{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -3|(-2(-3sin(1\u03c0(-3|(-4x^2 + 5x + 3) - 1|) - 3) - 2)^2 + 3(-3sin(1\u03c0(-3|(-4x^2 + 5x + 3) - 1|) - 3) - 2) + 4) - 1| - 2, g(x) = -1(-1(1(-5x - 3))^2 - 3(1(-5x - 3)) - 2) - 4, 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": "7.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 4(3|(5(3|(-3|x - 3| - 3) + 3| - 2) - 3) - 2|)^2 - 4(3|(5(3|(-3|x - 3| - 3) + 3| - 2) - 3) - 2|) + 1 and g(x) = (-1(3(-4((1x + 3)/(-3x + 2)) + 5)^2 - 1(-4((1x + 3)/(-3x + 2)) + 5) + 5) - 3)/(-1(3(-4((1x + 3)/(-3x + 2)) + 5)^2 - 1(-4((1x + 3)/(-3x + 2)) + 5) + 5)) from x = 2.7 to x = 2.8000000000000003. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "52.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3((3(-2(3e^(2(5x - 1)) + 1)^2 - 3(3e^(2(5x - 1)) + 1)) - 2)/(1(-2(3e^(2(5x - 1)) + 1)^2 - 3(3e^(2(5x - 1)) + 1)) + 3))^2 - 5((3(-2(3e^(2(5x - 1)) + 1)^2 - 3(3e^(2(5x - 1)) + 1)) - 2)/(1(-2(3e^(2(5x - 1)) + 1)^2 - 3(3e^(2(5x - 1)) + 1)) + 3)) + 4, g(x) = (3(-4(-3|(1x - 2) + 2| + 1)^2 - 4(-3|(1x - 2) + 2| + 1) + 2) - 3)/(3(-4(-3|(1x - 2) + 2| + 1)^2 - 4(-3|(1x - 2) + 2| + 1) + 2) + 1), 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": "9.8", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-1(-2sin(2\u03c0(1(2(-3x^2 + 1x + 2) - 2) - 5) - 3)) + 3)/(3(-2sin(2\u03c0(1(2(-3x^2 + 1x + 2) - 2) - 5) - 3))) and g(x) = -1(3((-2(-2|x + 2| - 1) - 3)/(1(-2|x + 2| - 1) + 2)) - 5)^2 - 5(3((-2(-2|x + 2| - 1) - 3)/(1(-2|x + 2| - 1) + 2)) - 5) + 4 between the vertical lines x = -1.8 and x = -1.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.6", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-3(1sin(1\u03c0(1(5(4x - 4) - 2) - 4) + 1) + 1) + 1)/(-3(1sin(1\u03c0(1(5(4x - 4) - 2) - 4) + 1) + 1)), g(x) = -4(-1(-3(-2|x + 1|)^2 + 5(-2|x + 1|) + 5)^2 + 2(-3(-2|x + 1|)^2 + 5(-2|x + 1|) + 5))^2 - 5(-1(-3(-2|x + 1|)^2 + 5(-2|x + 1|) + 5)^2 + 2(-3(-2|x + 1|)^2 + 5(-2|x + 1|) + 5)) + 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": "11.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -4(4(-3cos(1\u03c0(3|(1x + 5) - 1| - 1) - 1) - 2)^2 - 1(-3cos(1\u03c0(3|(1x + 5) - 1| - 1) - 1) - 2) - 5) + 4 and g(x) = (-3(-3|(-2(-2|x| + 1) - 1) - 2|) + 1)/(3(-3|(-2(-2|x| + 1) - 1) - 2|) + 1) from x = -1.2 to x = -1.1. 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(1(-1(-1(5x - 4) + 3)^2 + 5(-1(5x - 4) + 3) + 1) - 1) - 2)/(-2(1(-1(-1(5x - 4) + 3)^2 + 5(-1(5x - 4) + 3) + 1) - 1)) and g(x) = -1|(4(-2(-2|x + 1| - 1)^2 + 1(-2|x + 1| - 1) + 4) + 5)| 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": "1.6", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3|(2|(-4(2e^(2(-1x + 3)) - 1) - 2) + 1| - 2) + 2| - 2, g(x) = -2|(2|(1sin(1\u03c0(2x^2 + 1x + 5) + 2) + 2)| - 2) - 2| + 2, x = 3.4, 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1(-1|(-3|(-3(-2x + 1) - 2)|) - 1|)^2 - 5(-1|(-3|(-3(-2x + 1) - 2)|) - 1|) - 2, g(x) = 3((-1(2(4x + 1)^2 - 5(4x + 1)) + 3)/(2(2(4x + 1)^2 - 5(4x + 1)) + 1))^2 + 4((-1(2(4x + 1)^2 - 5(4x + 1)) + 3)/(2(2(4x + 1)^2 - 5(4x + 1)) + 1)) - 2, x = -0.2, and x = 0.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "154.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (1(-2(-5(3|(-1x^2 + 5x - 4) - 2| - 3) - 2) - 5) - 2)/(-2(-2(-5(3|(-1x^2 + 5x - 4) - 2| - 3) - 2) - 5) - 2) and g(x) = -1(3|(4((1x + 3)/(-1x - 2))^2 + 4((1x + 3)/(-1x - 2)) - 4) - 3| - 2)^2 - 4(3|(4((1x + 3)/(-1x - 2))^2 + 4((1x + 3)/(-1x - 2)) - 4) - 3| - 2) + 4 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": "1.5", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (2(1((-3(2sin(2\u03c0(2x + 5)) + 3) - 3)/(-1(2sin(2\u03c0(2x + 5)) + 3) - 2))^2 - 2((-3(2sin(2\u03c0(2x + 5)) + 3) - 3)/(-1(2sin(2\u03c0(2x + 5)) + 3) - 2)) - 1) + 1)/(-1(1((-3(2sin(2\u03c0(2x + 5)) + 3) - 3)/(-1(2sin(2\u03c0(2x + 5)) + 3) - 2))^2 - 2((-3(2sin(2\u03c0(2x + 5)) + 3) - 3)/(-1(2sin(2\u03c0(2x + 5)) + 3) - 2)) - 1)), g(x) = 3(-2((-1((-1x + 2)/(1x)) - 2)/(-3((-1x + 2)/(1x)) + 2))^2 - 4) - 3, x = -2.0, and x = -1.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (1(-1|(2|(-2|(-1x^2 - 2x) + 1| - 3) - 1| - 2) + 3| - 3) - 1)/(2(-1|(2|(-2|(-1x^2 - 2x) + 1| - 3) - 1| - 2) + 3| - 3) - 1) and g(x) = 2(-3|(2(2x + 2)^2 - 3) + 1| + 3) - 4 from x = -1.5 to x = -1.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2((2(-1|(2sin(2\u03c0(-3x^2 - 5x + 1) - 3) - 2) - 2| - 1) + 3)/(-2(-1|(2sin(2\u03c0(-3x^2 - 5x + 1) - 3) - 2) - 2| - 1) + 3)) - 1 and g(x) = 1cos(3\u03c0(-5(-3((2x - 2)/(-1x + 3)) - 4)^2 - 3(-3((2x - 2)/(-1x + 3)) - 4) - 1) + 3) + 1 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1|(-1|(4(-1|(3sin(1\u03c0x - 1) + 2) - 3| + 1) + 5)| + 1) + 1| + 1 and g(x) = 2(-5((-1(2|x + 2| + 1) + 3)/(3(2|x + 2| + 1)))) + 1 between the vertical lines x = 1.6 and x = 2.0. 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) = (2(2|(5(-1((-2x + 2)/(-2x + 1))^2 + 5((-2x + 2)/(-2x + 1)) + 5) - 3) + 3| + 2) - 3)/(-1(2|(5(-1((-2x + 2)/(-2x + 1))^2 + 5((-2x + 2)/(-2x + 1)) + 5) - 3) + 3| + 2) + 3), g(x) = (1((-2(-1(-3x - 4)^2 + 1) - 2)/(-2(-1(-3x - 4)^2 + 1) + 3)) - 1)/(1((-2(-1(-3x - 4)^2 + 1) - 2)/(-2(-1(-3x - 4)^2 + 1) + 3)) + 1), x = -1.7, 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": "12.4", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -3(-3|(2(-2e^(1(-5x^2 + 2x + 1)) + 2) - 4) + 1| + 1) - 4, g(x) = -2(5(-3|(2cos(1\u03c0x + 3) + 2) - 3| + 2) + 3) + 1, x = 2.6, and x = 2.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.5", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1(3((3(2(-3x + 5) - 2) - 3)/(-1(2(-3x + 5) - 2) + 3))^2 - 4) + 4, g(x) = 3cos(1\u03c0((-1((-1(-5x - 3) + 2)/(3(-5x - 3) - 1)) - 1)/(-3((-1(-5x - 3) + 2)/(3(-5x - 3) - 1)) - 2)) + 1) + 2, 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": "3.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -4((3((-1(-3|(1x + 4) + 3| - 2) - 2)/(3(-3|(1x + 4) + 3| - 2) - 2)) - 1)/(-1((-1(-3|(1x + 4) + 3| - 2) - 2)/(3(-3|(1x + 4) + 3| - 2) - 2)) - 1))^2 - 5((3((-1(-3|(1x + 4) + 3| - 2) - 2)/(3(-3|(1x + 4) + 3| - 2) - 2)) - 1)/(-1((-1(-3|(1x + 4) + 3| - 2) - 2)/(3(-3|(1x + 4) + 3| - 2) - 2)) - 1)) + 2, g(x) = -2|(3|((1(1|x - 2| - 2) + 1)/(3(1|x - 2| - 2) + 2)) + 1| - 3)| - 3, x = 0.7, and x = 3.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "97.4", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2(-1((-2((-1(2|x - 2|) - 3)/(-2(2|x - 2|) - 1)) + 3)/(1((-1(2|x - 2|) - 3)/(-2(2|x - 2|) - 1))))^2 + 1((-2((-1(2|x - 2|) - 3)/(-2(2|x - 2|) - 1)) + 3)/(1((-1(2|x - 2|) - 3)/(-2(2|x - 2|) - 1)))) - 4)^2 + 1(-1((-2((-1(2|x - 2|) - 3)/(-2(2|x - 2|) - 1)) + 3)/(1((-1(2|x - 2|) - 3)/(-2(2|x - 2|) - 1))))^2 + 1((-2((-1(2|x - 2|) - 3)/(-2(2|x - 2|) - 1)) + 3)/(1((-1(2|x - 2|) - 3)/(-2(2|x - 2|) - 1)))) - 4) + 4 and g(x) = (1((1((-1(2|x + 1| - 2) + 3)/(-2(2|x + 1| - 2) - 3)) + 2)/(-3((-1(2|x + 1| - 2) + 3)/(-2(2|x + 1| - 2) - 3)) + 1)) - 2)/(3((1((-1(2|x + 1| - 2) + 3)/(-2(2|x + 1| - 2) - 3)) + 2)/(-3((-1(2|x + 1| - 2) + 3)/(-2(2|x + 1| - 2) - 3)) + 1)) - 1) between the vertical lines x = -2.1 and x = 0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "246.6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -5(-2e^(1(3|(2(-3x - 1)^2 + 3(-3x - 1) - 3)| - 3)) - 1) + 1 and g(x) = 3|(3cos(3\u03c0((-2(-4x) - 3)/(-1(-4x) - 3)) + 2) - 1) + 2| - 2 from x = 0.4 to x = 0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 5(2(1|(1|(-3|x - 1| + 1) - 3| + 1) + 3|) - 5) + 1 and g(x) = (2(-3|(-2((-1x + 3)/(-3x - 1))^2 + 5((-1x + 3)/(-3x - 1)) + 5) - 3| + 1) + 3)/(-1(-3|(-2((-1x + 3)/(-3x - 1))^2 + 5((-1x + 3)/(-3x - 1)) + 5) - 3| + 1) - 2) from x = 1.0 to x = 1.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-1(-1|(-2|((-3(1x^2 - 4x + 1))/(1(1x^2 - 4x + 1) + 3)) - 1| - 1) + 3| - 3) + 2)/(-1(-1|(-2|((-3(1x^2 - 4x + 1))/(1(1x^2 - 4x + 1) + 3)) - 1| - 1) + 3| - 3) - 1) and g(x) = 5(3|((1(1x^2 - 5x))/(-1(1x^2 - 5x) + 2)) + 3| - 3) + 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": "0.7", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2|(2(-2sin(3\u03c0(5(-3|x + 2| + 3)^2) - 2) + 2)^2) - 1| - 2 and g(x) = -1|(-3|((2(-2|x + 3| - 3) - 2)/(2(-2|x + 3| - 3) + 1)) + 1| + 3) - 2| between the vertical lines x = -2.3 and x = -2.1999999999999997. 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) = -4((-3(1(2(-3|x + 1|) + 3)^2 + 1(2(-3|x + 1|) + 3) + 4) - 2)/(-1(1(2(-3|x + 1|) + 3)^2 + 1(2(-3|x + 1|) + 3) + 4) + 2))^2 + 2((-3(1(2(-3|x + 1|) + 3)^2 + 1(2(-3|x + 1|) + 3) + 4) - 2)/(-1(1(2(-3|x + 1|) + 3)^2 + 1(2(-3|x + 1|) + 3) + 4) + 2)) + 2 and g(x) = -3((1(3(-3x + 1)^2 - 5(-3x + 1) - 4) - 2)/(-1(3(-3x + 1)^2 - 5(-3x + 1) - 4) - 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": "77.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2(2((3(-2(-1x^2 + 3x - 1) - 1) - 1)/(2(-2(-1x^2 + 3x - 1) - 1) - 1)))^2 + 3, g(x) = 2|(-4((-2(1|x - 3| + 3) - 1)/(-3(1|x - 3| + 3) - 1))^2 + 2) + 1| + 2, x = 0.1, 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": "38.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -3|(2|(2e^(2(-2|(1|x - 2| + 1) + 2| - 3)) - 2) + 2| - 3)| - 1, g(x) = -1|(-1|(1(-3|x - 1| - 2)^2 + 5(-3|x - 1| - 2) + 2) - 3| - 1) + 1| + 2, x = -0.6, and x = 2.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21.8", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 4((-1(1(2e^(2((-2x - 2)/(-1x))) - 1) + 3) + 3)/(-2(1(2e^(2((-2x - 2)/(-1x))) - 1) + 3) + 3)) - 4, g(x) = -3(3(-2((-3x + 3)/(1x + 1)) + 4) - 3)^2 + 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": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 4(1|(-2|(4((-3x + 3)/(2x))^2 - 5((-3x + 3)/(2x)) - 2) + 3| - 3) + 3|)^2 + 5(1|(-2|(4((-3x + 3)/(2x))^2 - 5((-3x + 3)/(2x)) - 2) + 3| - 3) + 3|) - 5 and g(x) = -2e^(2(-3((3(-2|x - 1| - 2) + 3)/(3(-2|x - 1| - 2) - 2))^2 + 3((3(-2|x - 1| - 2) + 3)/(3(-2|x - 1| - 2) - 2)) - 1)) - 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -3|(3(5((1(1|x + 1| - 3) + 1)/(2(1|x + 1| - 3) - 1))^2 + 5((1(1|x + 1| - 3) + 1)/(2(1|x + 1| - 3) - 1)) + 1) + 2) + 1| + 2, g(x) = (3(3|(3((-1x - 1)/(-1x + 3))^2 + 2((-1x - 1)/(-1x + 3)) - 2) + 2| - 1) + 2)/(-2(3|(3((-1x - 1)/(-1x + 3))^2 + 2((-1x - 1)/(-1x + 3)) - 2) + 2| - 1) + 3), x = -2.8, 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": "121.9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2((-3(5(3cos(1\u03c0((2x - 2)/(-1x + 2)) + 2) + 3) - 5))/(2(5(3cos(1\u03c0((2x - 2)/(-1x + 2)) + 2) + 3) - 5) + 1)) - 5 and g(x) = -2|(-3e^(2((3(1x + 5) - 1)/(1(1x + 5) + 3))) - 3) + 2| + 3 from x = -4.4 to x = -1.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "158.6", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 4(-3|(-1(-1|(-1cos(3\u03c0x + 2) + 2) + 1|)^2 + 1(-1|(-1cos(3\u03c0x + 2) + 2) + 1|)) - 1| - 2) + 3 and g(x) = -2e^(-1(1((2((2x - 2)/(1x + 3)) - 3)/(3((2x - 2)/(1x + 3)) + 3))^2 + 5((2((2x - 2)/(1x + 3)) - 3)/(3((2x - 2)/(1x + 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": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2(3|(3|(-4((1x + 1)/(-3x + 1))^2 - 1((1x + 1)/(-3x + 1)) + 3) + 1| + 1) - 3| - 3)^2 + 3(3|(3|(-4((1x + 1)/(-3x + 1))^2 - 1((1x + 1)/(-3x + 1)) + 3) + 1| + 1) - 3| - 3) - 2 and g(x) = 3|(-4(-1(-1x^2 - 5x + 2))^2 + 2(-1(-1x^2 - 5x + 2)) - 4) - 3| - 2 between the vertical lines x = -0.1 and x = 0.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8.9", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1|((-2((2(2(4x^2 + 5x - 3)) - 2)/(2(2(4x^2 + 5x - 3)) + 2)))/(1((2(2(4x^2 + 5x - 3)) - 2)/(2(2(4x^2 + 5x - 3)) + 2)) + 2)) + 3| - 3 and g(x) = (2(1|(5(-1sin(1\u03c0x - 2) - 1)^2 - 4(-1sin(1\u03c0x - 2) - 1) - 2) - 1| + 1) + 1)/(-1(1|(5(-1sin(1\u03c0x - 2) - 1)^2 - 4(-1sin(1\u03c0x - 2) - 1) - 2) - 1| + 1) + 3) between the vertical lines x = -4.3 and x = -3.4. 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": "Find the area of the region bounded by the curves f(x) = -4(5((2((-3(-1x + 5) + 3)/(3(-1x + 5) - 2)) - 3)/(-2((-3(-1x + 5) + 3)/(3(-1x + 5) - 2)))) + 4) + 3, g(x) = (-3(3cos(2\u03c0((-1((3x + 3)/(1x)) + 1)/(2((3x + 3)/(1x)) - 1)) + 3) - 3) + 1)/(-3(3cos(2\u03c0((-1((3x + 3)/(1x)) + 1)/(2((3x + 3)/(1x)) - 1)) + 3) - 3) - 3), x = -1.2, and x = -1.0999999999999999. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2|((-3(3(2cos(3\u03c0((-1x + 3)/(-3x + 1)) - 3) - 2) - 5) + 3)/(3(3(2cos(3\u03c0((-1x + 3)/(-3x + 1)) - 3) - 2) - 5) - 2)) + 3| and g(x) = -1(-1(5((3x - 3)/(1x + 3))^2 + 1((3x - 3)/(1x + 3)) - 2)^2 + 1(5((3x - 3)/(1x + 3))^2 + 1((3x - 3)/(1x + 3)) - 2)) - 4 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2e^(1(-5(-4(-1(1x^2 - 4x + 2)^2 - 1(1x^2 - 4x + 2))^2 + 3(-1(1x^2 - 4x + 2)^2 - 1(1x^2 - 4x + 2)) + 2))) + 2, g(x) = (-2(1(-2(3cos(1\u03c0x + 2) + 1)^2 - 3(3cos(1\u03c0x + 2) + 1) - 5) - 5) + 1)/(-1(1(-2(3cos(1\u03c0x + 2) + 1)^2 - 3(3cos(1\u03c0x + 2) + 1) - 5) - 5) + 2), x = 2.8, and x = 3.