-4((-3x + 1)/(-3x - 2))^2 + 3((-3x + 1)/(-3x - 2)) - 3) - 3) + 3) + 1)/(2(-3sin(3\u03c0(-4((-3x + 1)/(-3x - 2))^2 + 3((-3x + 1)/(-3x - 2)) - 3) - 3) + 3) - 3))) - 2)/(-2(1((-2(-3sin(3\u03c0(-4((-3x + 1)/(-3x - 2))^2 + 3((-3x + 1)/(-3x - 2)) - 3) - 3) + 3) + 1)/(2(-3sin(3\u03c0(-4((-3x + 1)/(-3x - 2))^2 + 3((-3x + 1)/(-3x - 2)) - 3) - 3) + 3) - 3))^2 + 1((-2(-3sin(3\u03c0(-4((-3x + 1)/(-3x - 2))^2 + 3((-3x + 1)/(-3x - 2)) - 3) - 3) + 3) + 1)/(2(-3sin(3\u03c0(-4((-3x + 1)/(-3x - 2))^2 + 3((-3x + 1)/(-3x - 2)) - 3) - 3) + 3) - 3)))) and g(x) = 2(-1(-3|((-1(1|x - 1|) + 1)/(-1(1|x - 1|) + 2)) + 3| + 1) + 3) - 2 from x = 2.4 to x = 2.9. Round 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) = -2e^(1((2(-5(5(-4(-1|x| + 3) + 4) + 4)) + 2)/(-3(-5(5(-4(-1|x| + 3) + 4) + 4)) - 1))) and g(x) = 1(-3(5(-3(-1|x - 3| + 2)^2 - 4(-1|x - 3| + 2)) - 3)^2 + 4(5(-3(-1|x - 3| + 2)^2 - 4(-1|x - 3| + 2)) - 3) + 4)^2 - 3(-3(5(-3(-1|x - 3| + 2)^2 - 4(-1|x - 3| + 2)) - 3)^2 + 4(5(-3(-1|x - 3| + 2)^2 - 4(-1|x - 3| + 2)) - 3) + 4) - 4 from x = 0.8 to x = 0.9. 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": "Calculate the area enclosed between the functions f(x) = -5(3sin(2\u03c0((-2(2|(-2|(1|x - 2| - 3) + 1| - 1) - 1| + 3) + 2)/(-2(2|(-2|(1|x - 2| - 3) + 1| - 1) - 1| + 3) + 3)) + 2) - 2)^2 + 5(3sin(2\u03c0((-2(2|(-2|(1|x - 2| - 3) + 1| - 1) - 1| + 3) + 2)/(-2(2|(-2|(1|x - 2| - 3) + 1| - 1) - 1| + 3) + 3)) + 2) - 2) - 4 and g(x) = 1(-1|(1(-2|(4x - 1)|)^2 - 2(-2|(4x - 1)|) + 2) + 1| - 3) + 3 from x = 0.1 to 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": "Determine the area of the region enclosed by the graphs of f(x) = (2((-3(5(-5(2|(-4x) + 3| + 2)^2 + 4(2|(-4x) + 3| + 2) - 3)^2 - 4(-5(2|(-4x) + 3| + 2)^2 + 4(2|(-4x) + 3| + 2) - 3) - 4) - 3)/(1(5(-5(2|(-4x) + 3| + 2)^2 + 4(2|(-4x) + 3| + 2) - 3)^2 - 4(-5(2|(-4x) + 3| + 2)^2 + 4(2|(-4x) + 3| + 2) - 3) - 4) - 2)) + 1)/(-2((-3(5(-5(2|(-4x) + 3| + 2)^2 + 4(2|(-4x) + 3| + 2) - 3)^2 - 4(-5(2|(-4x) + 3| + 2)^2 + 4(2|(-4x) + 3| + 2) - 3) - 4) - 3)/(1(5(-5(2|(-4x) + 3| + 2)^2 + 4(2|(-4x) + 3| + 2) - 3)^2 - 4(-5(2|(-4x) + 3| + 2)^2 + 4(2|(-4x) + 3| + 2) - 3) - 4) - 2)) + 1) and g(x) = -5(2((-2((-2(2x^2 - 4x - 1) + 3)/(-1(2x^2 - 4x - 1) - 1)) + 2)/(1((-2(2x^2 - 4x - 1) + 3)/(-1(2x^2 - 4x - 1) - 1)))) + 1) + 3 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": "149.