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 3((-2((-3((3(2|x + 2| + 3) + 3)/(-1(2|x + 2| + 3) - 3)) - 2)/(1((3(2|x + 2| + 3) + 3)/(-1(2|x + 2| + 3) - 3)) + 2)) + 3)/(-3((-3((3(2|x + 2| + 3) + 3)/(-1(2|x + 2| + 3) - 3)) - 2)/(1((3(2|x + 2| + 3) + 3)/(-1(2|x + 2| + 3) - 3)) + 2)) + 4)) and g(x) = (2(3|(-2cos(1\u03c0(1x) + 2)) - 2|) - 1)/(-2(3|(-2cos(1\u03c0(1x) + 2)) - 2|) + 3) between the vertical lines x = 4.2 and x = 4.6. 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) = (1((2(-1(-3(-1|x - 1|)^2 - 5(-1|x - 1|) - 4)^2 - 2(-3(-1|x - 1|)^2 - 5(-1|x - 1|) - 4) + 1) + 1)/(2(-1(-3(-1|x - 1|)^2 - 5(-1|x - 1|) - 4)^2 - 2(-3(-1|x - 1|)^2 - 5(-1|x - 1|) - 4) + 1) + 2)) - 1)/(2((2(-1(-3(-1|x - 1|)^2 - 5(-1|x - 1|) - 4)^2 - 2(-3(-1|x - 1|)^2 - 5(-1|x - 1|) - 4) + 1) + 1)/(2(-1(-3(-1|x - 1|)^2 - 5(-1|x - 1|) - 4)^2 - 2(-3(-1|x - 1|)^2 - 5(-1|x - 1|) - 4) + 1) + 2)) - 1), g(x) = 5((-3(-1|(2|x + 2| - 3) + 3|) - 1)/(3(-1|(2|x + 2| - 3) + 3|) + 2))^2 + 4((-3(-1|(2|x + 2| - 3) + 3|) - 1)/(3(-1|(2|x + 2| - 3) + 3|) + 2)) + 2, x = -0.3, and x = 0.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-1(3(2sin(2\u03c0(1(-4x - 1)^2 + 2(-4x - 1) + 2) - 3) + 2)^2 + 1(2sin(2\u03c0(1(-4x - 1)^2 + 2(-4x - 1) + 2) - 3) + 2) - 3))/(-1(3(2sin(2\u03c0(1(-4x - 1)^2 + 2(-4x - 1) + 2) - 3) + 2)^2 + 1(2sin(2\u03c0(1(-4x - 1)^2 + 2(-4x - 1) + 2) - 3) + 2) - 3) - 2), g(x) = -3(4(-2|(2x - 1) - 3| - 1) - 5) + 5, 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": "9.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2(1(1(-2((2x - 3)/(-2x - 1)) - 1))^2 + 4(1(-2((2x - 3)/(-2x - 1)) - 1)) - 1) - 4 and g(x) = -3((1((1(2x - 2) - 3)/(3(2x - 2) + 2)))/(-3((1(2x - 2) - 3)/(3(2x - 2) + 2)) + 4)) - 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 5(1|(1((1((1x + 1)/(2x + 2)) - 3)/(-1((1x + 1)/(2x + 2))))^2 - 3((1((1x + 1)/(2x + 2)) - 3)/(-1((1x + 1)/(2x + 2)))) + 3) + 3| - 3)^2 - 3(1|(1((1((1x + 1)/(2x + 2)) - 3)/(-1((1x + 1)/(2x + 2))))^2 - 3((1((1x + 1)/(2x + 2)) - 3)/(-1((1x + 1)/(2x + 2)))) + 3) + 3| - 3) + 3, g(x) = 5(3((-2(2x) - 1)/(-1(2x) - 3))^2 - 2((-2(2x) - 1)/(-1(2x) - 3)) + 3) + 1, x = -2.0, and x = -1.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-27362.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 3(4(-3cos(1\u03c0((2((1x - 3)/(-2x - 3)) - 3)/(1((1x - 3)/(-2x - 3)) + 1)) + 3) + 1)^2 + 5(-3cos(1\u03c0((2((1x - 3)/(-2x - 3)) - 3)/(1((1x - 3)/(-2x - 3)) + 1)) + 3) + 1) - 1) + 3 and g(x) = 1|((-1(-2|(3e^(-2x) + 3) - 3|) + 1)/(3(-2|(3e^(-2x) + 3) - 3|) + 1))| + 2 between the vertical lines x = -3.7 and x = -3.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2|(-3(-2(2|(3|x - 1| + 1) - 1| - 2)^2 - 1(2|(3|x - 1| + 1) - 1| - 2) + 2)^2 + 5(-2(2|(3|x - 1| + 1) - 1| - 2)^2 - 1(2|(3|x - 1| + 1) - 1| - 2) + 2) - 4) + 2| + 2 and g(x) = -2cos(2\u03c0((-3((-2(3x^2 - 1x - 3) + 1)/(3(3x^2 - 1x - 3) - 1)) - 1)/(-1((-2(3x^2 - 1x - 3) + 1)/(3(3x^2 - 1x - 3) - 1)) - 3)) + 1) - 3 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2((1((3(-2|(3x - 2) - 1| - 3) + 1)/(-2(-2|(3x - 2) - 1| - 3))) + 1)/(-2((3(-2|(3x - 2) - 1| - 3) + 1)/(-2(-2|(3x - 2) - 1| - 3))) - 1)) - 2 and g(x) = -2|((-1((-2(-2x^2 + 4x + 3) - 3)/(2(-2x^2 + 4x + 3) - 1)) + 2)/(1((-2(-2x^2 + 4x + 3) - 3)/(2(-2x^2 + 4x + 3) - 1)) + 1)) + 3| + 2 from x = 0.0 to x = 2.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7.9", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1((-1(-3sin(3\u03c0(-1(-3|x + 3| - 2) + 3) + 3) - 2))/(2(-3sin(3\u03c0(-1(-3|x + 3| - 2) + 3) + 3) - 2) + 2))^2 + 1((-1(-3sin(3\u03c0(-1(-3|x + 3| - 2) + 3) + 3) - 2))/(2(-3sin(3\u03c0(-1(-3|x + 3| - 2) + 3) + 3) - 2) + 2)) and g(x) = 1cos(1\u03c0(-5(3|(5x^2 + 4x - 4) - 2| + 1)^2 - 4(3|(5x^2 + 4x - 4) - 2| + 1)) - 1) + 3 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": "3.7", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2|((2((1(1cos(1\u03c0(2x - 3) - 2) + 2) + 2)/(-2(1cos(1\u03c0(2x - 3) - 2) + 2) - 1)) + 3)/(3((1(1cos(1\u03c0(2x - 3) - 2) + 2) + 2)/(-2(1cos(1\u03c0(2x - 3) - 2) + 2) - 1)) + 2)) + 1| - 3, g(x) = 2sin(3\u03c0(-1(-4(3x + 3)^2 - 1(3x + 3) - 2) + 1) - 2) - 2, x = -2.7, and x = -2.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-1(4(-1|((-2(3|x - 3| + 1) - 1)/(2(3|x - 3| + 1) - 3)) + 3| - 2)^2 + 2(-1|((-2(3|x - 3| + 1) - 1)/(2(3|x - 3| + 1) - 3)) + 3| - 2)) - 2)/(2(4(-1|((-2(3|x - 3| + 1) - 1)/(2(3|x - 3| + 1) - 3)) + 3| - 2)^2 + 2(-1|((-2(3|x - 3| + 1) - 1)/(2(3|x - 3| + 1) - 3)) + 3| - 2)) + 2) and g(x) = 4((2(1sin(3\u03c0(-2|x + 1|) + 2) - 1) + 1)/(-2(1sin(3\u03c0(-2|x + 1|) + 2) - 1) + 1)) from x = 3.6 to x = 3.8. 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": "Determine the area of the region enclosed by the graphs of f(x) = 2(-1(-2sin(3\u03c0(-1|((1x - 2)/(-3x - 2)) + 2| + 1) + 2) + 2)^2 - 4(-2sin(3\u03c0(-1|((1x - 2)/(-3x - 2)) + 2| + 1) + 2) + 2) - 2) + 4 and g(x) = 3(-3(-2|(1x + 4) - 3| + 1)^2 + 4(-2|(1x + 4) - 3| + 1) + 5) - 1 between the vertical lines x = -2.0 and x = -0.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "79.4", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-2((-2(-1(1(-2x^2 - 1x - 4) + 5) + 3))/(-1(-1(1(-2x^2 - 1x - 4) + 5) + 3) - 1)) + 1)/(-1((-2(-1(1(-2x^2 - 1x - 4) + 5) + 3))/(-1(-1(1(-2x^2 - 1x - 4) + 5) + 3) - 1)) - 2) and g(x) = (3(3cos(3\u03c0((-2(-1x - 2) - 2)/(3(-1x - 2) - 2)) - 1) - 2) - 3)/(-3(3cos(3\u03c0((-2(-1x - 2) - 2)/(3(-1x - 2) - 2)) - 1) - 2) - 3) between the vertical lines x = -2.4 and x = -2.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-1((2(-2e^(2(-2|(-3x^2 + 2x - 5)|)) + 1) - 1)/(3(-2e^(2(-2|(-3x^2 + 2x - 5)|)) + 1))) - 1)/(1((2(-2e^(2(-2|(-3x^2 + 2x - 5)|)) + 1) - 1)/(3(-2e^(2(-2|(-3x^2 + 2x - 5)|)) + 1))) + 3) and g(x) = 2cos(2\u03c0((3(-1(-3|x + 2| + 3) + 2) + 2)/(-3(-1(-3|x + 2| + 3) + 2))) - 1) - 1 between the vertical lines x = -2.1 and 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": "Find the area of the region bounded by the curves f(x) = -2|(1(2(-2(1x + 3) - 4) - 1) - 1) + 1| - 3, g(x) = (1((3(2(-2e^(1x) + 3)^2 - 1(-2e^(1x) + 3) - 5))/(3(2(-2e^(1x) + 3)^2 - 1(-2e^(1x) + 3) - 5) - 1)) - 2)/(3((3(2(-2e^(1x) + 3)^2 - 1(-2e^(1x) + 3) - 5))/(3(2(-2e^(1x) + 3)^2 - 1(-2e^(1x) + 3) - 5) - 1)) - 2), x = -0.5, and x = 0.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "62.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3((-3(-2(5(-2|x - 2| + 2)^2 + 1(-2|x - 2| + 2) + 1) - 1))/(2(-2(5(-2|x - 2| + 2)^2 + 1(-2|x - 2| + 2) + 1) - 1) - 1))^2 + 4((-3(-2(5(-2|x - 2| + 2)^2 + 1(-2|x - 2| + 2) + 1) - 1))/(2(-2(5(-2|x - 2| + 2)^2 + 1(-2|x - 2| + 2) + 1) - 1) - 1)) + 5, g(x) = 4((-3(-2|(1x^2 - 2x - 4) + 2| - 1) + 2)/(2(-2|(1x^2 - 2x - 4) + 2| - 1) - 1))^2 + 2((-3(-2|(1x^2 - 2x - 4) + 2| - 1) + 2)/(2(-2|(1x^2 - 2x - 4) + 2| - 1) - 1)) - 2, x = -0.7, 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": "3.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -4(-2((3(-1|(3|x - 2| + 1) + 3| + 1) - 1)/(3(-1|(3|x - 2| + 1) + 3| + 1) + 1)))^2 + 5(-2((3(-1|(3|x - 2| + 1) + 3| + 1) - 1)/(3(-1|(3|x - 2| + 1) + 3| + 1) + 1))) + 3, g(x) = -4(2|(-1((3x + 1)/(-2x + 1))^2 + 1) + 1| - 3)^2 + 3(2|(-1((3x + 1)/(-2x + 1))^2 + 1) + 1| - 3) + 5, x = 0.1, and x = 0.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.6", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1(-2(-1(3|(1e^(1x)) - 2|)^2 + 4(3|(1e^(1x)) - 2|) + 3)^2 + 1(-1(3|(1e^(1x)) - 2|)^2 + 4(3|(1e^(1x)) - 2|) + 3) + 3)^2 + 2, g(x) = (-1(-1(3(-1|x - 1| - 3) - 3) - 5) - 2)/(-2(-1(3(-1|x - 1| - 3) - 3) - 5) + 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": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3(1(-5(5(3|x - 3| - 2) + 4)^2 + 5(5(3|x - 3| - 2) + 4) + 5)^2 - 5(-5(5(3|x - 3| - 2) + 4)^2 + 5(5(3|x - 3| - 2) + 4) + 5) - 1) - 5, g(x) = 1(1((2(-3x^2 - 5x + 5))/(-2(-3x^2 - 5x + 5) - 2)) - 1)^2 - 3(1((2(-3x^2 - 5x + 5))/(-2(-3x^2 - 5x + 5) - 2)) - 1) - 3, 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": "15.4", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -4(-2|(-2|(-5(1|x + 2|) - 2) - 2| - 1) - 3| + 2) - 4 and g(x) = 1|((2(2sin(1\u03c0(-1x - 1) - 1) - 2) + 1)/(-2(2sin(1\u03c0(-1x - 1) - 1) - 2) - 2)) - 1| + 3 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": "13.8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (2(-4(-1(2(2x^2 + 4x - 2)^2 - 4(2x^2 + 4x - 2) - 1) - 4)^2 - 4(-1(2(2x^2 + 4x - 2)^2 - 4(2x^2 + 4x - 2) - 1) - 4) + 2) - 1)/(-3(-4(-1(2(2x^2 + 4x - 2)^2 - 4(2x^2 + 4x - 2) - 1) - 4)^2 - 4(-1(2(2x^2 + 4x - 2)^2 - 4(2x^2 + 4x - 2) - 1) - 4) + 2) + 1) and g(x) = (-2((3(1|(-5x^2 - 3x) - 3| + 2) - 2)/(-2(1|(-5x^2 - 3x) - 3| + 2) + 3)) - 2)/(3((3(1|(-5x^2 - 3x) - 3| + 2) - 2)/(-2(1|(-5x^2 - 3x) - 3| + 2) + 3)) + 2) 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2sin(1\u03c0((-3(-1(1|(-5x + 5) - 3| + 1)) - 3)/(-3(-1(1|(-5x + 5) - 3| + 1)))) + 2) - 1, g(x) = -4(3cos(2\u03c0(1(-1x^2) - 4) + 3) + 1) - 1, x = 2.3, and x = 2.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-3(2|(-5(-2(1e^(-1x) + 2) + 4)^2 - 4(-2(1e^(-1x) + 2) + 4) + 4) - 2| + 1))/(2(2|(-5(-2(1e^(-1x) + 2) + 4)^2 - 4(-2(1e^(-1x) + 2) + 4) + 4) - 2| + 1) + 2) and g(x) = -3((1(4(-1|x - 1| + 1)^2 - 3) + 1)/(2(4(-1|x - 1| + 1)^2 - 3)))^2 + 4((1(4(-1|x - 1| + 1)^2 - 3) + 1)/(2(4(-1|x - 1| + 1)^2 - 3))) - 2 from x = 1.4 to x = 2.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -3sin(3\u03c0((1(-3|(4(2|x - 3| - 2)^2 + 1(2|x - 3| - 2) + 1) + 1| - 1) + 3)/(2(-3|(4(2|x - 3| - 2)^2 + 1(2|x - 3| - 2) + 1) + 1| - 1) - 1)) - 2) + 2, g(x) = (2(1((3((-1x + 1)/(1x)) - 3)/(-3((-1x + 1)/(1x)) + 2)) + 1) + 1)/(1(1((3((-1x + 1)/(1x)) - 3)/(-3((-1x + 1)/(1x)) + 2)) + 1) - 3), x = 1.9, 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": "Calculate the area enclosed between the functions f(x) = (-2(1(-2(2(-1|x - 2| - 2) - 3) + 3)^2 + 1) - 1)/(3(1(-2(2(-1|x - 2| - 2) - 3) + 3)^2 + 1) + 2) and g(x) = -1sin(2\u03c0(1((-3((-2x + 2)/(2x - 1)) - 2)/(2((-2x + 2)/(2x - 1)) + 3))^2 + 2((-3((-2x + 2)/(2x - 1)) - 2)/(2((-2x + 2)/(2x - 1)) + 3)) + 4) + 1) from x = -0.0 to x = 0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 4(-1((-1(2(4x^2 - 5x + 4)^2 - 2(4x^2 - 5x + 4) + 3))/(1(2(4x^2 - 5x + 4)^2 - 2(4x^2 - 5x + 4) + 3) + 1)) - 5)^2 + 2(-1((-1(2(4x^2 - 5x + 4)^2 - 2(4x^2 - 5x + 4) + 3))/(1(2(4x^2 - 5x + 4)^2 - 2(4x^2 - 5x + 4) + 3) + 1)) - 5) and g(x) = 5((-3(-2e^(2(-3x^2 + 3x - 1)) + 1) - 2)/(-2(-2e^(2(-3x^2 + 3x - 1)) + 1) + 3))^2 + 3((-3(-2e^(2(-3x^2 + 3x - 1)) + 1) - 2)/(-2(-2e^(2(-3x^2 + 3x - 1)) + 1) + 3)) + 4 between the vertical lines x = -0.1 and x = 1.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "51.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1|((2(-4(-1|(1x^2 + 5x - 2) - 2|) + 5) - 1)/(-2(-4(-1|(1x^2 + 5x - 2) - 2|) + 5) + 3)) + 2| - 3, g(x) = -5(-1(2|(-3sin(3\u03c0x + 2) - 1) + 3| - 3)) + 1, x = -3.9, 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": "10.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-1(-1|(4(-2(-1|x - 3| + 3) - 5) - 3) + 3| - 3) - 2)/(3(-1|(4(-2(-1|x - 3| + 3) - 5) - 3) + 3| - 3)), g(x) = (2(-3|(1e^(-2(2x - 2)) - 2) - 3| + 3) + 1)/(-1(-3|(1e^(-2(2x - 2)) - 2) - 3| + 3) - 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": "Find the area of the region bounded by the curves f(x) = (-1(-2(-3(-2|((2x)/(-1x + 2)) - 3| - 1) - 1) + 2) - 1)/(3(-2(-3(-2|((2x)/(-1x + 2)) - 3| - 1) - 1) + 2) + 3), g(x) = (3((3((1(-2sin(3\u03c0x - 2) + 2) - 1)/(-2(-2sin(3\u03c0x - 2) + 2) - 2)) + 2)/(2((1(-2sin(3\u03c0x - 2) + 2) - 1)/(-2(-2sin(3\u03c0x - 2) + 2) - 2)) + 2)) - 2)/(-2((3((1(-2sin(3\u03c0x - 2) + 2) - 1)/(-2(-2sin(3\u03c0x - 2) + 2) - 2)) + 2)/(2((1(-2sin(3\u03c0x - 2) + 2) - 1)/(-2(-2sin(3\u03c0x - 2) + 2) - 2)) + 2)) - 2), x = -4.2, 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2(4(-1(-2e^(2(2|x| - 3)) - 3)^2 - 5(-2e^(2(2|x| - 3)) - 3) + 1) - 2) and g(x) = -2cos(3\u03c0((-3(-1(1|x - 1| - 2) - 2) - 3)/(1(-1(1|x - 1| - 2) - 2) + 3))) - 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": "146.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1(1cos(2\u03c0(2(-1(-3|x| - 1)^2 - 3) + 4) - 2) + 2)^2 - 5(1cos(2\u03c0(2(-1(-3|x| - 1)^2 - 3) + 4) - 2) + 2) - 4 and g(x) = -3|(3|(-2sin(1\u03c0(-1|x + 2| - 2)) + 2) - 3| - 3) + 3| + 3 from x = 3.4 to x = 3.