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 4(1sin(2\u03c0((-2(4(4(2x + 4)^2 + 1(2x + 4) - 1) - 4) - 1)/(-1(4(4(2x + 4)^2 + 1(2x + 4) - 1) - 4) + 2)) + 2) + 1)^2 + 3(1sin(2\u03c0((-2(4(4(2x + 4)^2 + 1(2x + 4) - 1) - 4) - 1)/(-1(4(4(2x + 4)^2 + 1(2x + 4) - 1) - 4) + 2)) + 2) + 1) - 3 and g(x) = (3(-5(4(-3(1x - 2)^2 + 4(1x - 2) - 2) + 4)^2 + 4) + 1)/(-3(-5(4(-3(1x - 2)^2 + 4(1x - 2) - 2) + 4)^2 + 4) - 2) between the vertical lines x = -2.5 and 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": "Find the area of the region bounded by the curves f(x) = (-3(3(-1(-1(-2cos(2\u03c0((2x + 3)/(1x - 2)) - 2) - 2)^2 - 3(-2cos(2\u03c0((2x + 3)/(1x - 2)) - 2) - 2) - 5)^2 - 4(-1(-2cos(2\u03c0((2x + 3)/(1x - 2)) - 2) - 2)^2 - 3(-2cos(2\u03c0((2x + 3)/(1x - 2)) - 2) - 2) - 5) + 2)^2 + 3(-1(-1(-2cos(2\u03c0((2x + 3)/(1x - 2)) - 2) - 2)^2 - 3(-2cos(2\u03c0((2x + 3)/(1x - 2)) - 2) - 2) - 5)^2 - 4(-1(-2cos(2\u03c0((2x + 3)/(1x - 2)) - 2) - 2)^2 - 3(-2cos(2\u03c0((2x + 3)/(1x - 2)) - 2) - 2) - 5) + 2) - 4) - 1)/(2(3(-1(-1(-2cos(2\u03c0((2x + 3)/(1x - 2)) - 2) - 2)^2 - 3(-2cos(2\u03c0((2x + 3)/(1x - 2)) - 2) - 2) - 5)^2 - 4(-1(-2cos(2\u03c0((2x + 3)/(1x - 2)) - 2) - 2)^2 - 3(-2cos(2\u03c0((2x + 3)/(1x - 2)) - 2) - 2) - 5) + 2)^2 + 3(-1(-1(-2cos(2\u03c0((2x + 3)/(1x - 2)) - 2) - 2)^2 - 3(-2cos(2\u03c0((2x + 3)/(1x - 2)) - 2) - 2) - 5)^2 - 4(-1(-2cos(2\u03c0((2x + 3)/(1x - 2)) - 2) - 2)^2 - 3(-2cos(2\u03c0((2x + 3)/(1x - 2)) - 2) - 2) - 5) + 2) - 4) - 1), g(x) = 2(-1(1|((-1(5x^2 + 4x - 1) + 1)/(1(5x^2 + 4x - 1))) - 2| + 3))^2 + 3(-1(1|((-1(5x^2 + 4x - 1) + 1)/(1(5x^2 + 4x - 1))) - 2| + 3)) + 2, x = -3.5, 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": "130.9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 5(2(-2sin(2\u03c0((-3(-2|((-2x + 1)/(-2x + 3)) - 1| - 3) + 2)/(-1(-2|((-2x + 1)/(-2x + 3)) - 1| - 3) - 3)) + 1) + 3) - 5)^2 - 2(2(-2sin(2\u03c0((-3(-2|((-2x + 1)/(-2x + 3)) - 1| - 3) + 2)/(-1(-2|((-2x + 1)/(-2x + 3)) - 1| - 3) - 3)) + 1) + 3) - 5) - 4 and g(x) = 1|(2e^(1(-4(-2(-2x - 1)^2 + 5)^2 + 3(-2(-2x - 1)^2 + 5) - 5)) + 1) + 3| + 3 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": "4.