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.7", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2(1sin(3\u03c0((-2(3(-2x^2 - 1x - 3)^2 - 5(-2x^2 - 1x - 3) - 4) + 1)/(3(3(-2x^2 - 1x - 3)^2 - 5(-2x^2 - 1x - 3) - 4) + 2)) + 1) - 2)^2 + 5(1sin(3\u03c0((-2(3(-2x^2 - 1x - 3)^2 - 5(-2x^2 - 1x - 3) - 4) + 1)/(3(3(-2x^2 - 1x - 3)^2 - 5(-2x^2 - 1x - 3) - 4) + 2)) + 1) - 2) - 4 and g(x) = 2(-3|(-3cos(2\u03c0(1|x + 2|) - 3)) - 1| - 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": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2sin(3\u03c0(-3|(-1|(5(-3x^2 + 1x + 4)^2 - 3) - 1| + 1) - 3| - 3) + 3), g(x) = 3(-1|(-1(2x + 3) + 3) - 3| + 3) + 3, 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-2(-1|((3(1(5x - 2) - 1) - 1)/(2(1(5x - 2) - 1) - 1)) - 2| + 1))/(-2(-1|((3(1(5x - 2) - 1) - 1)/(2(1(5x - 2) - 1) - 1)) - 2| + 1) - 3) and g(x) = -1sin(2\u03c0(-1(-3|((2x + 1)/(2x + 2)) + 2| - 2)^2 - 3(-3|((2x + 1)/(2x + 2)) + 2| - 2) - 5) + 2) + 1 between the vertical lines x = -2.0 and x = -1.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1|((1(3|(2(-2x - 1)^2 + 1(-2x - 1) - 1) - 1| - 3) + 2)/(-3(3|(2(-2x - 1)^2 + 1(-2x - 1) - 1) - 1| - 3) - 1))| and g(x) = 3|((-3(-3|(2cos(2\u03c0x + 3) - 1) - 2| + 1) + 3)/(2(-3|(2cos(2\u03c0x + 3) - 1) - 2| + 1) + 2)) + 3| + 2 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": "1.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 4((-1(5(-2cos(3\u03c0((3x - 3)/(2x + 2))) + 3)^2 - 3(-2cos(3\u03c0((3x - 3)/(2x + 2))) + 3) - 5) + 2)/(-1(5(-2cos(3\u03c0((3x - 3)/(2x + 2))) + 3)^2 - 3(-2cos(3\u03c0((3x - 3)/(2x + 2))) + 3) - 5) - 1)) - 4 and g(x) = (-2(2|(1sin(2\u03c0(4x + 5)) + 3) + 2| - 1) + 2)/(1(2|(1sin(2\u03c0(4x + 5)) + 3) + 2| - 1) + 3) 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": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1(1(2|(4(-1sin(2\u03c0x + 3) - 2)^2 - 2(-1sin(2\u03c0x + 3) - 2) - 1) - 2| - 2) - 3)^2 - 3(1(2|(4(-1sin(2\u03c0x + 3) - 2)^2 - 2(-1sin(2\u03c0x + 3) - 2) - 1) - 2| - 2) - 3) - 5 and g(x) = -1|((-3(2|(-2|x + 1| + 1) - 2|) - 3)/(-1(2|(-2|x + 1| + 1) - 2|) + 3)) - 2| 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": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1cos(1\u03c0(1|((2((-1((1x + 1)/(-3x + 4)) - 2)/(-3((1x + 1)/(-3x + 4)) - 3)))/(2((-1((1x + 1)/(-3x + 4)) - 2)/(-3((1x + 1)/(-3x + 4)) - 3)) - 1)) - 2| - 3) + 2) + 1, g(x) = (1((3(-1(-2x^2 - 5x + 5)) - 3)/(2(-1(-2x^2 - 5x + 5)) - 3)) + 1)/(-2((3(-1(-2x^2 - 5x + 5)) - 3)/(2(-1(-2x^2 - 5x + 5)) - 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 3|(2(2sin(2\u03c0(-1(-5x^2 - 4x + 1)^2 + 4) + 3) + 2) + 4) + 1| - 1 and g(x) = -3(-3sin(2\u03c0(3(5x^2 - 4x + 1) - 5) - 3) - 3) + 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": "0.9", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 4((3(2cos(3\u03c0((-2(1|x - 3| + 3) - 1)/(-3(1|x - 3| + 3) - 3)))))/(2(2cos(3\u03c0((-2(1|x - 3| + 3) - 1)/(-3(1|x - 3| + 3) - 3)))) + 1)) + 3, g(x) = 2(2|(1|(2x + 3) - 2| + 1) - 3| + 3)^2 - 2(2|(1|(2x + 3) - 2| + 1) - 3| + 3) - 5, 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2|(-4(4(3cos(3\u03c0(3x^2 - 1x - 3) + 3) + 1) + 5) - 5) - 3| + 3 and g(x) = -1sin(3\u03c0(-1|(5(3x^2 - 4x - 3)^2 - 4(3x^2 - 4x - 3) - 2) + 2| + 2)) + 3 from x = 2.1 to x = 2.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "63.6", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -4(3(-2sin(2\u03c0(3|(-2x^2 + 2x + 1) - 3| - 3) - 1) - 1) - 3)^2 - 1(3(-2sin(2\u03c0(3|(-2x^2 + 2x + 1) - 3| - 3) - 1) - 1) - 3) and g(x) = 1(1(-1|(-3x + 3) + 2| + 3) + 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": "21.9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 5(4((1((-1(5x^2 - 4x + 2) + 1)/(2(5x^2 - 4x + 2) - 3)) - 2)/(3((-1(5x^2 - 4x + 2) + 1)/(2(5x^2 - 4x + 2) - 3)) + 2)) + 4)^2 + 5(4((1((-1(5x^2 - 4x + 2) + 1)/(2(5x^2 - 4x + 2) - 3)) - 2)/(3((-1(5x^2 - 4x + 2) + 1)/(2(5x^2 - 4x + 2) - 3)) + 2)) + 4) + 3 and g(x) = -4(-2(-3cos(2\u03c0(1x^2 + 3x - 2) + 1) + 1)^2 + 2) - 3 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": "4.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (3(-1|((-1(3((-1x + 1)/(-1x - 3))^2 - 3((-1x + 1)/(-1x - 3)) - 4) - 1)/(-1(3((-1x + 1)/(-1x - 3))^2 - 3((-1x + 1)/(-1x - 3)) - 4) - 1))| - 3) - 2)/(-2(-1|((-1(3((-1x + 1)/(-1x - 3))^2 - 3((-1x + 1)/(-1x - 3)) - 4) - 1)/(-1(3((-1x + 1)/(-1x - 3))^2 - 3((-1x + 1)/(-1x - 3)) - 4) - 1))| - 3) + 3) and g(x) = -5(3(2((-2x - 2)/(3x + 2))^2 - 5((-2x - 2)/(3x + 2)) - 4)^2 - 4)^2 + 1(3(2((-2x - 2)/(3x + 2))^2 - 5((-2x - 2)/(3x + 2)) - 4)^2 - 4) + 2 from x = 1.0 to x = 1.5. 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) = 5(-2(-4(1(1|x + 3| - 1) + 1)^2 + 4(1(1|x + 3| - 1) + 1) + 1) + 4) + 4, g(x) = 1|(2(5(1cos(3\u03c0x - 3) - 1)^2 + 5(1cos(3\u03c0x - 3) - 1) - 5)^2 + 3(5(1cos(3\u03c0x - 3) - 1)^2 + 5(1cos(3\u03c0x - 3) - 1) - 5)) + 2| - 3, x = -4.2, and x = -4.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (2(2sin(3\u03c0(-2|(-4((-2x - 2)/(2x - 1))) - 2|)) + 1) - 1)/(3(2sin(3\u03c0(-2|(-4((-2x - 2)/(2x - 1))) - 2|)) + 1) + 1) and g(x) = -2(-2|(2(-3x - 4)^2 - 5(-3x - 4) + 2) + 3| + 2) - 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": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (2(-2(-1sin(1\u03c0(2|(5x^2 - 3x + 1) - 3| - 3) - 1))^2) - 2)/(1(-2(-1sin(1\u03c0(2|(5x^2 - 3x + 1) - 3| - 3) - 1))^2) + 3) and g(x) = 1(1(-2|(-3x - 2) - 1|) + 4)^2 + 5(1(-2|(-3x - 2) - 1|) + 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (1((-3(-3|(-2sin(2\u03c0((-1x - 1)/(2x + 1)) - 1) + 1) + 2| + 3) - 1)/(1(-3|(-2sin(2\u03c0((-1x - 1)/(2x + 1)) - 1) + 1) + 2| + 3) - 2)) - 3)/(1((-3(-3|(-2sin(2\u03c0((-1x - 1)/(2x + 1)) - 1) + 1) + 2| + 3) - 1)/(1(-3|(-2sin(2\u03c0((-1x - 1)/(2x + 1)) - 1) + 1) + 2| + 3) - 2))), g(x) = 5(-2(-2|((-1x + 3)/(1x)) + 2|) - 1) - 4, 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": "5.8", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -4(1(-1(2(2|x - 1| - 3) - 5) - 3)^2 + 1(-1(2(2|x - 1| - 3) - 5) - 3) - 3)^2 - 3(1(-1(2(2|x - 1| - 3) - 5) - 3)^2 + 1(-1(2(2|x - 1| - 3) - 5) - 3) - 3) + 3 and g(x) = -2|(5(-2|(-1|x + 2| + 3) + 1|) + 2) - 1| + 1 between the vertical lines x = 2.6 and x = 2.9. 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": "Find the area of the region bounded by the curves f(x) = 2(1(3e^(-1(3|(-2|x| - 3)| + 1)) + 1) + 2)^2 + 4(1(3e^(-1(3|(-2|x| - 3)| + 1)) + 1) + 2) - 5, g(x) = 4((2(1|(-1cos(2\u03c0x - 2) - 2) - 2|) + 2)/(-2(1|(-1cos(2\u03c0x - 2) - 2) - 2|) + 3))^2 - 4((2(1|(-1cos(2\u03c0x - 2) - 2) - 2|) + 2)/(-2(1|(-1cos(2\u03c0x - 2) - 2) - 2|) + 3)) + 1, x = -4.4, and x = -3.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3((2(-4(1((-1x - 3)/(2x - 1))^2 + 2((-1x - 3)/(2x - 1)) + 2)^2 - 4(1((-1x - 3)/(2x - 1))^2 + 2((-1x - 3)/(2x - 1)) + 2) + 3) - 2)/(2(-4(1((-1x - 3)/(2x - 1))^2 + 2((-1x - 3)/(2x - 1)) + 2)^2 - 4(1((-1x - 3)/(2x - 1))^2 + 2((-1x - 3)/(2x - 1)) + 2) + 3))) + 2 and g(x) = -3(-4(-3(4x - 4) - 1)^2 + 3(-3(4x - 4) - 1) + 1)^2 - 4(-4(-3(4x - 4) - 1)^2 + 3(-3(4x - 4) - 1) + 1) + 5 between the vertical lines x = 0.8 and x = 0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2|(-1cos(2\u03c0((-2(2|(3|x - 3| + 3) + 2| + 2) - 3)/(-2(2|(3|x - 3| + 3) + 2| + 2) + 3)) + 1) + 2) - 1| - 2 and g(x) = (-1(2|(-1(-2|x + 3| - 1)^2 - 5(-2|x + 3| - 1) + 1) + 1| - 3))/(-2(2|(-1(-2|x + 3| - 1)^2 - 5(-2|x + 3| - 1) + 1) + 1| - 3) - 3) between the vertical lines x = -0.9 and x = -0.7. 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|(-1((3(-3|(-1x^2 + 4x + 2) - 2| + 1) + 3)/(1(-3|(-1x^2 + 4x + 2) - 2| + 1) - 2))^2 - 4((3(-3|(-1x^2 + 4x + 2) - 2| + 1) + 3)/(1(-3|(-1x^2 + 4x + 2) - 2| + 1) - 2)) + 4) - 2| + 2 and g(x) = (1(4((-2(5x^2 + 5) - 1)/(-3(5x^2 + 5) + 1))^2 + 2((-2(5x^2 + 5) - 1)/(-3(5x^2 + 5) + 1)) + 1) + 2)/(2(4((-2(5x^2 + 5) - 1)/(-3(5x^2 + 5) + 1))^2 + 2((-2(5x^2 + 5) - 1)/(-3(5x^2 + 5) + 1)) + 1) - 1) 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (2(-1|(3e^(1(5((1x - 3)/(2x - 1))^2 - 2((1x - 3)/(2x - 1)) + 4)) + 1) + 2|) - 3)/(-3(-1|(3e^(1(5((1x - 3)/(2x - 1))^2 - 2((1x - 3)/(2x - 1)) + 4)) + 1) + 2|) + 4), g(x) = -4(-2((-3((2x - 2)/(-2x - 2)) - 2)/(1((2x - 2)/(-2x - 2)) + 1))^2 - 2((-3((2x - 2)/(-2x - 2)) - 2)/(1((2x - 2)/(-2x - 2)) + 1)) + 3)^2 + 1(-2((-3((2x - 2)/(-2x - 2)) - 2)/(1((2x - 2)/(-2x - 2)) + 1))^2 - 2((-3((2x - 2)/(-2x - 2)) - 2)/(1((2x - 2)/(-2x - 2)) + 1)) + 3) + 2, x = 1.1, and x = 1.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2((2(-4(4(1x + 3) + 2)^2 - 3))/(-2(-4(4(1x + 3) + 2)^2 - 3) - 2)) - 5 and g(x) = -5(-4(-1|(2e^(1x)) - 2| + 1) + 1) - 4 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": "5.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2(-2(-3|((-2(-1|x + 2| + 2) - 2)/(-1(-1|x + 2| + 2) + 2))| + 1) - 3)^2 - 5(-2(-3|((-2(-1|x + 2| + 2) - 2)/(-1(-1|x + 2| + 2) + 2))| + 1) - 3) - 3, g(x) = -4(-4(-3cos(2\u03c0(5x - 3) - 3)) - 1)^2 - 5, 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": "27.7", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2(2|((-3(-5(2|x - 3| - 2) + 4) + 3)/(1(-5(2|x - 3| - 2) + 4))) - 3| + 3), g(x) = -1(-5(5(2|x + 2| - 3)) + 5), x = -3.0, 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": "49.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 5((-2(-3e^(1(-3(-1|x| + 2)^2 + 1(-1|x| + 2) + 2)) + 2) + 1)/(-2(-3e^(1(-3(-1|x| + 2)^2 + 1(-1|x| + 2) + 2)) + 2) - 3))^2 - 1((-2(-3e^(1(-3(-1|x| + 2)^2 + 1(-1|x| + 2) + 2)) + 2) + 1)/(-2(-3e^(1(-3(-1|x| + 2)^2 + 1(-1|x| + 2) + 2)) + 2) - 3)) + 5 and g(x) = -4(-3|(3e^(1(1x^2 - 3x))) - 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": "153.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (2(5((1((2(5x^2 + 3x - 3) - 2)/(-2(5x^2 + 3x - 3))) + 2)/(-1((2(5x^2 + 3x - 3) - 2)/(-2(5x^2 + 3x - 3))) - 3))^2 - 2) + 1)/(2(5((1((2(5x^2 + 3x - 3) - 2)/(-2(5x^2 + 3x - 3))) + 2)/(-1((2(5x^2 + 3x - 3) - 2)/(-2(5x^2 + 3x - 3))) - 3))^2 - 2) - 1), g(x) = (3(-2|(1|(-1x + 1) - 2| + 3) + 1| + 2) - 3)/(-1(-2|(1|(-1x + 1) - 2| + 3) + 1| + 2)), x = -1.2, 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": "7.4", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1(-3(-3cos(1\u03c0(3|(1x^2 - 5x) - 2| - 2) - 1) - 3) + 1), g(x) = 1(1(2(-3sin(2\u03c0x) + 1)^2 + 5(-3sin(2\u03c0x) + 1) - 3) + 3)^2 - 3(1(2(-3sin(2\u03c0x) + 1)^2 + 5(-3sin(2\u03c0x) + 1) - 3) + 3) - 4, 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": "0.9", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3(-2sin(2\u03c0(2|(1(-3|x - 2| + 3)^2 + 4(-3|x - 2| + 3) - 5) + 1| - 1) - 2) + 1)^2 + 3(-2sin(2\u03c0(2|(1(-3|x - 2| + 3)^2 + 4(-3|x - 2| + 3) - 5) + 1| - 1) - 2) + 1) - 3 and g(x) = 1cos(3\u03c0((3((-2(2|x - 3|))/(2(2|x - 3|) + 3)) - 3)/(2((-2(2|x - 3|))/(2(2|x - 3|) + 3)) + 2)) - 2) - 2 between the vertical lines x = 4.6 and x = 4.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2sin(3\u03c0(2|(-4(-3|((-1x - 2)/(-2x)) - 1| - 2) - 5) - 1| - 1) - 2) - 2, g(x) = -1|(-4(5(3x + 1)^2 - 5(3x + 1) - 1)^2 - 1(5(3x + 1)^2 - 5(3x + 1) - 1)) + 1| + 2, x = -0.0, and x = 0.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-1((-2(-4((-2((-3x + 2)/(2x - 1)) - 1)/(1((-3x + 2)/(2x - 1)) + 1)) + 1) - 1)/(1(-4((-2((-3x + 2)/(2x - 1)) - 1)/(1((-3x + 2)/(2x - 1)) + 1)) + 1))) - 3)/(-3((-2(-4((-2((-3x + 2)/(2x - 1)) - 1)/(1((-3x + 2)/(2x - 1)) + 1)) + 1) - 1)/(1(-4((-2((-3x + 2)/(2x - 1)) - 1)/(1((-3x + 2)/(2x - 1)) + 1)) + 1))) + 2), g(x) = (-3(4(2|(2e^(1x) - 2) + 1| - 2)^2 + 1(2|(2e^(1x) - 2) + 1| - 2) - 4) - 2)/(2(4(2|(2e^(1x) - 2) + 1| - 2)^2 + 1(2|(2e^(1x) - 2) + 1| - 2) - 4) + 2), 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": "0.9", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2|(1(-3cos(2\u03c0(-1|(-2x + 4) - 2| - 1) - 2) - 2)^2 + 5(-3cos(2\u03c0(-1|(-2x + 4) - 2| - 1) - 2) - 2) + 4) + 3| - 2, g(x) = 1(4((2(-3cos(3\u03c0x + 1) - 2) + 3)/(3(-3cos(3\u03c0x + 1) - 2) - 2))^2 - 4((2(-3cos(3\u03c0x + 1) - 2) + 3)/(3(-3cos(3\u03c0x + 1) - 2) - 2)) + 1)^2 - 5(4((2(-3cos(3\u03c0x + 1) - 2) + 3)/(3(-3cos(3\u03c0x + 1) - 2) - 2))^2 - 4((2(-3cos(3\u03c0x + 1) - 2) + 3)/(3(-3cos(3\u03c0x + 1) - 2) - 2)) + 1) - 4, x = 3.7, and x = 3.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2(-2sin(2\u03c0(-1(-5(2|x - 1| - 3)^2 - 4(2|x - 1| - 3) + 3) - 2) + 3) + 1)^2 - 3(-2sin(2\u03c0(-1(-5(2|x - 1| - 3)^2 - 4(2|x - 1| - 3) + 3) - 2) + 3) + 1) - 1, g(x) = (1(-5(5(-5x^2 + 3x - 1)^2 + 3(-5x^2 + 3x - 1) - 4)^2 - 5(5(-5x^2 + 3x - 1)^2 + 3(-5x^2 + 3x - 1) - 4) - 4) - 1)/(-3(-5(5(-5x^2 + 3x - 1)^2 + 3(-5x^2 + 3x - 1) - 4)^2 - 5(5(-5x^2 + 3x - 1)^2 + 3(-5x^2 + 3x - 1) - 4) - 4) + 1), 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": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1cos(2\u03c0(-1|(-3(-3|((1x)/(-2x - 3)) + 1| - 1) - 1) - 3| + 3) - 2) - 2, g(x) = -1|(-3sin(3\u03c0(-1|(1x^2 - 5x + 1) + 3| + 2) + 1) - 3) + 3| - 2, x = -1.5, and x = -1.