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1(-3(4((2(-1((2x - 2)/(-1x + 2))^2 + 5((2x - 2)/(-1x + 2)) - 4) + 2)/(-1(-1((2x - 2)/(-1x + 2))^2 + 5((2x - 2)/(-1x + 2)) - 4) - 2))^2 + 4((2(-1((2x - 2)/(-1x + 2))^2 + 5((2x - 2)/(-1x + 2)) - 4) + 2)/(-1(-1((2x - 2)/(-1x + 2))^2 + 5((2x - 2)/(-1x + 2)) - 4) - 2)) + 2)^2 + 4(4((2(-1((2x - 2)/(-1x + 2))^2 + 5((2x - 2)/(-1x + 2)) - 4) + 2)/(-1(-1((2x - 2)/(-1x + 2))^2 + 5((2x - 2)/(-1x + 2)) - 4) - 2))^2 + 4((2(-1((2x - 2)/(-1x + 2))^2 + 5((2x - 2)/(-1x + 2)) - 4) + 2)/(-1(-1((2x - 2)/(-1x + 2))^2 + 5((2x - 2)/(-1x + 2)) - 4) - 2)) + 2) - 2) + 2, g(x) = -1|((2(5((-1(5x^2 + 2x - 4) - 3)/(2(5x^2 + 2x - 4) + 2))^2 + 2((-1(5x^2 + 2x - 4) - 3)/(2(5x^2 + 2x - 4) + 2)) + 4) - 3)/(-1(5((-1(5x^2 + 2x - 4) - 3)/(2(5x^2 + 2x - 4) + 2))^2 + 2((-1(5x^2 + 2x - 4) - 3)/(2(5x^2 + 2x - 4) + 2)) + 4) + 3)) - 1|, 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": "0.7", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (1(3|((3(2e^(2(-3((-3x)/(-3x - 3)) + 4)) - 2) - 3)/(2(2e^(2(-3((-3x)/(-3x - 3)) + 4)) - 2))) - 2|) - 1)/(1(3|((3(2e^(2(-3((-3x)/(-3x - 3)) + 4)) - 2) - 3)/(2(2e^(2(-3((-3x)/(-3x - 3)) + 4)) - 2))) - 2|) + 2) and g(x) = (3(-1((2(-2(-3|x - 3|)) - 3)/(1(-2(-3|x - 3|)) - 3)) - 4) - 1)/(-2(-1((2(-2(-3|x - 3|)) - 3)/(1(-2(-3|x - 3|)) - 3)) - 4)) between the vertical lines x = 2.6 and x = 3.4. 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) = -2sin(1\u03c0(1(-2|(1(-2|(2x + 4) + 1|)^2 - 1(-2|(2x + 4) + 1|) - 4) + 2| - 3))) - 2, g(x) = -2|(-1((-3(3(-1e^(-2x) - 2)^2 + 3(-1e^(-2x) - 2) + 2) - 2)/(-3(3(-1e^(-2x) - 2)^2 + 3(-1e^(-2x) - 2) + 2) + 4))^2 + 5((-3(3(-1e^(-2x) - 2)^2 + 3(-1e^(-2x) - 2) + 2) - 2)/(-3(3(-1e^(-2x) - 2)^2 + 3(-1e^(-2x) - 2) + 2) + 4)) - 2) - 1| + 2, x = 4.5, 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2|(1sin(3\u03c0(4(-1|(2|((-1x + 3)/(1x + 2)) - 1| - 1) + 3|) + 2) - 2) - 2) + 3| + 3, g(x) = -2(-3(-1((2((1x - 2)/(2x - 1)) + 1)/(-3((1x - 2)/(2x - 1)))) + 5)^2 - 5(-1((2((1x - 2)/(2x - 1)) + 1)/(-3((1x - 2)/(2x - 1)))) + 5) - 1) - 2, x = 1.8, 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": "1.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2(-3|(-1cos(2\u03c0((2(2|(1|x| - 2) + 1| - 1) + 2)/(-1(2|(1|x| - 2) + 1| - 1) - 2)) + 1) + 1) + 1| - 1) - 5 and g(x) = (1(1|(-1|(3cos(2\u03c0(3|x - 3|))) + 2| + 3) + 3| - 1) + 2)/(2(1|(-1|(3cos(2\u03c0(3|x - 3|))) + 2| + 3) + 3| - 1) - 1) 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": "3.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1|(-1cos(3\u03c0((-2(-5(-5(-2|x + 2| - 1)^2 + 1(-2|x + 2| - 1) + 1) + 2) + 1)/(3(-5(-5(-2|x + 2| - 1)^2 + 1(-2|x + 2| - 1) + 1) + 2))) + 3)) + 1| + 2 and g(x) = -1e^(-2((-1(-3|(-4(1|x| - 1)^2 + 5(1|x| - 1)) - 2| + 2) - 2)/(-1(-3|(-4(1|x| - 1)^2 + 5(1|x| - 1)) - 2| + 2) + 3))) + 1 between the vertical lines x = -2.1 and x = -1.2. 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) = -5((-2(-2(3(-1|(2|x + 3| + 3) - 1| - 1) - 3)^2 + 3(3(-1|(2|x + 3| + 3) - 1| - 1) - 3) + 5) - 1)/(3(-2(3(-1|(2|x + 3| + 3) - 1| - 1) - 3)^2 + 3(3(-1|(2|x + 3| + 3) - 1| - 1) - 3) + 5) - 2))^2 + 3((-2(-2(3(-1|(2|x + 3| + 3) - 1| - 1) - 3)^2 + 3(3(-1|(2|x + 3| + 3) - 1| - 1) - 3) + 5) - 1)/(3(-2(3(-1|(2|x + 3| + 3) - 1| - 1) - 3)^2 + 3(3(-1|(2|x + 3| + 3) - 1| - 1) - 3) + 5) - 2)) - 2 and g(x) = 3((3(-2|(-2((3x - 1)/(1x - 2))^2 + 4((3x - 1)/(1x - 2)) + 4) + 1| + 1) - 2)/(3(-2|(-2((3x - 1)/(1x - 2))^2 + 4((3x - 1)/(1x - 2)) + 4) + 1| + 1) - 1)) + 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": "1.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1|(3sin(2\u03c0(-4(-4((1(3x^2 + 5x - 5) + 2)/(3(3x^2 + 5x - 5))) - 2) + 2)) + 2) + 3| - 1 and g(x) = 2(1(-1|(1(-2|x - 1| - 1) - 4) + 2| + 3)^2 + 4(-1|(1(-2|x - 1| - 1) - 4) + 2| + 3) + 3) + 4 from x = 0.7 to x = 0.7999999999999999. 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|(1(-2(-3|(-1(1|x - 3| + 1)^2 - 1(1|x - 3| + 1) + 4) - 1| + 2) + 5)^2 - 3(-2(-3|(-1(1|x - 3| + 1)^2 - 1(1|x - 3| + 1) + 4) - 1| + 2) + 5) - 3) + 1| - 1 and g(x) = (-1((-2((-1(2cos(2\u03c0(2x - 2) + 3) - 2) + 2)/(-1(2cos(2\u03c0(2x - 2) + 3) - 2) - 2)) - 1)/(-1((-1(2cos(2\u03c0(2x - 2) + 3) - 2) + 2)/(-1(2cos(2\u03c0(2x - 2) + 3) - 2) - 2)) - 1)))/(3((-2((-1(2cos(2\u03c0(2x - 2) + 3) - 2) + 2)/(-1(2cos(2\u03c0(2x - 2) + 3) - 2) - 2)) - 1)/(-1((-1(2cos(2\u03c0(2x - 2) + 3) - 2) + 2)/(-1(2cos(2\u03c0(2x - 2) + 3) - 2) - 2)) - 1)) + 2) between the vertical lines x = 2.6 and x = 2.7. 