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1e^(-1(3|(2(4(3x^2 - 3x - 5) + 1) + 4) - 3| - 3)) - 2 and g(x) = 3((3(5(2|x + 2| - 2)^2 + 5(2|x + 2| - 2) - 3) + 2)/(-2(5(2|x + 2| - 2)^2 + 5(2|x + 2| - 2) - 3) + 1)) + 4 between the vertical lines x = -1.9 and x = -0.6. Round 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) = -3(1|((2(-3|((-1x + 1)/(3x)) - 2| + 3))/(-2(-3|((-1x + 1)/(3x)) - 2| + 3) - 2)) - 1| - 3)^2 + 4(1|((2(-3|((-1x + 1)/(3x)) - 2| + 3))/(-2(-3|((-1x + 1)/(3x)) - 2| + 3) - 2)) - 1| - 3) + 5, g(x) = 4((-1((-2(-1x^2 + 3x - 4))/(-1(-1x^2 + 3x - 4) - 2)) - 2)/(-3((-2(-1x^2 + 3x - 4))/(-1(-1x^2 + 3x - 4) - 2)) - 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": "0.7", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 5(2|((-2(-3(3e^(1x) + 2)^2 - 4(3e^(1x) + 2) + 4) - 1)/(3(-3(3e^(1x) + 2)^2 - 4(3e^(1x) + 2) + 4) - 1)) - 3| + 1) - 3, g(x) = 5(5(1|(-1x^2 + 5x + 1)| - 1)^2 - 5(1|(-1x^2 + 5x + 1)| - 1) + 4)^2 - 5(5(1|(-1x^2 + 5x + 1)| - 1)^2 - 5(1|(-1x^2 + 5x + 1)| - 1) + 4) - 2, x = 4.8, and x = 5.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1|(-5(-1|(-3cos(2\u03c0(1|x - 3|) + 3)) + 3| - 2) + 5) + 1| + 2 and g(x) = (-2(1sin(1\u03c0(-1(1x - 4)^2 + 2(1x - 4) + 1) + 2) - 1) + 3)/(-3(1sin(1\u03c0(-1(1x - 4)^2 + 2(1x - 4) + 1) + 2) - 1) - 3) from x = 0.4 to x = 0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.9", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-1(-4((2(1e^(-1((-2x - 1)/(-2x - 3))) + 3) + 2)/(2(1e^(-1((-2x - 1)/(-2x - 3))) + 3))) - 1) + 1)/(-1(-4((2(1e^(-1((-2x - 1)/(-2x - 3))) + 3) + 2)/(2(1e^(-1((-2x - 1)/(-2x - 3))) + 3))) - 1) - 2) and g(x) = -1((-2(-3(5x^2 - 2x - 1)^2 + 1(5x^2 - 2x - 1) + 3) - 1)/(-1(-3(5x^2 - 2x - 1)^2 + 1(5x^2 - 2x - 1) + 3) - 3))^2 + 4((-2(-3(5x^2 - 2x - 1)^2 + 1(5x^2 - 2x - 1) + 3) - 1)/(-1(-3(5x^2 - 2x - 1)^2 + 1(5x^2 - 2x - 1) + 3) - 3)) + 5 between the vertical lines x = 0.4 and x = 0.9. 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) = (-2(-3cos(3\u03c0(2|(1((2x - 1)/(1x + 2))^2 + 1)|) - 3) + 3) + 3)/(-2(-3cos(3\u03c0(2|(1((2x - 1)/(1x + 2))^2 + 1)|) - 3) + 3) + 1) and g(x) = 2|(1(-1|((-2x + 1)/(1x + 1)) + 3| + 3)^2 - 3(-1|((-2x + 1)/(1x + 1)) + 3| + 3) + 1) + 3| from x = -2.3 to x = -2.2. 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(2e^(-1(1|(-2|x + 1|) + 2| - 2))) + 1)/(3(2e^(-1(1|(-2|x + 1|) + 2| - 2))) + 3)) - 3)/(1((3(2e^(-1(1|(-2|x + 1|) + 2| - 2))) + 1)/(3(2e^(-1(1|(-2|x + 1|) + 2| - 2))) + 3)) - 3) and g(x) = -2sin(1\u03c0(2|((-2((-1x + 3)/(-2x - 1)) + 2)/(2((-1x + 3)/(-2x - 1)) + 2)) - 1|) + 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2|((-1((-3(5(1|x| - 1) - 5) - 1)/(1(5(1|x| - 1) - 5) - 2)) + 3)/(-3((-3(5(1|x| - 1) - 5) - 1)/(1(5(1|x| - 1) - 5) - 2)) - 2)) - 1| + 3, g(x) = (2(1(-5((-3x + 3)/(1x + 1))^2 - 4) + 4) + 1)/(-3(1(-5((-3x + 3)/(1x + 1))^2 - 4) + 4) + 1), x = -1.6, 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": "9.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-1(-1(-1(1|(-4x - 1) + 2|) + 2)^2 + 3) + 3)/(2(-1(-1(1|(-4x - 1) + 2|) + 2)^2 + 3) - 1) and g(x) = (-2(-1(1(-5x)^2 + 4(-5x) + 2) - 4) - 2)/(3(-1(1(-5x)^2 + 4(-5x) + 2) - 4) + 1) from x = -1.1 to x = 1.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3|(2e^(2((-2(-1((-3x + 1)/(3x - 1)) + 4) + 3)/(-3(-1((-3x + 1)/(3x - 1)) + 4) - 1))))| + 3, g(x) = 2|(3(4(3sin(3\u03c0x)) + 4)^2 - 1(4(3sin(3\u03c0x)) + 4) - 3) - 2| - 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": "23.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3|(-2cos(2\u03c0((3(3|((3x - 1)/(1x + 2)) - 2| + 1) + 1)/(2(3|((3x - 1)/(1x + 2)) - 2| + 1) - 1)) + 3) + 1) - 2| + 2 and g(x) = -3cos(3\u03c0((2(4(4x + 3)^2 + 5(4x + 3) + 3))/(1(4(4x + 3)^2 + 5(4x + 3) + 3) + 2)) + 3) - 3 between the vertical lines x = 4.5 and x = 4.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.6", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-1(2|((2(-1((-2x - 1)/(-2x + 3))^2 + 2((-2x - 1)/(-2x + 3))) - 3)/(2(-1((-2x - 1)/(-2x + 3))^2 + 2((-2x - 1)/(-2x + 3))) - 1)) + 1| - 3) + 1)/(1(2|((2(-1((-2x - 1)/(-2x + 3))^2 + 2((-2x - 1)/(-2x + 3))) - 3)/(2(-1((-2x - 1)/(-2x + 3))^2 + 2((-2x - 1)/(-2x + 3))) - 1)) + 1| - 3) - 3) and g(x) = 2|((1(-2(2x + 1)^2 + 4(2x + 1) - 3) - 2)/(3(-2(2x + 1)^2 + 4(2x + 1) - 3))) - 1| + 2 between the vertical lines x = -2.2 and x = 0.1. 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) = (2(-3sin(2\u03c0((-2(-4(-5x^2 - 3x + 3) - 3))/(3(-4(-5x^2 - 3x + 3) - 3) - 2))) - 2) + 3)/(1(-3sin(2\u03c0((-2(-4(-5x^2 - 3x + 3) - 3))/(3(-4(-5x^2 - 3x + 3) - 3) - 2))) - 2)) and g(x) = 3(-1(1e^(1(-1x - 4)) + 1)^2 - 3(1e^(1(-1x - 4)) + 1) - 1) + 5 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": "1.9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1(3|(5(1((-2x + 1)/(1x - 2))) + 5) + 1| - 2) - 4 and g(x) = (1(1|((2(-3cos(1\u03c0x + 1) + 2) - 2)/(-1(-3cos(1\u03c0x + 1) + 2))) + 1| - 1))/(2(1|((2(-3cos(1\u03c0x + 1) + 2) - 2)/(-1(-3cos(1\u03c0x + 1) + 2))) + 1| - 1) + 1) from x = -3.9 to x = -3.4. 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) = -5(-3(1|(4((-2x + 1)/(-2x - 1))^2 + 3((-2x + 1)/(-2x - 1)) - 2) - 3| - 2)^2 + 5(1|(4((-2x + 1)/(-2x - 1))^2 + 3((-2x + 1)/(-2x - 1)) - 2) - 3| - 2))^2 - 4(-3(1|(4((-2x + 1)/(-2x - 1))^2 + 3((-2x + 1)/(-2x - 1)) - 2) - 3| - 2)^2 + 5(1|(4((-2x + 1)/(-2x - 1))^2 + 3((-2x + 1)/(-2x - 1)) - 2) - 3| - 2)) - 1, g(x) = (3(-3|(-2cos(1\u03c0(-2|x - 2| - 2) - 1) - 1) + 2| - 2) - 2)/(-2(-3|(-2cos(1\u03c0(-2|x - 2| - 2) - 1) - 1) + 2| - 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": "7.8", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3|(2|(-2(5(-3|x| + 1) + 1)^2 + 2(5(-3|x| + 1) + 1) + 5) - 2| - 2) + 3|, g(x) = 2|(-2|(1(-1cos(3\u03c0x + 2) + 3) + 4) + 1|) - 2| + 1, 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": "5.7", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-3(-2(2(-3sin(3\u03c0((1x + 1)/(3x)) - 2) - 2)^2 - 2(-3sin(3\u03c0((1x + 1)/(3x)) - 2) - 2) - 5)^2 - 1(2(-3sin(3\u03c0((1x + 1)/(3x)) - 2) - 2)^2 - 2(-3sin(3\u03c0((1x + 1)/(3x)) - 2) - 2) - 5) + 1) - 1)/(-1(-2(2(-3sin(3\u03c0((1x + 1)/(3x)) - 2) - 2)^2 - 2(-3sin(3\u03c0((1x + 1)/(3x)) - 2) - 2) - 5)^2 - 1(2(-3sin(3\u03c0((1x + 1)/(3x)) - 2) - 2)^2 - 2(-3sin(3\u03c0((1x + 1)/(3x)) - 2) - 2) - 5) + 1)), g(x) = (3(3(-3(-3cos(2\u03c0x) - 2)^2 + 1(-3cos(2\u03c0x) - 2) + 5)^2 - 4(-3(-3cos(2\u03c0x) - 2)^2 + 1(-3cos(2\u03c0x) - 2) + 5) + 2) - 3)/(-1(3(-3(-3cos(2\u03c0x) - 2)^2 + 1(-3cos(2\u03c0x) - 2) + 5)^2 - 4(-3(-3cos(2\u03c0x) - 2)^2 + 1(-3cos(2\u03c0x) - 2) + 5) + 2) + 2), x = 2.3, 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": "2.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1sin(1\u03c0(-3|((-2(2|(-2x^2 + 3x + 4) - 3|))/(-1(2|(-2x^2 + 3x + 4) - 3|) - 3)) - 3|) + 1) + 2 and g(x) = (-2((-1(-5((2x - 1)/(3x + 3)) + 3) - 2)/(-1(-5((2x - 1)/(3x + 3)) + 3) - 1)))/(-1((-1(-5((2x - 1)/(3x + 3)) + 3) - 2)/(-1(-5((2x - 1)/(3x + 3)) + 3) - 1)) - 1) between the vertical lines x = -0.9 and x = -0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-3(4(-2e^(1(1(-2|x + 3| + 3) + 5)))^2 + 5(-2e^(1(1(-2|x + 3| + 3) + 5)))) - 2)/(-2(4(-2e^(1(1(-2|x + 3| + 3) + 5)))^2 + 5(-2e^(1(1(-2|x + 3| + 3) + 5)))) - 3) and g(x) = 1|(1(2((2x + 2)/(1x + 3)) + 4) + 5) + 1| + 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": "Calculate the area enclosed between the functions f(x) = (-1(-2cos(1\u03c0(2|(1(-5x) + 3) - 2|) - 2) + 3) + 3)/(3(-2cos(1\u03c0(2|(1(-5x) + 3) - 2|) - 2) + 3) + 1) and g(x) = -4(-3|((3(2e^(-1x) - 2))/(-2(2e^(-1x) - 2) - 1)) + 1| + 2) + 2 from x = -3.8 to x = -3.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 3e^(1((-2(-1|((-1((1x + 1)/(3x + 2)) + 1)/(1((1x + 1)/(3x + 2)) + 3)) - 2| - 3) + 3)/(3(-1|((-1((1x + 1)/(3x + 2)) + 1)/(1((1x + 1)/(3x + 2)) + 3)) - 2| - 3) - 2))) + 3 and g(x) = -3(-1((-2((-1x)/(-1x - 1)) + 2)/(2((-1x)/(-1x - 1)) - 1))^2 + 4((-2((-1x)/(-1x - 1)) + 2)/(2((-1x)/(-1x - 1)) - 1)) - 5)^2 - 4(-1((-2((-1x)/(-1x - 1)) + 2)/(2((-1x)/(-1x - 1)) - 1))^2 + 4((-2((-1x)/(-1x - 1)) + 2)/(2((-1x)/(-1x - 1)) - 1)) - 5) + 5 from x = 1.7 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": "Determine the area of the region enclosed by the graphs of f(x) = 1|((3(5(-3(-1x^2 - 4x + 5) + 5)^2 + 4(-3(-1x^2 - 4x + 5) + 5) - 2) + 3)/(2(5(-3(-1x^2 - 4x + 5) + 5)^2 + 4(-3(-1x^2 - 4x + 5) + 5) - 2) - 1)) - 1| and g(x) = -1cos(1\u03c0(-1|(1(1x + 3)^2 + 2(1x + 3) + 2) + 2| + 2) - 3) - 1 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": "9.8", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-3((1(-1(3|(-2|x - 2| - 3) - 3| - 1)^2 - 1(3|(-2|x - 2| - 3) - 3| - 1) + 5) - 1)/(1(-1(3|(-2|x - 2| - 3) - 3| - 1)^2 - 1(3|(-2|x - 2| - 3) - 3| - 1) + 5))) - 3)/(-3((1(-1(3|(-2|x - 2| - 3) - 3| - 1)^2 - 1(3|(-2|x - 2| - 3) - 3| - 1) + 5) - 1)/(1(-1(3|(-2|x - 2| - 3) - 3| - 1)^2 - 1(3|(-2|x - 2| - 3) - 3| - 1) + 5))) + 2) and g(x) = 3(-1(1(-2x + 4) + 5)^2 - 4(1(-2x + 4) + 5) + 2)^2 + 4(-1(1(-2x + 4) + 5)^2 - 4(1(-2x + 4) + 5) + 2) + 4 between the vertical lines x = 4.1 and x = 4.3. 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": "Calculate the area enclosed between the functions f(x) = -1|(2(3|((-1(3|x - 2| - 1) - 2)/(-1(3|x - 2| - 1))) + 3| - 1) + 5) - 3| + 3 and g(x) = 4(-4(-3(3sin(2\u03c0x + 3) + 3) + 2)^2)^2 + 3(-4(-3(3sin(2\u03c0x + 3) + 3) + 2)^2) - 2 from x = 2.2 to x = 2.3000000000000003. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "68.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -5((-3(-1|(-2sin(3\u03c0(1x^2 + 1x - 3) + 3) + 3) - 1| + 1) - 1)/(-2(-1|(-2sin(3\u03c0(1x^2 + 1x - 3) + 3) + 3) - 1| + 1)))^2 - 2((-3(-1|(-2sin(3\u03c0(1x^2 + 1x - 3) + 3) + 3) - 1| + 1) - 1)/(-2(-1|(-2sin(3\u03c0(1x^2 + 1x - 3) + 3) + 3) - 1| + 1))) + 3 and g(x) = (3(-3e^(-1((-2((-2x + 3)/(2x - 1)) - 2)/(-1((-2x + 3)/(2x - 1)) - 2))) - 3) + 1)/(2(-3e^(-1((-2((-2x + 3)/(2x - 1)) - 2)/(-1((-2x + 3)/(2x - 1)) - 2))) - 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": "233.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -3(1|((1((-1(2cos(2\u03c0x + 2) + 3) + 3)/(3(2cos(2\u03c0x + 2) + 3) - 1)) - 1)/(-2((-1(2cos(2\u03c0x + 2) + 3) + 3)/(3(2cos(2\u03c0x + 2) + 3) - 1)) - 1)) + 1| - 3)^2 - 2, g(x) = (1((1(-1(-3sin(3\u03c0x - 2) + 2)^2 + 2(-3sin(3\u03c0x - 2) + 2) - 1) + 3)/(-3(-1(-3sin(3\u03c0x - 2) + 2)^2 + 2(-3sin(3\u03c0x - 2) + 2) - 1))))/(2((1(-1(-3sin(3\u03c0x - 2) + 2)^2 + 2(-3sin(3\u03c0x - 2) + 2) - 1) + 3)/(-3(-1(-3sin(3\u03c0x - 2) + 2)^2 + 2(-3sin(3\u03c0x - 2) + 2) - 1))) - 3), x = -2.1, and x = -1.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.7", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 4(2|(-1|((2(-3x - 4) - 1)/(-3(-3x - 4) + 2)) - 1| - 1) + 3| + 2) + 2, g(x) = (3(-2(5((2x)/(-1x + 2))^2 - 1((2x)/(-1x + 2))) + 4) + 1)/(-1(-2(5((2x)/(-1x + 2))^2 - 1((2x)/(-1x + 2))) + 4) + 3), x = -0.4, and x = 0.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "43.9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3(-3(1sin(1\u03c0(-2|(-1x + 5) - 1| - 1)) + 2) + 3)^2 + 2(-3(1sin(1\u03c0(-2|(-1x + 5) - 1| - 1)) + 2) + 3) - 5 and g(x) = -1e^(2(-3(-2|(-4x^2 + 5) - 1| + 1) - 4)) - 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": "28.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2(4((-2(2(2|x| - 3) - 5) - 1)/(1(2(2|x| - 3) - 5)))^2 + 1((-2(2(2|x| - 3) - 5) - 1)/(1(2(2|x| - 3) - 5))) - 1) - 1 and g(x) = -3e^(1(-1(3(-1x^2 + 4x + 4)^2 - 3(-1x^2 + 4x + 4) + 5)^2 + 3(3(-1x^2 + 4x + 4)^2 - 3(-1x^2 + 4x + 4) + 5) - 5)) - 2 between the vertical lines x = -2.6 and x = 2.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "103.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 5((2((-2(-4(2e^(-2x) - 2)^2 + 2(2e^(-2x) - 2) - 3) + 2)/(-1(-4(2e^(-2x) - 2)^2 + 2(2e^(-2x) - 2) - 3) - 3)) - 2)/(-1((-2(-4(2e^(-2x) - 2)^2 + 2(2e^(-2x) - 2) - 3) + 2)/(-1(-4(2e^(-2x) - 2)^2 + 2(2e^(-2x) - 2) - 3) - 3)) + 2)) + 4 and g(x) = (-2(3sin(1\u03c0(-1((-1x - 3)/(-2x + 3)) + 1) - 1) + 3) - 2)/(-2(3sin(1\u03c0(-1((-1x - 3)/(-2x + 3)) + 1) - 1) + 3) + 1) between the vertical lines x = 0.9 and x = 1.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.5", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-2(1|(1(-4((-1x + 3)/(1x)) - 4)^2 - 2(-4((-1x + 3)/(1x)) - 4) - 4) - 3|) - 2)/(1(1|(1(-4((-1x + 3)/(1x)) - 4)^2 - 2(-4((-1x + 3)/(1x)) - 4) - 4) - 3|) - 3), g(x) = (1(-4(-1|(-2|x + 3| + 3) + 3| + 3)^2 - 2(-1|(-2|x + 3| + 3) + 3| + 3) + 1) - 1)/(-1(-4(-1|(-2|x + 3| + 3) + 3| + 3)^2 - 2(-1|(-2|x + 3| + 3) + 3| + 3) + 1)), x = 1.3, 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": "5.4", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1|(-3sin(2\u03c0(2(-1(-2|x + 1| + 3)^2 - 3(-2|x + 1| + 3))^2 - 2(-1(-2|x + 1| + 3)^2 - 3(-2|x + 1| + 3)) + 5)) - 2) - 1| - 3, g(x) = -3(-1(-2|(-3sin(2\u03c0x - 3) + 3) - 1| + 1)^2 + 3(-2|(-3sin(2\u03c0x - 3) + 3) - 1| + 1) - 3)^2 + 3(-1(-2|(-3sin(2\u03c0x - 3) + 3) - 1| + 1)^2 + 3(-2|(-3sin(2\u03c0x - 3) + 3) - 1| + 1) - 3), 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": "21.