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": "Calculate the area enclosed between the functions f(x) = -4(-1sin(2\u03c0(-2|(-1(-3(3x - 5) + 3) - 1)| - 1) - 1) + 1) - 3 and g(x) = 3(2(-1(3(-4x + 3) - 5)^2 + 2(3(-4x + 3) - 5) - 4) + 5) + 1 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1(3|((-1(-4(1|(5x^2 - 3)| - 1)^2 + 3) + 3)/(-3(-4(1|(5x^2 - 3)| - 1)^2 + 3) + 2)) - 1| - 1)^2 + 5(3|((-1(-4(1|(5x^2 - 3)| - 1)^2 + 3) + 3)/(-3(-4(1|(5x^2 - 3)| - 1)^2 + 3) + 2)) - 1| - 1) and g(x) = (1(-3cos(1\u03c0(2(1|(-1|x + 2| - 3) + 3| + 2)^2 - 4(1|(-1|x + 2| - 3) + 3| + 2) - 2) - 3) + 3) - 1)/(-1(-3cos(1\u03c0(2(1|(-1|x + 2| - 3) + 3| + 2)^2 - 4(1|(-1|x + 2| - 3) + 3| + 2) - 2) - 3) + 3)) between the vertical lines x = 4.2 and x = 4.3. 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": "Determine the area of the region enclosed by the graphs of f(x) = -2|(1((-1((-1(-1|((-2x + 1)/(3x - 2)) + 3| - 3) + 2)/(2(-1|((-2x + 1)/(3x - 2)) + 3| - 3) - 3)) - 1)/(1((-1(-1|((-2x + 1)/(3x - 2)) + 3| - 3) + 2)/(2(-1|((-2x + 1)/(3x - 2)) + 3| - 3) - 3)) + 1))^2 + 4((-1((-1(-1|((-2x + 1)/(3x - 2)) + 3| - 3) + 2)/(2(-1|((-2x + 1)/(3x - 2)) + 3| - 3) - 3)) - 1)/(1((-1(-1|((-2x + 1)/(3x - 2)) + 3| - 3) + 2)/(2(-1|((-2x + 1)/(3x - 2)) + 3| - 3) - 3)) + 1)) + 2) - 3| and g(x) = -4((1((2((-1((2x + 3)/(-2x + 3)) - 3)/(-2((2x + 3)/(-2x + 3)) + 3)) + 2)/(-3((-1((2x + 3)/(-2x + 3)) - 3)/(-2((2x + 3)/(-2x + 3)) + 3)) - 2)))/(-2((2((-1((2x + 3)/(-2x + 3)) - 3)/(-2((2x + 3)/(-2x + 3)) + 3)) + 2)/(-3((-1((2x + 3)/(-2x + 3)) - 3)/(-2((2x + 3)/(-2x + 3)) + 3)) - 2)) - 1))^2 + 1((1((2((-1((2x + 3)/(-2x + 3)) - 3)/(-2((2x + 3)/(-2x + 3)) + 3)) + 2)/(-3((-1((2x + 3)/(-2x + 3)) - 3)/(-2((2x + 3)/(-2x + 3)) + 3)) - 2)))/(-2((2((-1((2x + 3)/(-2x + 3)) - 3)/(-2((2x + 3)/(-2x + 3)) + 3)) + 2)/(-3((-1((2x + 3)/(-2x + 3)) - 3)/(-2((2x + 3)/(-2x + 3)) + 3)) - 2)) - 1)) + 5 between the vertical lines x = -0.7 and x = 0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-18.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2(-1(5(4((3(-2x^2 + 4x - 1) + 2)/(1(-2x^2 + 4x - 1) + 2))^2 + 1((3(-2x^2 + 4x - 1) + 2)/(1(-2x^2 + 4x - 1) + 2)) - 5)^2 + 3(4((3(-2x^2 + 4x - 1) + 2)/(1(-2x^2 + 4x - 1) + 2))^2 + 1((3(-2x^2 + 4x - 1) + 2)/(1(-2x^2 + 4x - 1) + 2)) - 5) + 4) + 3) + 2 and g(x) = -1(2|(-1(-5(-3sin(2\u03c0x - 3) + 1)^2 - 4(-3sin(2\u03c0x - 3) + 1) + 1)^2 + 3(-5(-3sin(2\u03c0x - 3) + 1)^2 - 4(-3sin(2\u03c0x - 3) + 1) + 1) + 2)| - 3) + 2 from x = -2.8 to x = -2.