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1(-3cos(3\u03c0(-2|(-2|((2x - 1)/(-1x - 3)) + 3| + 2) + 3|) - 3) + 3)^2 + 4(-3cos(3\u03c0(-2|(-2|((2x - 1)/(-1x - 3)) + 3| + 2) + 3|) - 3) + 3) - 4 and g(x) = 2e^(-1(-1(1|((-3x + 2)/(3x)) - 2|)^2 + 5(1|((-3x + 2)/(3x)) - 2|) + 4)) + 2 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": "2.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-1(1((-1(-2(2x^2 + 3x) - 3) + 2)/(2(-2(2x^2 + 3x) - 3) - 1))^2 - 1((-1(-2(2x^2 + 3x) - 3) + 2)/(2(-2(2x^2 + 3x) - 3) - 1)) - 3) + 2)/(-3(1((-1(-2(2x^2 + 3x) - 3) + 2)/(2(-2(2x^2 + 3x) - 3) - 1))^2 - 1((-1(-2(2x^2 + 3x) - 3) + 2)/(2(-2(2x^2 + 3x) - 3) - 1)) - 3)) and g(x) = (2(2|(2|((-1x)/(-2x + 3)) + 1| - 2)|))/(2(2|(2|((-1x)/(-2x + 3)) + 1| - 2)|)) from x = -1.0 to x = -0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1(4(-1|(4(-5x^2 - 2x + 1)^2 + 5(-5x^2 - 2x + 1) - 3) - 2| + 2)^2 - 3(-1|(4(-5x^2 - 2x + 1)^2 + 5(-5x^2 - 2x + 1) - 3) - 2| + 2) + 5) + 4, g(x) = 5(1|(1|(-2sin(3\u03c0x - 2) + 3) - 1| + 3) - 1| + 2)^2 - 5(1|(1|(-2sin(3\u03c0x - 2) + 3) - 1| + 3) - 1| + 2) + 5, x = -1.0, and x = -0.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "81.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3((-1(2sin(1\u03c0(3|(4x^2 - 2x - 4) + 3| - 3) + 2) + 3) + 3)/(1(2sin(1\u03c0(3|(4x^2 - 2x - 4) + 3| - 3) + 2) + 3) - 3)) + 4 and g(x) = -4((-3(-2|((1x - 3)/(-3x + 2)) + 2| + 2) - 2)/(-3(-2|((1x - 3)/(-3x + 2)) + 2| + 2) + 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": "45.9", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1|(-3|((3(1((-2x + 3)/(-2x + 1)) + 1) + 2)/(2(1((-2x + 3)/(-2x + 1)) + 1))) - 1| + 3)| - 3 and g(x) = (2(2(-2(1|x + 3| - 2) + 4)^2 - 5(-2(1|x + 3| - 2) + 4)) - 3)/(1(2(-2(1|x + 3| - 2) + 4)^2 - 5(-2(1|x + 3| - 2) + 4))) 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": "53.7", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1(4((-1(-1cos(3\u03c0(5x^2 + 4x - 1) - 1) + 1) + 3)/(-2(-1cos(3\u03c0(5x^2 + 4x - 1) - 1) + 1) + 3)) - 1) and g(x) = -2((-3((2(2x - 5) - 2)/(-2(2x - 5) - 3)))/(3((2(2x - 5) - 2)/(-2(2x - 5) - 3)) - 2)) - 2 between the vertical lines x = 2.7 and x = 2.8000000000000003. 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) = -1e^(1((2(-3|(4(-1x^2 + 2x + 1)^2 - 3(-1x^2 + 2x + 1) - 4) + 1| - 2) - 2)/(1(-3|(4(-1x^2 + 2x + 1)^2 - 3(-1x^2 + 2x + 1) - 4) + 1| - 2) - 3))) + 2, g(x) = 3cos(1\u03c0((-3(2(-3x - 1) - 2) + 2)/(2(2(-3x - 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3cos(1\u03c0(1|(4(-3|(2|x| + 3) - 2| - 3) + 1) - 2|) + 2) + 3, g(x) = 2|(1cos(3\u03c0((-1(2|x - 1| - 2) + 2)/(-1(2|x - 1| - 2) + 2)) - 2) - 1) - 2| - 1, 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-1(4(1|(2(-3x + 5)^2 + 5(-3x + 5) + 3)| - 3)^2 - 1(1|(2(-3x + 5)^2 + 5(-3x + 5) + 3)| - 3) - 3) - 1)/(2(4(1|(2(-3x + 5)^2 + 5(-3x + 5) + 3)| - 3)^2 - 1(1|(2(-3x + 5)^2 + 5(-3x + 5) + 3)| - 3) - 3)), g(x) = 3|(3(-3(3x + 5)^2 + 4(3x + 5)) + 5) - 2| - 2, 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3(1(-1(2((3x + 1)/(3x - 2))^2 - 3((3x + 1)/(3x - 2)) - 4) - 2)^2 - 1(-1(2((3x + 1)/(3x - 2))^2 - 3((3x + 1)/(3x - 2)) - 4) - 2) - 2) + 5, g(x) = -3sin(2\u03c0(-4(5((-1x - 3)/(-2x - 2)) - 4)^2 - 1(5((-1x - 3)/(-2x - 2)) - 4) + 2) - 1) + 2, x = -0.2, and x = -0.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -5((1(5(4(-1|x| + 1) + 2) + 4) - 3)/(2(5(4(-1|x| + 1) + 2) + 4))) + 2 and g(x) = (-2((3(1(2|x| + 3) + 3) - 3)/(1(1(2|x| + 3) + 3) + 2)))/(-3((3(1(2|x| + 3) + 3) - 3)/(1(1(2|x| + 3) + 3) + 2))) from x = -1.4 to x = 1.4. 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) = (-2(-2(2(5(2|x - 3| + 2) - 4)^2 + 1(5(2|x - 3| + 2) - 4)) + 4) - 1)/(-1(-2(2(5(2|x - 3| + 2) - 4)^2 + 1(5(2|x - 3| + 2) - 4)) + 4) + 2) and g(x) = (-2(-5(-3(-4x^2 - 5x + 5)^2 + 4(-4x^2 - 5x + 5) + 5) + 3) + 1)/(-2(-5(-3(-4x^2 - 5x + 5)^2 + 4(-4x^2 - 5x + 5) + 5) + 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": "2.4", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1(-1(-3((-2(2|x - 1|))/(-1(2|x - 1|) + 3)) - 5)^2 + 4(-3((-2(2|x - 1|))/(-1(2|x - 1|) + 3)) - 5)) - 4 and g(x) = -3((-2(2|(-2sin(1\u03c0x) + 3) - 3| + 2) + 3)/(-2(2|(-2sin(1\u03c0x) + 3) - 3| + 2) - 1))^2 - 2((-2(2|(-2sin(1\u03c0x) + 3) - 3| + 2) + 3)/(-2(2|(-2sin(1\u03c0x) + 3) - 3| + 2) - 1)) between the vertical lines x = 1.7 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": "Calculate the area enclosed between the functions f(x) = (3(2(4(-2|(-4x - 3) + 2| + 2)^2 + 4(-2|(-4x - 3) + 2| + 2) - 5)^2 + 2(4(-2|(-4x - 3) + 2| + 2)^2 + 4(-2|(-4x - 3) + 2| + 2) - 5)) + 2)/(-2(2(4(-2|(-4x - 3) + 2| + 2)^2 + 4(-2|(-4x - 3) + 2| + 2) - 5)^2 + 2(4(-2|(-4x - 3) + 2| + 2)^2 + 4(-2|(-4x - 3) + 2| + 2) - 5)) + 3) and g(x) = -3|(-4(3(-3|x + 1|) + 1) - 4) + 1| + 2 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1((-3(-2|(-3|(1x^2 - 4x + 3) - 2| + 3) - 3| + 2) - 1)/(-1(-2|(-3|(1x^2 - 4x + 3) - 2| + 3) - 3| + 2))) + 2 and g(x) = 5((2(3|((-1x + 3)/(2x)) - 3| + 3) + 1)/(2(3|((-1x + 3)/(2x)) - 3| + 3) + 1))^2 + 4((2(3|((-1x + 3)/(2x)) - 3| + 3) + 1)/(2(3|((-1x + 3)/(2x)) - 3| + 3) + 1)) + 4 between the vertical lines x = 3.6 and x = 3.8. 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) = -1(-3|(1|(-1(2e^(2x) + 1) + 2) - 1| - 2) - 2| + 2)^2 + 5(-3|(1|(-1(2e^(2x) + 1) + 2) - 1| - 2) - 2| + 2) - 2 and g(x) = 4(1e^(-1(1|(-1x + 1) - 1|)) - 1)^2 - 4(1e^(-1(1|(-1x + 1) - 1|)) - 1) - 1 from x = 0.3 to x = 0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -5(1(3(1|(2x^2 + 2x + 3) - 3| - 1) + 4)^2 - 2(3(1|(2x^2 + 2x + 3) - 3| - 1) + 4) - 1) + 1 and g(x) = 3|((3((-2(1x^2 - 4) - 2)/(-3(1x^2 - 4) - 1)) + 3)/(-3((-2(1x^2 - 4) - 2)/(-3(1x^2 - 4) - 1)) - 3)) + 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": "1.6", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-1(3|(-2cos(3\u03c0(1|(4x^2 + 1x - 5) - 3| - 1))) - 1| - 1) - 3)/(2(3|(-2cos(3\u03c0(1|(4x^2 + 1x - 5) - 3| - 1))) - 1| - 1) + 3), g(x) = (-2(3|(5(-4x + 4)^2 + 1(-4x + 4) - 3)| - 2) - 1)/(-1(3|(5(-4x + 4)^2 + 1(-4x + 4) - 3)| - 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": "1.5", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1|(2(2|(4(-5x + 5) - 2) - 2| - 3)^2 - 5(2|(4(-5x + 5) - 2) - 2| - 3) + 1) + 1| - 1, g(x) = 1(-1(-3|(2|x|)| - 1) - 1)^2 + 2(-1(-3|(2|x|)| - 1) - 1) - 3, 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": "3.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-1(-1|(-3sin(2\u03c0(4(-4x^2 - 3x - 4) + 3) - 3) + 1)| - 2) - 2)/(3(-1|(-3sin(2\u03c0(4(-4x^2 - 3x - 4) + 3) - 3) + 1)| - 2)), g(x) = -3|(3|(-4(-1x^2 - 3x + 3) - 2) + 3| + 1) - 1| + 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": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2|(2(3cos(2\u03c0(4((-2x + 3)/(-2x - 2))^2 + 4)) - 2)^2 - 3(3cos(2\u03c0(4((-2x + 3)/(-2x - 2))^2 + 4)) - 2) - 4) + 2| - 2 and g(x) = 1(2sin(2\u03c0(3(-1x + 2) + 2) + 1) + 1) + 3 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": "4.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 4(3|(-4((-1(-2|x - 1| + 3) + 3)/(-3(-2|x - 1| + 3) - 2))^2 + 4((-1(-2|x - 1| + 3) + 3)/(-3(-2|x - 1| + 3) - 2))) + 1| - 3)^2 + 1(3|(-4((-1(-2|x - 1| + 3) + 3)/(-3(-2|x - 1| + 3) - 2))^2 + 4((-1(-2|x - 1| + 3) + 3)/(-3(-2|x - 1| + 3) - 2))) + 1| - 3) + 1 and g(x) = (3(5(-2(1x^2 - 2x - 5) + 1)^2 - 3(-2(1x^2 - 2x - 5) + 1) + 2) + 1)/(3(5(-2(1x^2 - 2x - 5) + 1)^2 - 3(-2(1x^2 - 2x - 5) + 1) + 2) + 3) between the vertical lines x = 0.0 and x = 0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-2(-1|(2(-1|(-2x + 2)|) + 2) + 2|))/(-3(-1|(2(-1|(-2x + 2)|) + 2) + 2|) - 2) and g(x) = 1e^(1(1(1(-5x^2 + 2) + 5) - 4)) + 3 between the vertical lines x = 1.8 and x = 2.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9.9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 4(-1|((3(3((-2x)/(2x + 1))^2 - 1((-2x)/(2x + 1)) + 3))/(-3(3((-2x)/(2x + 1))^2 - 1((-2x)/(2x + 1)) + 3) - 1)) + 3|) + 5 and g(x) = 2|(-5(-1cos(2\u03c0(-1x + 2) + 2) + 3) - 2) - 1| - 1 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": "229.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3|(-1(-1|(3cos(2\u03c0(-1x) - 3) + 1) + 3|)^2 - 1(-1|(3cos(2\u03c0(-1x) - 3) + 1) + 3|) + 1) + 3| - 1 and g(x) = 1((-3((1((3x - 2)/(1x + 1)) + 3)/(-3((3x - 2)/(1x + 1)) - 1)) - 3)/(-1((1((3x - 2)/(1x + 1)) + 3)/(-3((3x - 2)/(1x + 1)) - 1)) + 3)) - 4 between the vertical lines x = -2.1 and x = -1.8. 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) = -1e^(-2(3(4(3((-1x + 3)/(3x + 1))^2 - 4((-1x + 3)/(3x + 1)) + 3)^2 + 3(3((-1x + 3)/(3x + 1))^2 - 4((-1x + 3)/(3x + 1)) + 3) - 1) + 5)) and g(x) = -3|(1cos(1\u03c0(-4(-1x^2 - 5x - 3) - 4) - 3))| + 3 from x = 1.7 to x = 1.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1|((-2(-2e^(-1((-3((1x - 3)/(2x - 3)) + 1)/(-2((1x - 3)/(2x - 3)) - 2)))) - 3)/(2(-2e^(-1((-3((1x - 3)/(2x - 3)) + 1)/(-2((1x - 3)/(2x - 3)) - 2)))) + 1)) + 2| + 2, g(x) = -1|(1sin(2\u03c0(-2|(-1|x + 3| + 1) + 1| + 2) - 2) - 3) + 2| + 1, x = -3.2, and x = -2.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 4((-1(-2(5(-1x^2 + 3x - 3)^2 - 5(-1x^2 + 3x - 3) + 2) + 1) - 3)/(-3(-2(5(-1x^2 + 3x - 3)^2 - 5(-1x^2 + 3x - 3) + 2) + 1) + 1)) - 2, g(x) = (2(2|(-3|(1x^2 + 3x - 3) - 2| - 3) - 1| - 3) - 1)/(-2(2|(-3|(1x^2 + 3x - 3) - 2| - 3) - 1| - 3) - 2), 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": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1|(1sin(3\u03c0(3(-2(-4x + 1)^2 - 3(-4x + 1) - 1)^2 + 3(-2(-4x + 1)^2 - 3(-4x + 1) - 1) + 5) + 1) - 1) - 3| + 1, g(x) = (-1(3cos(1\u03c0((1(-1x^2 - 1) - 2)/(2(-1x^2 - 1) + 3)) - 2)))/(3(3cos(1\u03c0((1(-1x^2 - 1) - 2)/(2(-1x^2 - 1) + 3)) - 2)) + 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": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 3((-1(-3(1|((-3x + 3)/(2x + 2)) + 3| + 2)))/(2(-3(1|((-3x + 3)/(2x + 2)) + 3| + 2)) - 3)) + 5 and g(x) = (1((1(-3(-3|x - 1| + 3)^2 + 4(-3|x - 1| + 3) + 5) + 1)/(1(-3(-3|x - 1| + 3)^2 + 4(-3|x - 1| + 3) + 5))) + 3)/(-3((1(-3(-3|x - 1| + 3)^2 + 4(-3|x - 1| + 3) + 5) + 1)/(1(-3(-3|x - 1| + 3)^2 + 4(-3|x - 1| + 3) + 5))) - 2) from x = -0.3 to x = 0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -4(-1|(2cos(2\u03c0(-5(-2|x + 3| + 1) - 5) - 2)) - 2| - 1)^2 + 3 and g(x) = -1|(3(-2|((1x - 3)/(-2x)) - 3| - 1) - 2) + 1| + 2 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": "3.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -4(-3((2(-2(-1cos(3\u03c0x - 2)) + 3) - 3)/(1(-2(-1cos(3\u03c0x - 2)) + 3) - 2)) + 5) - 3 and g(x) = -5((2(2|(3x + 4) - 2| + 2) - 1)/(1(2|(3x + 4) - 2| + 2) - 2)) - 2 from x = 4.5 to x = 4.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -5(1(-1cos(3\u03c0(2(-1x^2 - 1x - 4)^2 - 5(-1x^2 - 1x - 4) + 1)) - 2) - 1)^2 - 3(1(-1cos(3\u03c0(2(-1x^2 - 1x - 4)^2 - 5(-1x^2 - 1x - 4) + 1)) - 2) - 1) + 1 and g(x) = -1(1(-3e^(-2((-1x - 2)/(3x + 2))))^2 - 1(-3e^(-2((-1x - 2)/(3x + 2)))) + 1)^2 - 1(1(-3e^(-2((-1x - 2)/(3x + 2))))^2 - 1(-3e^(-2((-1x - 2)/(3x + 2)))) + 1) + 3 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": "1.7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 3cos(1\u03c0(-2|((2(-5((2x)/(3x + 2)) + 3) - 3)/(-3(-5((2x)/(3x + 2)) + 3) + 2))| + 3) - 3) - 2 and g(x) = -2|(-3|(-3(-2e^(-2x))^2 + 5(-2e^(-2x)) + 2) + 1| + 2) + 3| - 2 from x = 1.1 to x = 1.2000000000000002. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (2(3(-3((2((-2x)/(2x + 3)) + 3)/(1((-2x)/(2x + 3)) + 2))^2 + 4((2((-2x)/(2x + 3)) + 3)/(1((-2x)/(2x + 3)) + 2)) - 2)^2 - 1(-3((2((-2x)/(2x + 3)) + 3)/(1((-2x)/(2x + 3)) + 2))^2 + 4((2((-2x)/(2x + 3)) + 3)/(1((-2x)/(2x + 3)) + 2)) - 2) - 1) - 3)/(-3(3(-3((2((-2x)/(2x + 3)) + 3)/(1((-2x)/(2x + 3)) + 2))^2 + 4((2((-2x)/(2x + 3)) + 3)/(1((-2x)/(2x + 3)) + 2)) - 2)^2 - 1(-3((2((-2x)/(2x + 3)) + 3)/(1((-2x)/(2x + 3)) + 2))^2 + 4((2((-2x)/(2x + 3)) + 3)/(1((-2x)/(2x + 3)) + 2)) - 2) - 1) - 2) and g(x) = 1(3((-2(-2x^2 - 1))/(3(-2x^2 - 1) + 2))^2 + 3((-2(-2x^2 - 1))/(3(-2x^2 - 1) + 2)) - 3)^2 - 5(3((-2(-2x^2 - 1))/(3(-2x^2 - 1) + 2))^2 + 3((-2(-2x^2 - 1))/(3(-2x^2 - 1) + 2)) - 3) - 2 between the vertical lines x = -0.3 and x = 0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-1((-2(-1|(-3((2x - 3)/(2x)) - 2) - 1| + 2) + 1)/(1(-1|(-3((2x - 3)/(2x)) - 2) - 1| + 2) - 2)) + 2)/(2((-2(-1|(-3((2x - 3)/(2x)) - 2) - 1| + 2) + 1)/(1(-1|(-3((2x - 3)/(2x)) - 2) - 1| + 2) - 2)) + 1) and g(x) = -3|(1(-5(5x + 3)^2 - 1(5x + 3) - 5) + 5) + 2| + 2 between the vertical lines x = -0.5 and x = -0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (1(3(2|((1(1x^2 + 4x) + 2)/(-2(1x^2 + 4x))) + 1| - 3)^2 + 1(2|((1(1x^2 + 4x) + 2)/(-2(1x^2 + 4x))) + 1| - 3) + 4))/(2(3(2|((1(1x^2 + 4x) + 2)/(-2(1x^2 + 4x))) + 1| - 3)^2 + 1(2|((1(1x^2 + 4x) + 2)/(-2(1x^2 + 4x))) + 1| - 3) + 4) - 3) and g(x) = (-1(1(3sin(1\u03c0((2x + 3)/(2x - 1)) + 3) + 1) - 4) + 3)/(-2(1(3sin(1\u03c0((2x + 3)/(2x - 1)) + 3) + 1) - 4) + 3) from x = -3.8 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) = (2(-2(5(1(-5x + 2) - 3) + 3)^2 + 4(5(1(-5x + 2) - 3) + 3) + 2))/(2(-2(5(1(-5x + 2) - 3) + 3)^2 + 4(5(1(-5x + 2) - 3) + 3) + 2) - 1) and g(x) = (-1(-2e^(-2(1|((-1x - 3)/(2x)) + 1|)) + 2) + 2)/(2(-2e^(-2(1|((-1x - 3)/(2x)) + 1|)) + 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 3(-2|(3sin(3\u03c0(1(-4x - 2) - 2) + 2) - 1)|)^2 + 4(-2|(3sin(3\u03c0(1(-4x - 2) - 2) + 2) - 1)|) and g(x) = (1((-3(-1((-2x + 2)/(1x))^2 - 1((-2x + 2)/(1x)) + 4) + 2)/(-2(-1((-2x + 2)/(1x))^2 - 1((-2x + 2)/(1x)) + 4) + 3)) - 1)/(-3((-3(-1((-2x + 2)/(1x))^2 - 1((-2x + 2)/(1x)) + 4) + 2)/(-2(-1((-2x + 2)/(1x))^2 - 1((-2x + 2)/(1x)) + 4) + 3)) - 2) 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": "3.8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 3(-2|(-2cos(2\u03c0(5(2|x - 3|)^2 + 4(2|x - 3|) + 2) + 3) + 3) - 3| + 3)^2 - 2(-2|(-2cos(2\u03c0(5(2|x - 3|)^2 + 4(2|x - 3|) + 2) + 3) + 3) - 3| + 3) - 4 and g(x) = (2(2|(-2e^(1((-1x - 2)/(1x + 3))) + 3) - 1| + 1) + 2)/(2(2|(-2e^(1((-1x - 2)/(1x + 3))) + 3) - 1| + 1) + 2) from x = -3.8 to x = -3.6999999999999997. 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(-5(-5(-1|x - 3| + 3)) + 1) - 2)/(-3(-5(-5(-1|x - 3| + 3)) + 1) + 2)) + 2| - 2 and g(x) = (-1((-1(2e^(-1(-4x + 1)) + 3) + 1)/(-2(2e^(-1(-4x + 1)) + 3) + 3)))/(1((-1(2e^(-1(-4x + 1)) + 3) + 1)/(-2(2e^(-1(-4x + 1)) + 3) + 3)) - 2) between the vertical lines x = -0.0 and x = 0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 3|(2|(1|((-2(3cos(1\u03c0x + 2) + 2) - 1)/(-2(3cos(1\u03c0x + 2) + 2) - 2))|) + 2| + 1) - 2| - 2 and g(x) = 2|(2|((-3(3e^(-2x) + 1) + 2)/(2(3e^(-2x) + 1) + 2)) - 1| + 1) - 1| - 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 4((-3(1|(1|((-3x - 2)/(-1x + 2)) + 3| + 2) - 3| + 1) + 3)/(-3(1|(1|((-3x - 2)/(-1x + 2)) + 3| + 2) - 3| + 1))) + 2 and g(x) = (-3(-2|(-5(1sin(1\u03c0x - 1) + 3)^2 - 4(1sin(1\u03c0x - 1) + 3))| - 1) - 1)/(-1(-2|(-5(1sin(1\u03c0x - 1) + 3)^2 - 4(1sin(1\u03c0x - 1) + 3))| - 1)) 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2cos(3\u03c0(-5(4(-3((-3x - 1)/(3x + 3)) - 2) - 4) - 3) - 2) + 3 and g(x) = -2((-2((2(-2x^2 + 2x - 1) + 3)/(2(-2x^2 + 2x - 1) + 1)) - 3)/(1((2(-2x^2 + 2x - 1) + 3)/(2(-2x^2 + 2x - 1) + 1)) + 3))^2 - 5((-2((2(-2x^2 + 2x - 1) + 3)/(2(-2x^2 + 2x - 1) + 1)) - 3)/(1((2(-2x^2 + 2x - 1) + 3)/(2(-2x^2 + 2x - 1) + 1)) + 3)) + 4 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) = (1((-2(1|((2(-1x + 4) - 1)/(-2(-1x + 4) - 2)) + 1|) - 3)/(3(1|((2(-1x + 4) - 1)/(-2(-1x + 4) - 2)) + 1|) + 3)) - 2)/(2((-2(1|((2(-1x + 4) - 1)/(-2(-1x + 4) - 2)) + 1|) - 3)/(3(1|((2(-1x + 4) - 1)/(-2(-1x + 4) - 2)) + 1|) + 3)) + 3), g(x) = -3(4(-5(-4x + 5)^2 - 2(-4x + 5) + 5)^2 + 4(-5(-4x + 5)^2 - 2(-4x + 5) + 5)) + 4, 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": "107.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3(3sin(1\u03c0(-3(1((-2x)/(-1x + 2))^2 + 1((-2x)/(-1x + 2)) - 1) - 2) - 1) - 3)^2 - 5(3sin(1\u03c0(-3(1((-2x)/(-1x + 2))^2 + 1((-2x)/(-1x + 2)) - 1) - 2) - 1) - 3) - 3 and g(x) = (-3(-3((-2((-1x + 1)/(-2x)) + 1)/(1((-1x + 1)/(-2x)) - 3))^2 + 4((-2((-1x + 1)/(-2x)) + 1)/(1((-1x + 1)/(-2x)) - 3)) + 4))/(2(-3((-2((-1x + 1)/(-2x)) + 1)/(1((-1x + 1)/(-2x)) - 3))^2 + 4((-2((-1x + 1)/(-2x)) + 1)/(1((-1x + 1)/(-2x)) - 3)) + 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (2((1((-1(-3|(-3|x - 2| - 2) + 3| + 1) - 1)/(1(-3|(-3|x - 2| - 2) + 3| + 1) + 3)) + 2)/(-1((-1(-3|(-3|x - 2| - 2) + 3| + 1) - 1)/(1(-3|(-3|x - 2| - 2) + 3| + 1) + 3)))) + 1)/(-1((1((-1(-3|(-3|x - 2| - 2) + 3| + 1) - 1)/(1(-3|(-3|x - 2| - 2) + 3| + 1) + 3)) + 2)/(-1((-1(-3|(-3|x - 2| - 2) + 3| + 1) - 1)/(1(-3|(-3|x - 2| - 2) + 3| + 1) + 3))))), g(x) = 1sin(2\u03c0(-2|(-2((-1x - 2)/(2x + 3))^2 + 4((-1x - 2)/(2x + 3)) + 1) - 3| + 3)), x = 1.2, 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": "4.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1((2(-5(2(3|x + 2| + 2) - 5)^2 - 5(2(3|x + 2| + 2) - 5) - 1))/(-3(-5(2(3|x + 2| + 2) - 5)^2 - 5(2(3|x + 2| + 2) - 5) - 1) - 1)) - 4, g(x) = (1(5(-3|(2sin(2\u03c0x - 3) - 1) + 3| + 2) - 1) - 2)/(1(5(-3|(2sin(2\u03c0x - 3) - 1) + 3| + 2) - 1) + 3), x = 1.4, and x = 2.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2|(1((3(-1|((1x - 3)/(2x + 1)) + 2| - 2) - 2)/(3(-1|((1x - 3)/(2x + 1)) + 2| - 2) - 1))^2 - 3((3(-1|((1x - 3)/(2x + 1)) + 2| - 2) - 2)/(3(-1|((1x - 3)/(2x + 1)) + 2| - 2) - 1)) - 2) - 2| + 1 and g(x) = -3((-2(2|(3|x + 3| - 3) - 3| - 1))/(3(2|(3|x + 3| - 3) - 3| - 1) + 2)) - 5 from x = -5.0 to x = -1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "83.4", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1((1(2e^(-1(5((-2x + 3)/(-2x + 3))^2 + 5((-2x + 3)/(-2x + 3)) - 5)) + 3) + 3)/(-3(2e^(-1(5((-2x + 3)/(-2x + 3))^2 + 5((-2x + 3)/(-2x + 3)) - 5)) + 3) - 2)) - 3 and g(x) = -3(-1sin(2\u03c0(-4(2|x - 1| - 3)^2 + 3(2|x - 1| - 3) + 1) + 1) - 2)^2 - 4(-1sin(2\u03c0(-4(2|x - 1| - 3)^2 + 3(2|x - 1| - 3) + 1) + 1) - 2) + 2 between the vertical lines x = -0.1 and x = 0.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1((-2(1(-3sin(1\u03c0(-2x + 1) - 2))^2 - 5(-3sin(1\u03c0(-2x + 1) - 2))) - 2)/(-3(1(-3sin(1\u03c0(-2x + 1) - 2))^2 - 5(-3sin(1\u03c0(-2x + 1) - 2))) - 1)) + 1, g(x) = -1(1|(-2|(-1x^2 - 1x + 2) + 1| - 3) + 3|)^2 - 2(1|(-2|(-1x^2 - 1x + 2) + 1| - 3) + 3|) - 1, x = -2.3, 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": "117.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1|(4(2|(4(1|x - 2| + 1) - 2) - 1|)^2 + 3(2|(4(1|x - 2| + 1) - 2) - 1|) + 2) - 1|, g(x) = -3(-4(-1(4x - 1) - 4) + 4) + 4, x = 1.6, and x = 2.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -5(1|(-1((1(4x^2 + 5x + 5) - 1)/(3(4x^2 + 5x + 5) - 2)) + 3) + 1| - 2)^2 - 1(1|(-1((1(4x^2 + 5x + 5) - 1)/(3(4x^2 + 5x + 5) - 2)) + 3) + 1| - 2) + 1 and g(x) = (3((-1(-5(1x^2 + 2x + 1)^2 + 1) - 2)/(-3(-5(1x^2 + 2x + 1)^2 + 1) + 4)) - 1)/(-1((-1(-5(1x^2 + 2x + 1)^2 + 1) - 2)/(-3(-5(1x^2 + 2x + 1)^2 + 1) + 4))) from x = -1.8 to x = -0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17.5", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3|(-1|(4(-2((3x - 1)/(3x - 1))^2 - 2((3x - 1)/(3x - 1)) + 3) - 5) + 2| + 3) + 1| - 1, g(x) = 1|(1(-1(3|x| - 1)^2 - 5(3|x| - 1) - 4)^2 + 5(-1(3|x| - 1)^2 - 5(3|x| - 1) - 4)) - 1| - 1, 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": "4.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3e^(-2(4((3(3(2x + 2)^2 - 3(2x + 2) - 2) - 3)/(-2(3(2x + 2)^2 - 3(2x + 2) - 2) + 1))^2 + 2)) + 3, g(x) = (-2((-2(-2|(3|x + 1| + 3) - 2| + 3) - 2)/(2(-2|(3|x + 1| + 3) - 2| + 3) - 3)) - 3)/(-2((-2(-2|(3|x + 1| + 3) - 2| + 3) - 2)/(2(-2|(3|x + 1| + 3) - 2| + 3) - 3)) + 1), 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1(-1(2(3((2x + 1)/(2x)) - 5) + 3))^2 + 3(-1(2(3((2x + 1)/(2x)) - 5) + 3)) - 3 and g(x) = -5(3|(-1(3x)) - 3| - 1)^2 - 5(3|(-1(3x)) - 3| - 1) + 5 from x = -0.7 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": "Determine the area of the region enclosed by the graphs of f(x) = -3|((3(-4(-3|(-5x^2 + 5x + 3) - 3| + 3) + 4))/(-2(-4(-3|(-5x^2 + 5x + 3) - 3| + 3) + 4) + 3)) + 1| - 1 and g(x) = (-3(-2(1sin(1\u03c0(-1x - 1) - 1) + 3) - 1) - 3)/(3(-2(1sin(1\u03c0(-1x - 1) - 1) + 3) - 1) + 3) 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": "10.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2sin(1\u03c0(1((-3(-3(-3x - 2) - 5) - 3)/(2(-3(-3x - 2) - 5) + 1))^2 + 2((-3(-3(-3x - 2) - 5) - 3)/(2(-3(-3x - 2) - 5) + 1)) + 1) - 3) + 1 and g(x) = -2((-2(-2((1x - 3)/(3x - 1))) - 1)/(-3(-2((1x - 3)/(3x - 1))) + 2))^2 + 3((-2(-2((1x - 3)/(3x - 1))) - 1)/(-3(-2((1x - 3)/(3x - 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -3e^(-1(5((-1(2|(1x + 3) + 2| - 2) - 1)/(1(2|(1x + 3) + 2| - 2) + 3))^2 - 4((-1(2|(1x + 3) + 2| - 2) - 1)/(1(2|(1x + 3) + 2| - 2) + 3)) - 5)) + 2, g(x) = 2|(-3cos(3\u03c0((2(1x^2 + 4) + 3)/(-3(1x^2 + 4) - 1)) - 3))| - 1, x = -1.0, and x = 1.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-3(-1|((-2(-2sin(2\u03c0(4x^2 + 4x + 1) - 1) - 2) - 2)/(1(-2sin(2\u03c0(4x^2 + 4x + 1) - 1) - 2))) - 1| + 1))/(-3(-1|((-2(-2sin(2\u03c0(4x^2 + 4x + 1) - 1) - 2) - 2)/(1(-2sin(2\u03c0(4x^2 + 4x + 1) - 1) - 2))) - 1| + 1) + 4), g(x) = 1(2(5((-3x + 3)/(1x))^2 - 1((-3x + 3)/(1x))) - 5) + 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2|(-5(2sin(2\u03c0(1((2x - 3)/(-3x + 2)) - 2)) - 1) + 2) + 2| + 3, g(x) = 2|(-3cos(1\u03c0(3|((1x + 1)/(-1x + 2)) + 1| - 3)) + 1) - 3| + 1, 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": "1.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1(-5((1(-3|(-5x + 2) - 3|) - 1)/(2(-3|(-5x + 2) - 3|) - 3)) + 2) + 5 and g(x) = 4(1|((2(2e^(-1x) + 3) - 2)/(3(2e^(-1x) + 3) + 1))|) + 3 from x = -1.9 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(-1((1x + 3)/(3x - 2))^2 + 1((1x + 3)/(3x - 2)) + 3)^2 + 1(-1((1x + 3)/(3x - 2))^2 + 1((1x + 3)/(3x - 2)) + 3) - 1)^2 + 1(-5(-1((1x + 3)/(3x - 2))^2 + 1((1x + 3)/(3x - 2)) + 3)^2 + 1(-1((1x + 3)/(3x - 2))^2 + 1((1x + 3)/(3x - 2)) + 3) - 1) - 5))/(-1(3(-5(-1((1x + 3)/(3x - 2))^2 + 1((1x + 3)/(3x - 2)) + 3)^2 + 1(-1((1x + 3)/(3x - 2))^2 + 1((1x + 3)/(3x - 2)) + 3) - 1)^2 + 1(-5(-1((1x + 3)/(3x - 2))^2 + 1((1x + 3)/(3x - 2)) + 3)^2 + 1(-1((1x + 3)/(3x - 2))^2 + 1((1x + 3)/(3x - 2)) + 3) - 1) - 5) + 2) and g(x) = -1(3|(-1e^(-1(3x^2 - 1x - 3))) - 2| + 3) + 1 between the vertical lines x = -0.2 and x = 1.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "63.9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2sin(2\u03c0(-1|(-5(2|(-1x^2 - 5x - 2) - 1| - 3) - 1) + 2| - 3) - 3) + 1 and g(x) = -1|((1((-3(5x + 4) - 2)/(2(5x + 4) - 1)) + 1)/(-2((-3(5x + 4) - 2)/(2(5x + 4) - 1)) + 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -5(1|((2((1(4x) + 2)/(2(4x) - 1)) + 2)/(-3((1(4x) + 2)/(2(4x) - 1)))) - 1| - 3), g(x) = (-3(-1cos(2\u03c0(-1|((1x - 2)/(1x + 1)) - 3| + 1) - 1) + 3) + 2)/(-3(-1cos(2\u03c0(-1|((1x - 2)/(1x + 1)) - 3| + 1) - 1) + 3) + 1), x = -0.4, and x = 4.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9.4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 3|((-2(1(5(3|x - 2| - 1) + 3) + 5) - 3)/(2(1(5(3|x - 2| - 1) + 3) + 5) + 1)) - 1| + 2 and g(x) = 1|(-1(-2e^(-1(2|x - 1|)) + 2)^2 - 4(-2e^(-1(2|x - 1|)) + 2) + 5) - 1| + 2 from x = -0.0 to x = 2.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-3((-2(-1sin(3\u03c0((-2(-1x + 2) - 1)/(2(-1x + 2) - 3)) - 2) - 2) - 1)/(-2(-1sin(3\u03c0((-2(-1x + 2) - 1)/(2(-1x + 2) - 3)) - 2) - 2) + 3)) + 3)/(2((-2(-1sin(3\u03c0((-2(-1x + 2) - 1)/(2(-1x + 2) - 3)) - 2) - 2) - 1)/(-2(-1sin(3\u03c0((-2(-1x + 2) - 1)/(2(-1x + 2) - 3)) - 2) - 2) + 3)) - 1) and g(x) = -1(1(-1|(-2sin(2\u03c0x + 2) - 1) - 3|)^2 + 4(-1|(-2sin(2\u03c0x + 2) - 1) - 3|) + 5)^2 + 2(1(-1|(-2sin(2\u03c0x + 2) - 1) - 3|)^2 + 4(-1|(-2sin(2\u03c0x + 2) - 1) - 3|) + 5) from x = 2.1 to x = 2.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-1(-3(-2((2((1x + 1)/(1x)) + 3)/(-3((1x + 1)/(1x)))) - 1)^2 - 4(-2((2((1x + 1)/(1x)) + 3)/(-3((1x + 1)/(1x)))) - 1) - 3) - 1)/(-1(-3(-2((2((1x + 1)/(1x)) + 3)/(-3((1x + 1)/(1x)))) - 1)^2 - 4(-2((2((1x + 1)/(1x)) + 3)/(-3((1x + 1)/(1x)))) - 1) - 3) - 3) and g(x) = 4((-2(-1(1e^(-2x) + 3)^2 + 1(1e^(-2x) + 3) + 4) - 1)/(3(-1(1e^(-2x) + 3)^2 + 1(1e^(-2x) + 3) + 4) - 1))^2 + 1((-2(-1(1e^(-2x) + 3)^2 + 1(1e^(-2x) + 3) + 4) - 1)/(3(-1(1e^(-2x) + 3)^2 + 1(1e^(-2x) + 3) + 4) - 1)) + 1 from x = -0.5 to x = 0.1. 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) = (-3(-1(2((2(-5x + 3) + 2)/(2(-5x + 3) - 3)) + 3) - 3) - 3)/(-1(-1(2((2(-5x + 3) + 2)/(2(-5x + 3) - 3)) + 3) - 3) + 2), g(x) = -1((2(5((-1x - 2)/(-2x - 1)) - 1) - 2)/(2(5((-1x - 2)/(-2x - 1)) - 1) - 1)) + 5, x = -3.5, 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": "7.6", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2(-1((-2(-2sin(2\u03c0(-5x - 5) + 3) + 2) + 2)/(-2(-2sin(2\u03c0(-5x - 5) + 3) + 2) - 3))^2 - 3((-2(-2sin(2\u03c0(-5x - 5) + 3) + 2) + 2)/(-2(-2sin(2\u03c0(-5x - 5) + 3) + 2) - 3)))^2 + 5(-1((-2(-2sin(2\u03c0(-5x - 5) + 3) + 2) + 2)/(-2(-2sin(2\u03c0(-5x - 5) + 3) + 2) - 3))^2 - 3((-2(-2sin(2\u03c0(-5x - 5) + 3) + 2) + 2)/(-2(-2sin(2\u03c0(-5x - 5) + 3) + 2) - 3))) - 2, g(x) = 3cos(3\u03c0(-2(2|(-2x + 4) - 3| - 3)^2 + 1(2|(-2x + 4) - 3| - 3) + 3) + 2) - 3, 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2sin(3\u03c0(3((-2(-1|(2|x - 3|) + 3| + 3) - 3)/(1(-1|(2|x - 3|) + 3| + 3) - 2))^2 - 1((-2(-1|(2|x - 3|) + 3| + 3) - 3)/(1(-1|(2|x - 3|) + 3| + 3) - 2)) - 4) - 1) - 2 and g(x) = 1e^(1((-1((1((-2x)/(2x - 3)) + 3)/(-1((-2x)/(2x - 3)) + 2)) + 1)/(3((1((-2x)/(2x - 3)) + 3)/(-1((-2x)/(2x - 3)) + 2)) + 2))) - 3 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 4(-2|(-2e^(1(-4((-2x)/(2x - 1))^2 + 4((-2x)/(2x - 1)) - 3)) + 2)| - 1)^2 + 3(-2|(-2e^(1(-4((-2x)/(2x - 1))^2 + 4((-2x)/(2x - 1)) - 3)) + 2)| - 1) + 3 and g(x) = 1|(-1(2|(5x - 2) - 2| + 1)^2 - 2(2|(5x - 2) - 2| + 1) - 4) + 3| + 2 from x = 0.2 to x = 1.