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "269.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2(-1|(3|((-3(-5(-5x + 2) - 2) - 3)/(2(-5(-5x + 2) - 2) + 3)) - 2| - 1) - 1| + 3) - 5 and g(x) = 3e^(-1((-2(-2(1(-3x^2 + 1x - 2)^2 - 1(-3x^2 + 1x - 2) - 1)^2 - 2(1(-3x^2 + 1x - 2)^2 - 1(-3x^2 + 1x - 2) - 1) + 1) - 3)/(-3(-2(1(-3x^2 + 1x - 2)^2 - 1(-3x^2 + 1x - 2) - 1)^2 - 2(1(-3x^2 + 1x - 2)^2 - 1(-3x^2 + 1x - 2) - 1) + 1) + 1))) - 1 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": "4.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3(3(-1|(-1(2(-3|x + 2| + 1) - 3) + 2) + 1| + 1) + 4) - 5 and g(x) = (-1(-3|(-1|(-1|(-2x - 3) + 3|) + 2|) + 1| + 1) - 1)/(1(-3|(-1|(-1|(-2x - 3) + 3|) + 2|) + 1| + 1)) from x = -1.3 to x = -0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2|(2(3|((3(-2|(3e^(2x) + 1)| + 3) + 3)/(3(-2|(3e^(2x) + 1)| + 3))) + 3| + 3) - 5) - 3| + 2 and g(x) = -3|(-4(3sin(2\u03c0(1(-1x^2 + 5x + 2)^2 + 3(-1x^2 + 5x + 2)) - 1) + 3) + 5) - 3| + 2 between the vertical lines x = -4.7 and x = -4.6000000000000005. 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) = (1(-3((-2(1|(-1sin(1\u03c0((1x - 1)/(1x + 2)) + 3) + 1) + 1| - 1) - 1)/(1(1|(-1sin(1\u03c0((1x - 1)/(1x + 2)) + 3) + 1) + 1| - 1)))^2 + 2((-2(1|(-1sin(1\u03c0((1x - 1)/(1x + 2)) + 3) + 1) + 1| - 1) - 1)/(1(1|(-1sin(1\u03c0((1x - 1)/(1x + 2)) + 3) + 1) + 1| - 1)))) - 3)/(2(-3((-2(1|(-1sin(1\u03c0((1x - 1)/(1x + 2)) + 3) + 1) + 1| - 1) - 1)/(1(1|(-1sin(1\u03c0((1x - 1)/(1x + 2)) + 3) + 1) + 1| - 1)))^2 + 2((-2(1|(-1sin(1\u03c0((1x - 1)/(1x + 2)) + 3) + 1) + 1| - 1) - 1)/(1(1|(-1sin(1\u03c0((1x - 1)/(1x + 2)) + 3) + 1) + 1| - 1)))) - 1), g(x) = 3(2sin(1\u03c0(1((1(3x + 3))/(-1(3x + 3) + 3))^2 + 1((1(3x + 3))/(-1(3x + 3) + 3)) - 2) + 3) - 2)^2 - 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": "1.8", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2(1|(1(2|(-3|((-3x - 3)/(3x - 2)) - 1| + 2)| - 1) + 2) - 2| + 1)^2 - 1(1|(1(2|(-3|((-3x - 3)/(3x - 2)) - 1| + 2)| - 1) + 2) - 2| + 1) - 3 and g(x) = -1|((-3(1cos(3\u03c0(2|(-2x^2 - 1x + 3) - 3| + 2)) + 1) - 3)/(1(1cos(3\u03c0(2|(-2x^2 - 1x + 3) - 3| + 2)) + 1))) + 3| + 1 between the vertical lines x = -0.8 and x = -0.7. 