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "70.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1|(1|(-1e^(-1(1((-2x - 1)/(-2x - 3))^2 - 5((-2x - 1)/(-2x - 3)) - 3)) - 2) + 2|)| - 1 and g(x) = (-1((1(4(1sin(3\u03c0x + 3) + 1)^2 + 4) - 1)/(2(4(1sin(3\u03c0x + 3) + 1)^2 + 4) - 1)) - 1)/(3((1(4(1sin(3\u03c0x + 3) + 1)^2 + 4) - 1)/(2(4(1sin(3\u03c0x + 3) + 1)^2 + 4) - 1)) - 1) 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": "2.4", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2((-3(-3(4(4x - 2)^2 - 5(4x - 2) - 5)) - 2)/(3(-3(4(4x - 2)^2 - 5(4x - 2) - 5)) - 2)) + 2 and g(x) = 3(3|(-1|(-2x^2 + 4) - 2| + 2)| - 3)^2 + 1(3|(-1|(-2x^2 + 4) - 2| + 2)| - 3) - 4 between the vertical lines x = 1.1 and x = 1.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2(1|(-4(2|(-2sin(2\u03c0x + 2) - 1) + 2| - 3)^2 - 2(2|(-2sin(2\u03c0x + 2) - 1) + 2| - 3) + 3) + 1| - 3) - 1 and g(x) = -2(-1sin(1\u03c0(-1(-5x^2 - 2x - 2) + 2) - 1))^2 + 5(-1sin(1\u03c0(-1(-5x^2 - 2x - 2) + 2) - 1)) - 4 from x = -5.0 to x = -4.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -5(-3|((-2(-3(-2x - 1) - 5) + 1)/(-1(-3(-2x - 1) - 5))) - 3| + 1) - 4 and g(x) = 3|(3|(-1(-1x - 5) + 2) - 2|) + 1| + 2 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": "108.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2|((3((2(-1|(2|x + 3| + 1) - 2| - 3) + 1)/(3(-1|(2|x + 3| + 1) - 2| - 3) + 3)) + 3)/(-1((2(-1|(2|x + 3| + 1) - 2| - 3) + 1)/(3(-1|(2|x + 3| + 1) - 2| - 3) + 3)))) + 2| and g(x) = -3(-2((2(-2x - 3) + 1)/(3(-2x - 3) - 2))^2 - 2((2(-2x - 3) + 1)/(3(-2x - 3) - 2)) + 4) - 4 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": "8.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1(-1|(-1(1|(-2|x - 1| + 3) + 3|) + 5) - 3| + 1)^2 + 1(-1|(-1(1|(-2|x - 1| + 3) + 3|) + 5) - 3| + 1) + 4 and g(x) = 1|(-1|(3|((-2x + 1)/(-3x + 1)) - 1|) - 2| + 2) - 1| - 1 from x = 0.3 to x = 0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13.9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (3(-3(-3sin(1\u03c0(-1|(-3|x|) - 1| + 1) + 3) + 1)^2 - 1(-3sin(1\u03c0(-1|(-3|x|) - 1| + 1) + 3) + 1) + 3) - 1)/(-1(-3(-3sin(1\u03c0(-1|(-3|x|) - 1| + 1) + 3) + 1)^2 - 1(-3sin(1\u03c0(-1|(-3|x|) - 1| + 1) + 3) + 1) + 3) + 2) and g(x) = -2sin(3\u03c0(3(1(5x - 5)^2 - 1(5x - 5) + 5) + 3) + 1) + 2 from x = 3.3 to x = 3.4. 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) = 3(-1cos(1\u03c0((3(2(2x^2 - 1x - 1) - 2) - 1)/(2(2(2x^2 - 1x - 1) - 2) - 1)) - 1)) - 1 and g(x) = -3cos(2\u03c0(4(-2|(4x + 2) + 1| - 1) - 2) - 2) between the vertical lines x = 3.2 and x = 3.3000000000000003. 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(3sin(3\u03c0(2|(3|(1x - 4) - 3| - 3) + 2| - 2) + 1) + 1)^2 + 1(3sin(3\u03c0(2|(3|(1x - 4) - 3| - 3) + 2| - 2) + 1) + 1) - 5 and g(x) = -2|(-1(2(-1x^2 + 2x + 3)^2 - 2(-1x^2 + 2x + 3) - 5)^2 + 3(2(-1x^2 + 2x + 3)^2 - 2(-1x^2 + 2x + 3) - 5) + 1) + 1| + 2 from x = -1.2 to x = -1.1. 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": "Calculate the area enclosed between the functions f(x) = 1|(3(3|(2|(3sin(3\u03c0x - 2) - 1) + 2|) - 3| + 3)^2 - 5(3|(2|(3sin(3\u03c0x - 2) - 1) + 2|) - 3| + 3) - 4) - 1| + 3 and g(x) = 2|(2(1(-2cos(2\u03c0x - 1) + 3)^2 + 2(-2cos(2\u03c0x - 1) + 3) - 4) + 2)| - 2 from x = 4.6 to x = 4.699999999999999. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3e^(-1((2((2(2|(-4x + 2) - 1|) + 1)/(1(2|(-4x + 2) - 1|) + 2)) + 3)/(2((2(2|(-4x + 2) - 1|) + 1)/(1(2|(-4x + 2) - 1|) + 2)) + 3))) - 1 and g(x) = -1|(-1e^(-1(3(-5x^2 + 4) - 1)) + 3) - 3| - 2 from x = -0.8 to x = 0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2|(1|(-2|(1(-4x - 4) - 1)| + 2) + 3| + 2) - 3| + 1 and g(x) = (-2(-3cos(2\u03c0((1(-3|x - 3| - 2) + 1)/(2(-3|x - 3| - 2))) - 2) - 1) + 1)/(-3(-3cos(2\u03c0((1(-3|x - 3| - 2) + 1)/(2(-3|x - 3| - 2))) - 2) - 1)) 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3(-4(-5(2|(-3sin(2\u03c0x - 3) - 2) + 3| + 1) + 4)^2 - 2) + 5, g(x) = -4(-5(-1|(1x^2 - 3x) - 3| - 2) - 1) + 5, 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": "67.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3|((-3((2(-3|(-2|x + 3|) + 2| + 1) + 2)/(2(-3|(-2|x + 3|) + 2| + 1) - 1)) - 2)/(3((2(-3|(-2|x + 3|) + 2| + 1) + 2)/(2(-3|(-2|x + 3|) + 2| + 1) - 1)) - 2)) - 1| - 1 and g(x) = 2((1(-2cos(1\u03c0((-3x + 1)/(-1x - 2)) - 1)) - 3)/(-3(-2cos(1\u03c0((-3x + 1)/(-1x - 2)) - 1)) - 3)) - 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": "1.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2(5(1cos(1\u03c0((1((-1x - 3)/(-3x)) + 2)/(2((-1x - 3)/(-3x)) + 3))) + 1) - 3)^2 - 2 and g(x) = 1(4(-3((-1x)/(-3x + 1))^2 - 4((-1x)/(-3x + 1)) - 2) + 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": "3.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2|(-1(-1cos(2\u03c0(4((2x - 3)/(1x))^2 + 4((2x - 3)/(1x)) + 4) + 1) + 2) + 1) + 2| + 2 and g(x) = -2sin(3\u03c0((-3(-3(-1x^2 + 5x - 5) + 3) + 2)/(1(-3(-1x^2 + 5x - 5) + 3) - 2)) - 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (2(-2((-3((3(-1x^2 - 1x + 5))/(-3(-1x^2 - 1x + 5) - 3)))/(1((3(-1x^2 - 1x + 5))/(-3(-1x^2 - 1x + 5) - 3)) - 2))^2 - 5((-3((3(-1x^2 - 1x + 5))/(-3(-1x^2 - 1x + 5) - 3)))/(1((3(-1x^2 - 1x + 5))/(-3(-1x^2 - 1x + 5) - 3)) - 2)) - 1) - 3)/(-3(-2((-3((3(-1x^2 - 1x + 5))/(-3(-1x^2 - 1x + 5) - 3)))/(1((3(-1x^2 - 1x + 5))/(-3(-1x^2 - 1x + 5) - 3)) - 2))^2 - 5((-3((3(-1x^2 - 1x + 5))/(-3(-1x^2 - 1x + 5) - 3)))/(1((3(-1x^2 - 1x + 5))/(-3(-1x^2 - 1x + 5) - 3)) - 2)) - 1) - 3) and g(x) = (-2((-2(2e^(-1((-2x - 3)/(-3x + 2))) - 2) + 1)/(2(2e^(-1((-2x - 3)/(-3x + 2))) - 2) + 2)) - 1)/(-3((-2(2e^(-1((-2x - 3)/(-3x + 2))) - 2) + 1)/(2(2e^(-1((-2x - 3)/(-3x + 2))) - 2) + 2)) - 2) between the vertical lines x = -3.0 and x = -2.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2(5((-1(1|(-3|x|) + 2| - 2) + 3)/(-3(1|(-3|x|) + 2| - 2) + 2)) - 3) + 5 and g(x) = 4(-2cos(1\u03c0(2|(1x^2 + 1x) - 3|) - 1) - 3)^2 + 2(-2cos(1\u03c0(2|(1x^2 + 1x) - 3|) - 1) - 3) + 1 from x = 1.2 to x = 1.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12.7", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1(-3sin(2\u03c0(1((2(-1x + 4) + 3)/(-1(-1x + 4) - 2))^2 + 4((2(-1x + 4) + 3)/(-1(-1x + 4) - 2)) - 3) + 2) + 2) - 1, g(x) = -3sin(3\u03c0(2((1(-2x + 3) - 3)/(1(-2x + 3) - 2)) - 2)) - 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2|(-5(5((-2(-5x^2 - 2x + 2) - 3)/(2(-5x^2 - 2x + 2) + 2))^2 + 3((-2(-5x^2 - 2x + 2) - 3)/(2(-5x^2 - 2x + 2) + 2)) + 1) - 5) + 2| - 3 and g(x) = -3|(2(-3sin(1\u03c0(-4x^2 - 4x - 1) - 2) - 1)^2 - 4(-3sin(1\u03c0(-4x^2 - 4x - 1) - 2) - 1) - 2) - 3| + 2 between the vertical lines x = 2.7 and x = 2.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1(2sin(3\u03c0((-2(-1(3x^2 + 2)^2 + 1(3x^2 + 2) + 5))/(3(-1(3x^2 + 2)^2 + 1(3x^2 + 2) + 5))) - 1) - 3) + 4 and g(x) = (-2(1(-3sin(3\u03c0(-4x) - 3) + 3)^2 - 1(-3sin(3\u03c0(-4x) - 3) + 3) - 3) - 3)/(-2(1(-3sin(3\u03c0(-4x) - 3) + 3)^2 - 1(-3sin(3\u03c0(-4x) - 3) + 3) - 3) - 2) from x = -2.8 to x = -2.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 5((-1(1((3(-2|x - 1| + 1) - 1)/(-3(-2|x - 1| + 1))) + 1) - 2)/(-3(1((3(-2|x - 1| + 1) - 1)/(-3(-2|x - 1| + 1))) + 1)))^2 + 1((-1(1((3(-2|x - 1| + 1) - 1)/(-3(-2|x - 1| + 1))) + 1) - 2)/(-3(1((3(-2|x - 1| + 1) - 1)/(-3(-2|x - 1| + 1))) + 1))) + 5 and g(x) = 4(2sin(3\u03c0(3(-1|x + 2| + 2) + 1) - 2) - 1)^2 - 3(2sin(3\u03c0(3(-1|x + 2| + 2) + 1) - 2) - 1) - 2 from x = 1.6 to x = 1.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.4", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2(1(-3sin(2\u03c0(3(-3x^2 + 1x + 4) - 5) - 2) + 2) - 1)^2 - 4(1(-3sin(2\u03c0(3(-3x^2 + 1x + 4) - 5) - 2) + 2) - 1) - 5 and g(x) = (-1(2(1((-2x - 2)/(3x - 2)) - 2) - 5) + 2)/(-3(2(1((-2x - 2)/(3x - 2)) - 2) - 5) - 3) between the vertical lines x = -2.0 and x = -1.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2|((-1(3|(-5(-3e^(1x) + 2) + 3) - 1|) + 3)/(-3(3|(-5(-3e^(1x) + 2) + 3) - 1|)))| - 1 and g(x) = (-2(-3(2|(3x^2 - 5x + 5) + 3| + 1)^2 + 4(2|(3x^2 - 5x + 5) + 3| + 1) - 5) - 2)/(3(-3(2|(3x^2 - 5x + 5) + 3| + 1)^2 + 4(2|(3x^2 - 5x + 5) + 3| + 1) - 5) - 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": "4.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (1(2(3(1(2e^(1x) - 2)^2 - 3(2e^(1x) - 2) - 5)^2 - 1(1(2e^(1x) - 2)^2 - 3(2e^(1x) - 2) - 5) + 1)^2 - 3(3(1(2e^(1x) - 2)^2 - 3(2e^(1x) - 2) - 5)^2 - 1(1(2e^(1x) - 2)^2 - 3(2e^(1x) - 2) - 5) + 1) + 5) + 3)/(-2(2(3(1(2e^(1x) - 2)^2 - 3(2e^(1x) - 2) - 5)^2 - 1(1(2e^(1x) - 2)^2 - 3(2e^(1x) - 2) - 5) + 1)^2 - 3(3(1(2e^(1x) - 2)^2 - 3(2e^(1x) - 2) - 5)^2 - 1(1(2e^(1x) - 2)^2 - 3(2e^(1x) - 2) - 5) + 1) + 5) - 1) and g(x) = (-2(1|(4((2x - 1)/(-3x + 4))^2 + 1((2x - 1)/(-3x + 4)) - 3) + 2| - 2) + 3)/(-1(1|(4((2x - 1)/(-3x + 4))^2 + 1((2x - 1)/(-3x + 4)) - 3) + 2| - 2) - 3) between the vertical lines x = 1.0 and x = 2.7. 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|((-3(-2|(1|(-2cos(3\u03c0x) - 2) - 3| - 1) - 2| - 3) + 3)/(-2(-2|(1|(-2cos(3\u03c0x) - 2) - 3| - 1) - 2| - 3) + 3)) + 2| - 1, g(x) = -5((-2(2cos(3\u03c0(3|x + 3| + 1))) + 3)/(2(2cos(3\u03c0(3|x + 3| + 1)))))^2 - 3((-2(2cos(3\u03c0(3|x + 3| + 1))) + 3)/(2(2cos(3\u03c0(3|x + 3| + 1))))) + 1, x = 0.7, and x = 0.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-0.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3cos(3\u03c0(-1((2(2(3x - 3) + 2) - 3)/(-1(2(3x - 3) + 2))) + 1) + 2) and g(x) = 2(-3cos(3\u03c0(2|(-1x^2 - 2x + 3) + 1| - 3) - 1) - 2) - 3 from x = -4.4 to x = -4.300000000000001. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-1(2|(1(-4(3|x + 2| + 2)^2 - 2(3|x + 2| + 2) - 2)^2 - 4(-4(3|x + 2| + 2)^2 - 2(3|x + 2| + 2) - 2) - 5) - 3| + 1) - 1)/(2(2|(1(-4(3|x + 2| + 2)^2 - 2(3|x + 2| + 2) - 2)^2 - 4(-4(3|x + 2| + 2)^2 - 2(3|x + 2| + 2) - 2) - 5) - 3| + 1) - 3) and g(x) = -3(-2(1(2|x + 3|)^2 - 1(2|x + 3|) - 4) + 2) + 2 between the vertical lines x = -4.4 and x = -1.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "56.9", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2((3(-2((-1(-3x - 2) - 1)/(1(-3x - 2) + 3)) + 3))/(1(-2((-1(-3x - 2) - 1)/(1(-3x - 2) + 3)) + 3)))^2 + 4((3(-2((-1(-3x - 2) - 1)/(1(-3x - 2) + 3)) + 3))/(1(-2((-1(-3x - 2) - 1)/(1(-3x - 2) + 3)) + 3))) - 5, g(x) = -1(4(-3(2cos(1\u03c0x) + 3)^2 + 1(2cos(1\u03c0x) + 3) + 3) - 5) + 2, x = -2.7, and x = -1.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "188.8", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2cos(3\u03c0(4(-5(1|(-3x + 1) + 1| - 2) - 2) + 3) - 2) - 3 and g(x) = -2|(-5(1cos(3\u03c0((-3x - 1)/(-1x + 3))))^2 + 1(1cos(3\u03c0((-3x - 1)/(-1x + 3)))) + 4) + 3| + 1 between the vertical lines x = 2.5 and x = 2.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (3((-1((1(-1(4x^2 + 3x - 3) - 2) + 1)/(2(-1(4x^2 + 3x - 3) - 2) + 3)) + 2)/(3((1(-1(4x^2 + 3x - 3) - 2) + 1)/(2(-1(4x^2 + 3x - 3) - 2) + 3)) - 2)) - 3)/(2((-1((1(-1(4x^2 + 3x - 3) - 2) + 1)/(2(-1(4x^2 + 3x - 3) - 2) + 3)) + 2)/(3((1(-1(4x^2 + 3x - 3) - 2) + 1)/(2(-1(4x^2 + 3x - 3) - 2) + 3)) - 2)) - 1) and g(x) = 2cos(1\u03c0(-1|(2|((1x + 3)/(-3x))| + 2) - 2| - 2) - 1) + 2 between the vertical lines x = 0.0 and x = 0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (1(2(3|(-1sin(1\u03c0((3x + 2)/(1x - 3)) - 2)) + 3| - 3) - 5) - 2)/(1(2(3|(-1sin(1\u03c0((3x + 2)/(1x - 3)) - 2)) + 3| - 3) - 5) - 3) and g(x) = -1|(5(-5(1|x - 2| + 1) + 3) - 4)| - 2 between the vertical lines x = 0.3 and x = 2.0. 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": "Find the area of the region bounded by the curves f(x) = 1(1((-1((-1((1x - 1)/(1x + 3)) - 2)/(2((1x - 1)/(1x + 3)) - 3)) - 2)/(1((-1((1x - 1)/(1x + 3)) - 2)/(2((1x - 1)/(1x + 3)) - 3)) + 1))^2 - 3((-1((-1((1x - 1)/(1x + 3)) - 2)/(2((1x - 1)/(1x + 3)) - 3)) - 2)/(1((-1((1x - 1)/(1x + 3)) - 2)/(2((1x - 1)/(1x + 3)) - 3)) + 1)) - 3) + 4, g(x) = 4(-2(1(-3sin(2\u03c0x + 1) + 1) - 3)^2 + 1)^2 + 4(-2(1(-3sin(2\u03c0x + 1) + 1) - 3)^2 + 1) + 4, 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": "0.7", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2cos(2\u03c0(3|((-1(-1((3x - 1)/(3x - 1)) + 2) + 1)/(1(-1((3x - 1)/(3x - 1)) + 2) - 3)) + 1|) + 2) + 1 and g(x) = 4((-1(2(-4x - 5) + 1) - 3)/(3(2(-4x - 5) + 1) + 3))^2 - 4((-1(2(-4x - 5) + 1) - 3)/(3(2(-4x - 5) + 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": "Calculate the area enclosed between the functions f(x) = 5(-3cos(3\u03c0(1|(-5(-5x^2 + 4x - 3)^2 + 5(-5x^2 + 4x - 3) - 4) - 2| + 1) + 3) + 2) - 1 and g(x) = -1sin(3\u03c0((-1(-4(3|x|) - 4) + 1)/(-1(-4(3|x|) - 4) + 2)) - 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": "1.