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": "Calculate the area enclosed between the functions f(x) = (-2((-2(-1|(-2|(-1(-2x - 3)) - 1| + 2) + 2| + 3) + 2)/(-2(-1|(-2|(-1(-2x - 3)) - 1| + 2) + 2| + 3) - 3)) + 1)/(2((-2(-1|(-2|(-1(-2x - 3)) - 1| + 2) + 2| + 3) + 2)/(-2(-1|(-2|(-1(-2x - 3)) - 1| + 2) + 2| + 3) - 3)) - 3) and g(x) = -2|((1(-3sin(2\u03c0((3((-1x - 3)/(3x - 2)))/(2((-1x - 3)/(3x - 2)) + 2)) + 3) + 2))/(-3(-3sin(2\u03c0((3((-1x - 3)/(3x - 2)))/(2((-1x - 3)/(3x - 2)) + 2)) + 3) + 2))) + 2| - 2 from x = -4.0 to x = 2.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "26.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1((-1(1((2((-2(-4x^2 + 2x - 4) + 2)/(-1(-4x^2 + 2x - 4))) + 2)/(-2((-2(-4x^2 + 2x - 4) + 2)/(-1(-4x^2 + 2x - 4))))) - 3) + 2)/(-2(1((2((-2(-4x^2 + 2x - 4) + 2)/(-1(-4x^2 + 2x - 4))) + 2)/(-2((-2(-4x^2 + 2x - 4) + 2)/(-1(-4x^2 + 2x - 4))))) - 3) - 3))^2 - 2((-1(1((2((-2(-4x^2 + 2x - 4) + 2)/(-1(-4x^2 + 2x - 4))) + 2)/(-2((-2(-4x^2 + 2x - 4) + 2)/(-1(-4x^2 + 2x - 4))))) - 3) + 2)/(-2(1((2((-2(-4x^2 + 2x - 4) + 2)/(-1(-4x^2 + 2x - 4))) + 2)/(-2((-2(-4x^2 + 2x - 4) + 2)/(-1(-4x^2 + 2x - 4))))) - 3) - 3)) - 3, g(x) = -5(3(-3(-1(2|x - 3|)^2 - 4(2|x - 3|) + 5) - 2) + 2)^2 - 4(3(-3(-1(2|x - 3|)^2 - 4(2|x - 3|) + 5) - 2) + 2), x = 3.5, 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": "6.7", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (2(-1(4(5(1(-2x + 3) + 5)^2 - 2(1(-2x + 3) + 5) + 5)^2 - 5(5(1(-2x + 3) + 5)^2 - 2(1(-2x + 3) + 5) + 5) + 2)^2 - 5) - 2)/(2(-1(4(5(1(-2x + 3) + 5)^2 - 2(1(-2x + 3) + 5) + 5)^2 - 5(5(1(-2x + 3) + 5)^2 - 2(1(-2x + 3) + 5) + 5) + 2)^2 - 5)), g(x) = -1|((-1(-1|((-2((-2x)/(2x - 1)) + 3)/(1((-2x)/(2x - 1)))) + 2| + 2) + 2)/(-3(-1|((-2((-2x)/(2x - 1)) + 3)/(1((-2x)/(2x - 1)))) + 2| + 2) - 1)) + 2| + 1, x = 0.3, 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": "1.6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 3((-3(3|(-2(1((1x + 3)/(-1x))^2 - 5((1x + 3)/(-1x)) + 4)^2 + 4(1((1x + 3)/(-1x))^2 - 5((1x + 3)/(-1x)) + 4) + 3) - 3| + 3) - 2)/(-1(3|(-2(1((1x + 3)/(-1x))^2 - 5((1x + 3)/(-1x)) + 4)^2 + 4(1((1x + 3)/(-1x))^2 - 5((1x + 3)/(-1x)) + 4) + 3) - 3| + 3) + 2)) and g(x) = (-2(-3(-2sin(2\u03c0((3(-1x^2 + 2x + 2) - 3)/(-1(-1x^2 + 2x + 2) - 3)) - 2) - 2)^2 - 3(-2sin(2\u03c0((3(-1x^2 + 2x + 2) - 3)/(-1(-1x^2 + 2x + 2) - 3)) - 2) - 2) - 1) - 3)/(2(-3(-2sin(2\u03c0((3(-1x^2 + 2x + 2) - 3)/(-1(-1x^2 + 2x + 2) - 3)) - 2) - 2)^2 - 3(-2sin(2\u03c0((3(-1x^2 + 2x + 2) - 3)/(-1(-1x^2 + 2x + 2) - 3)) - 2) - 2) - 1) + 1) from x = 0.4 to x = 0.9. 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) = (2(1((-1(2cos(2\u03c0((2(-1|x - 1| - 2) + 1)/(1(-1|x - 1| - 2))) - 3) + 1))/(1(2cos(2\u03c0((2(-1|x - 1| - 2) + 1)/(1(-1|x - 1| - 2))) - 3) + 1))) + 3) - 1)/(1(1((-1(2cos(2\u03c0((2(-1|x - 1| - 2) + 1)/(1(-1|x - 1| - 2))) - 3) + 1))/(1(2cos(2\u03c0((2(-1|x - 1| - 2) + 1)/(1(-1|x - 1| - 2))) - 3) + 1))) + 3)) and g(x) = (3(1e^(-1(-2((3(-3|x| + 1) - 2)/(-2(-3|x| + 1))))) - 2) - 2)/(2(1e^(-1(-2((3(-3|x| + 1) - 2)/(-2(-3|x| + 1))))) - 2) + 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3(1(-4(-3(-1e^(2(5x^2 - 4x + 1)) + 3) + 1) - 5)^2 + 1(-4(-3(-1e^(2(5x^2 - 4x + 1)) + 3) + 1) - 5) - 3) - 2, g(x) = 5((-1((-2(5(1cos(3\u03c0x - 1) + 2) - 5) + 3)/(1(5(1cos(3\u03c0x - 1) + 2) - 5) - 2)) - 2)/(1((-2(5(1cos(3\u03c0x - 1) + 2) - 5) + 3)/(1(5(1cos(3\u03c0x - 1) + 2) - 5) - 2)) - 2))^2 + 5((-1((-2(5(1cos(3\u03c0x - 1) + 2) - 5) + 3)/(1(5(1cos(3\u03c0x - 1) + 2) - 5) - 2)) - 2)/(1((-2(5(1cos(3\u03c0x - 1) + 2) - 5) + 3)/(1(5(1cos(3\u03c0x - 1) + 2) - 5) - 2)) - 2)) - 3, 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": "23.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 3cos(1\u03c0(2|(-2|(-2|((2(-1x^2 - 1) + 1)/(-3(-1x^2 - 1) - 2)) + 1| - 2) + 1| + 2) + 3| + 2) - 2) and g(x) = -1|(1((1(-5(-1x^2 - 1x + 5) - 1) - 2)/(-2(-5(-1x^2 - 1x + 5) - 1) + 3))^2 - 4((1(-5(-1x^2 - 1x + 5) - 1) - 2)/(-2(-5(-1x^2 - 1x + 5) - 1) + 3))) + 3| + 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": "Determine the area of the region enclosed by the graphs of f(x) = 3(1|(-3(1(-2|(-2x^2 + 2x - 2) + 3| + 3)^2 - 4(-2|(-2x^2 + 2x - 2) + 3| + 3) + 1)^2 - 4(1(-2|(-2x^2 + 2x - 2) + 3| + 3)^2 - 4(-2|(-2x^2 + 2x - 2) + 3| + 3) + 1) + 1) - 1| + 2) - 2 and g(x) = 4(-2e^(-2(2|(-5(-2x^2 - 4x + 2)^2 - 2(-2x^2 - 4x + 2) - 1) + 1| + 2)) - 2)^2 + 1(-2e^(-2(2|(-5(-2x^2 - 4x + 2)^2 - 2(-2x^2 - 4x + 2) - 1) + 1| + 2)) - 2) - 4 between the vertical lines x = 0.3 and x = 0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.7", "dataset": "MATH"}