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2sin(2\u03c0(-1(-2|(2(-5x - 1)^2 + 5(-5x - 1) + 5) + 2| - 3) + 4)) - 1, g(x) = -4((2(2|(-5x^2 + 3x + 5) - 3| - 2) - 2)/(-3(2|(-5x^2 + 3x + 5) - 3| - 2)))^2 - 1((2(2|(-5x^2 + 3x + 5) - 3| - 2) - 2)/(-3(2|(-5x^2 + 3x + 5) - 3| - 2))) + 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": "Calculate the area enclosed between the functions f(x) = -5(3|((-2(-2|(1x + 1) - 3|) - 2)/(-1(-2|(1x + 1) - 3|) + 2)) - 1|) and g(x) = (2(2|(-5(-3sin(3\u03c0x + 1) - 1)^2 - 3(-3sin(3\u03c0x + 1) - 1)) + 3| - 2) - 3)/(-1(2|(-5(-3sin(3\u03c0x + 1) - 1)^2 - 3(-3sin(3\u03c0x + 1) - 1)) + 3| - 2) + 3) 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": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1|((-1(-3sin(3\u03c0((-2((3x - 3)/(-1x - 3)) + 2)/(1((3x - 3)/(-1x - 3)) + 2)) + 2)) + 3)/(-3(-3sin(3\u03c0((-2((3x - 3)/(-1x - 3)) + 2)/(1((3x - 3)/(-1x - 3)) + 2)) + 2)) + 1)) - 1| - 3 and g(x) = 1sin(2\u03c0((-2(-2(-2|x + 3| + 3)^2 + 5(-2|x + 3| + 3) - 5) - 1)/(-2(-2(-2|x + 3| + 3)^2 + 5(-2|x + 3| + 3) - 5) - 3)) - 1) - 2 from x = -0.2 to x = -0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 3(-3|(-3(4(-2x - 4) + 5) + 1) + 3| + 1)^2 + 1(-3|(-3(4(-2x - 4) + 5) + 1) + 3| + 1) - 5 and g(x) = 2|((-2(-1|(2cos(2\u03c0x - 1) + 3) - 2| + 1) - 3)/(-1(-1|(2cos(2\u03c0x - 1) + 3) - 2| + 1) - 1)) - 1| + 1 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": "13.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 5(-2|(1(-3(-4x + 1)^2 - 1(-4x + 1) + 3) - 5) + 1|) - 3 and g(x) = -1(-1|(-3|(-2|x + 1| + 3) + 1| + 1) + 3| - 3)^2 + 5(-1|(-3|(-2|x + 1| + 3) + 1| + 1) + 3| - 3) - 5 from x = -0.0 to x = 0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2e^(2((-1((-3(1|(1x^2 - 5x)| + 1) - 1)/(-2(1|(1x^2 - 5x)| + 1) - 2)) - 1)/(-3((-3(1|(1x^2 - 5x)| + 1) - 1)/(-2(1|(1x^2 - 5x)| + 1) - 2)) - 2))) - 1 and g(x) = -5(1(-1(-5x^2 + 1x - 1)^2 - 4(-5x^2 + 1x - 1) + 5) + 4)^2 + 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": "1.8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2e^(-1(-1|((2(-2((1x - 1)/(2x - 1))^2 - 2((1x - 1)/(2x - 1)) - 3) + 2)/(1(-2((1x - 1)/(2x - 1))^2 - 2((1x - 1)/(2x - 1)) - 3) + 2)) - 3| + 2)) + 1 and g(x) = (3(-3(-2|(-3x + 3) + 1| - 2) + 1))/(-1(-3(-2|(-3x + 3) + 1| - 2) + 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1(-5(4((-2((2x - 2)/(-3x - 2)) + 2)/(-2((2x - 2)/(-3x - 2)) - 3))^2 - 4((-2((2x - 2)/(-3x - 2)) + 2)/(-2((2x - 2)/(-3x - 2)) - 3)) - 1) - 4) + 4 and g(x) = 5((1(-2|(-1sin(1\u03c0x - 2) - 1) - 1| + 1) - 2)/(1(-2|(-1sin(1\u03c0x - 2) - 1) - 1| + 1) - 3)) + 2 from x = -0.6 to x = -0.0. 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) = 2|(-3|(-3cos(1\u03c0(4((-3x)/(-1x))^2 + 4((-3x)/(-1x)) + 4) + 1) - 2) + 3| - 3) - 3| and g(x) = (-3((2(-3(-3x^2 + 1x + 5) - 3))/(-1(-3(-3x^2 + 1x + 5) - 3) - 2)))/(2((2(-3(-3x^2 + 1x + 5) - 3))/(-1(-3(-3x^2 + 1x + 5) - 3) - 2)) + 1) 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": "52.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 5(-5((1(-2|((-1x + 1)/(2x + 1)) - 1| + 2) - 1)/(3(-2|((-1x + 1)/(2x + 1)) - 1| + 2) - 1))^2 - 1((1(-2|((-1x + 1)/(2x + 1)) - 1| + 2) - 1)/(3(-2|((-1x + 1)/(2x + 1)) - 1| + 2) - 1)) + 4) - 2 and g(x) = 1|((-2(1cos(2\u03c0(-3x^2 - 3x - 2)) - 3) - 3)/(-2(1cos(2\u03c0(-3x^2 - 3x - 2)) - 3) + 3)) - 1| + 2 between the vertical lines x = 1.6 and x = 1.7000000000000002. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1(-4(-2|(3|(-3sin(2\u03c0x + 2) + 1) + 1| - 3)| + 2) - 2)^2 + 4(-4(-2|(3|(-3sin(2\u03c0x + 2) + 1) + 1| - 3)| + 2) - 2) + 5 and g(x) = (2(2|((3((2x + 1)/(1x + 1)) - 1)/(-2((2x + 1)/(1x + 1)) + 3)) + 1| + 1) + 1)/(-1(2|((3((2x + 1)/(1x + 1)) - 1)/(-2((2x + 1)/(1x + 1)) + 3)) + 1| + 1) + 2) 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": "4.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-3(4(3e^(2(-4(-2|x + 2|) - 5)) - 3)^2 - 3(3e^(2(-4(-2|x + 2|) - 5)) - 3) + 1))/(-1(4(3e^(2(-4(-2|x + 2|) - 5)) - 3)^2 - 3(3e^(2(-4(-2|x + 2|) - 5)) - 3) + 1) - 3) and g(x) = 3|(2|(1(2cos(2\u03c0x + 2) + 1)^2 - 1(2cos(2\u03c0x + 2) + 1)) + 1| - 1) - 3| - 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-3((-1(1((1(-3sin(1\u03c0x - 3)))/(-1(-3sin(1\u03c0x - 3)) + 2))^2 + 3((1(-3sin(1\u03c0x - 3)))/(-1(-3sin(1\u03c0x - 3)) + 2)) - 3) + 2)/(-3(1((1(-3sin(1\u03c0x - 3)))/(-1(-3sin(1\u03c0x - 3)) + 2))^2 + 3((1(-3sin(1\u03c0x - 3)))/(-1(-3sin(1\u03c0x - 3)) + 2)) - 3) - 1)))/(1((-1(1((1(-3sin(1\u03c0x - 3)))/(-1(-3sin(1\u03c0x - 3)) + 2))^2 + 3((1(-3sin(1\u03c0x - 3)))/(-1(-3sin(1\u03c0x - 3)) + 2)) - 3) + 2)/(-3(1((1(-3sin(1\u03c0x - 3)))/(-1(-3sin(1\u03c0x - 3)) + 2))^2 + 3((1(-3sin(1\u03c0x - 3)))/(-1(-3sin(1\u03c0x - 3)) + 2)) - 3) - 1))), g(x) = (-2((1(-1(-1x - 1)^2 - 4(-1x - 1) + 3) + 1)/(1(-1(-1x - 1)^2 - 4(-1x - 1) + 3) - 3)) + 3)/(3((1(-1(-1x - 1)^2 - 4(-1x - 1) + 3) + 1)/(1(-1(-1x - 1)^2 - 4(-1x - 1) + 3) - 3)) + 3), x = -1.3, and x = 3.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2|((-3(1|(5(2x + 5) - 2) + 1| + 2) - 1)/(1(1|(5(2x + 5) - 2) + 1| + 2) + 3)) - 3| + 1 and g(x) = (-3(2sin(1\u03c0(-1(4x - 1) - 3) + 3) - 2) - 1)/(1(2sin(1\u03c0(-1(4x - 1) - 3) + 3) - 2) + 1) 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": "4.4", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (1(2(2((-2((3x - 1)/(-2x - 3)) - 3)/(1((3x - 1)/(-2x - 3)) + 2)) + 5)^2 + 2(2((-2((3x - 1)/(-2x - 3)) - 3)/(1((3x - 1)/(-2x - 3)) + 2)) + 5) - 1))/(1(2(2((-2((3x - 1)/(-2x - 3)) - 3)/(1((3x - 1)/(-2x - 3)) + 2)) + 5)^2 + 2(2((-2((3x - 1)/(-2x - 3)) - 3)/(1((3x - 1)/(-2x - 3)) + 2)) + 5) - 1) + 1) and g(x) = -2(3(-1(-4x^2 + 3x + 1) + 5) - 3) - 5 between the vertical lines x = -3.3 and x = -2.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "212.6", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1(-3|((3(-1|(-4x + 4) + 2| + 2) - 2)/(-2(-1|(-4x + 4) + 2| + 2))) - 2| + 2) + 4, g(x) = (2(2(-2|(2x^2 - 1x + 3) + 3| + 3) - 2) - 3)/(2(2(-2|(2x^2 - 1x + 3) + 3| + 3) - 2) - 1), 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": "16.7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1cos(1\u03c0(4((-1(3|((-1x + 3)/(-2x)) + 1| + 3) + 1)/(-1(3|((-1x + 3)/(-2x)) + 1| + 3))) + 3)) - 2 and g(x) = -2|(-2|(1sin(3\u03c0((-2x + 2)/(-2x)) + 1) - 3) + 2| - 2) + 3| + 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": "Determine the area of the region enclosed by the graphs of f(x) = -2|((-1(1(-2(3cos(3\u03c0x + 3) + 2)^2 - 2(3cos(3\u03c0x + 3) + 2))^2 - 5(-2(3cos(3\u03c0x + 3) + 2)^2 - 2(3cos(3\u03c0x + 3) + 2)) + 2) + 2)/(-3(1(-2(3cos(3\u03c0x + 3) + 2)^2 - 2(3cos(3\u03c0x + 3) + 2))^2 - 5(-2(3cos(3\u03c0x + 3) + 2)^2 - 2(3cos(3\u03c0x + 3) + 2)) + 2) + 4)) - 3| + 3 and g(x) = -1(5(3|(2sin(1\u03c0x + 2) + 3) + 1|) - 5) + 5 between the vertical lines x = -4.6 and x = -3.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "76.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (1(3(-1sin(3\u03c0(-4(3|x - 2| - 1) + 3) + 2) - 1) - 2))/(3(3(-1sin(3\u03c0(-4(3|x - 2| - 1) + 3) + 2) - 1) - 2)) and g(x) = (2((-2(2|(3cos(2\u03c0x + 3)) + 1|) + 2)/(-3(2|(3cos(2\u03c0x + 3)) + 1|) - 1)) + 2)/(1((-2(2|(3cos(2\u03c0x + 3)) + 1|) + 2)/(-3(2|(3cos(2\u03c0x + 3)) + 1|) - 1))) from x = 3.8 to x = 3.9. 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": "Find the area of the region bounded by the curves f(x) = 1(-5((2(3(4x - 3)^2 + 1(4x - 3) - 1) + 2)/(-2(3(4x - 3)^2 + 1(4x - 3) - 1) - 2)) - 3)^2 + 5(-5((2(3(4x - 3)^2 + 1(4x - 3) - 1) + 2)/(-2(3(4x - 3)^2 + 1(4x - 3) - 1) - 2)) - 3), g(x) = 1((-3(2e^(1(-4x^2 + 3x - 2))) + 1)/(2(2e^(1(-4x^2 + 3x - 2))))) + 1, x = -0.4, and x = 1.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17.7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 3(-3|(1e^(-1(-2|((2x)/(-3x + 1)) + 3| + 2)) - 3) - 2| + 2) + 2 and g(x) = 5(2sin(3\u03c0(-1(-1x - 4) - 2)) - 2) - 4 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": "1.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1(1((2(3sin(1\u03c0(3x^2 + 1x - 4) - 2) - 2) + 1)/(-1(3sin(1\u03c0(3x^2 + 1x - 4) - 2) - 2) - 1))^2 + 5((2(3sin(1\u03c0(3x^2 + 1x - 4) - 2) - 2) + 1)/(-1(3sin(1\u03c0(3x^2 + 1x - 4) - 2) - 2) - 1)) - 1) - 2, g(x) = (1(-5(4(-1x - 1)^2 + 2(-1x - 1) + 1)^2 - 3(4(-1x - 1)^2 + 2(-1x - 1) + 1) - 1) + 1)/(2(-5(4(-1x - 1)^2 + 2(-1x - 1) + 1)^2 - 3(4(-1x - 1)^2 + 2(-1x - 1) + 1) - 1) - 1), 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": "0.9", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 5(5(3e^(-1((2(2x + 5))/(2(2x + 5) + 3))) - 1)^2 + 4(3e^(-1((2(2x + 5))/(2(2x + 5) + 3))) - 1) + 3) + 5 and g(x) = 1(-3((3(-2x^2 + 1) + 3)/(-3(-2x^2 + 1) - 1)) + 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": "39.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (1(1|(2cos(2\u03c0(1|(-2x + 5) + 3| + 1) - 3) - 1) + 2| - 2) - 2)/(-1(1|(2cos(2\u03c0(1|(-2x + 5) + 3| + 1) - 3) - 1) + 2| - 2)) and g(x) = -3((2(-2(5x^2 - 2x)^2 + 3(5x^2 - 2x) + 4) + 2)/(2(-2(5x^2 - 2x)^2 + 3(5x^2 - 2x) + 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2|(1(-2(-5(-1sin(3\u03c0x - 1) - 2)^2 - 2(-1sin(3\u03c0x - 1) - 2)) - 4) - 5)| + 1, g(x) = -2cos(1\u03c0(2|((-1(-5x - 4) + 3)/(-2(-5x - 4) + 3)) + 3| + 3) - 2) + 3, 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2cos(2\u03c0(-4(5((-2(3|x + 1| - 1) - 1)/(-2(3|x + 1| - 1) + 3))^2 + 2((-2(3|x + 1| - 1) - 1)/(-2(3|x + 1| - 1) + 3)) - 1)^2 - 5(5((-2(3|x + 1| - 1) - 1)/(-2(3|x + 1| - 1) + 3))^2 + 2((-2(3|x + 1| - 1) - 1)/(-2(3|x + 1| - 1) + 3)) - 1) - 3) - 1) and g(x) = -3|(4((2(1e^(2x) - 1) + 1)/(-1(1e^(2x) - 1) + 2))^2 + 4((2(1e^(2x) - 1) + 1)/(-1(1e^(2x) - 1) + 2)) - 2) + 3| - 1 between the vertical lines x = -4.4 and x = -4.300000000000001. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1(4(2sin(2\u03c0(-4(-5x^2 + 3x + 2)^2 - 5(-5x^2 + 3x + 2) - 5)) + 1)^2 - 5(2sin(2\u03c0(-4(-5x^2 + 3x + 2)^2 - 5(-5x^2 + 3x + 2) - 5)) + 1) + 5)^2 - 4(4(2sin(2\u03c0(-4(-5x^2 + 3x + 2)^2 - 5(-5x^2 + 3x + 2) - 5)) + 1)^2 - 5(2sin(2\u03c0(-4(-5x^2 + 3x + 2)^2 - 5(-5x^2 + 3x + 2) - 5)) + 1) + 5) + 2, g(x) = -2(3e^(-1(-4(-1|x + 2| + 1)^2 - 4(-1|x + 2| + 1))) - 2) - 3, 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": "18.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -5(1|(1(3sin(2\u03c0((3x + 2)/(-2x - 1)) + 1) - 1)) - 1| - 1) + 3 and g(x) = (-1(-5(4(1x^2 + 4x + 1) + 5) - 1) - 2)/(1(-5(4(1x^2 + 4x + 1) + 5) - 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": "0.7", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3|(-3((3(-1|(-1|x - 1| - 1)| - 1) + 1)/(-3(-1|(-1|x - 1| - 1)| - 1)))^2 + 2((3(-1|(-1|x - 1| - 1)| - 1) + 1)/(-3(-1|(-1|x - 1| - 1)| - 1))) + 4)| - 3, g(x) = 4((1(-2(-3cos(1\u03c0x + 3) - 2)^2 + 5(-3cos(1\u03c0x + 3) - 2) - 3) + 3)/(-1(-2(-3cos(1\u03c0x + 3) - 2)^2 + 5(-3cos(1\u03c0x + 3) - 2) - 3) + 2)) - 1, x = 0.4, 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": "2.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (1((-3((-1(-3(-2sin(1\u03c0x - 1) - 3)^2 + 4(-2sin(1\u03c0x - 1) - 3) + 1) + 2)/(1(-3(-2sin(1\u03c0x - 1) - 3)^2 + 4(-2sin(1\u03c0x - 1) - 3) + 1) + 1)))/(-2((-1(-3(-2sin(1\u03c0x - 1) - 3)^2 + 4(-2sin(1\u03c0x - 1) - 3) + 1) + 2)/(1(-3(-2sin(1\u03c0x - 1) - 3)^2 + 4(-2sin(1\u03c0x - 1) - 3) + 1) + 1)) - 3)) - 2)/(1((-3((-1(-3(-2sin(1\u03c0x - 1) - 3)^2 + 4(-2sin(1\u03c0x - 1) - 3) + 1) + 2)/(1(-3(-2sin(1\u03c0x - 1) - 3)^2 + 4(-2sin(1\u03c0x - 1) - 3) + 1) + 1)))/(-2((-1(-3(-2sin(1\u03c0x - 1) - 3)^2 + 4(-2sin(1\u03c0x - 1) - 3) + 1) + 2)/(1(-3(-2sin(1\u03c0x - 1) - 3)^2 + 4(-2sin(1\u03c0x - 1) - 3) + 1) + 1)) - 3)) - 2) and g(x) = 1|(1sin(1\u03c0(5(-1|x + 3| - 1) - 2))) + 2| from x = -4.9 to x = -4.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-3(-1|(3(1sin(3\u03c0((-1x - 2)/(3x - 1))) - 3)) - 1| - 1) + 2)/(-1(-1|(3(1sin(3\u03c0((-1x - 2)/(3x - 1))) - 3)) - 1| - 1) - 2) and g(x) = (3(2(-3cos(2\u03c0(-2|x - 2| - 2) + 2) + 2) + 2) + 1)/(3(2(-3cos(2\u03c0(-2|x - 2| - 2) + 2) + 2) + 2) - 2) 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": "1.7", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 4((-1((1(1(5x + 1)^2 + 4(5x + 1) + 2) + 1)/(1(1(5x + 1)^2 + 4(5x + 1) + 2) + 1)) - 2)/(-1((1(1(5x + 1)^2 + 4(5x + 1) + 2) + 1)/(1(1(5x + 1)^2 + 4(5x + 1) + 2) + 1)) + 3)) - 1, g(x) = -1|(4(1(-1|x + 1| - 3)^2 + 4(-1|x + 1| - 3) - 3) + 1)| + 1, x = -2.2, 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": "19.9", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 3|(-3((-2(-3(5x^2 - 2x + 5)^2 + 3(5x^2 - 2x + 5) + 1) - 3)/(-3(-3(5x^2 - 2x + 5)^2 + 3(5x^2 - 2x + 5) + 1) - 3))^2 - 3((-2(-3(5x^2 - 2x + 5)^2 + 3(5x^2 - 2x + 5) + 1) - 3)/(-3(-3(5x^2 - 2x + 5)^2 + 3(5x^2 - 2x + 5) + 1) - 3)) - 5) - 3| - 3 and g(x) = 4(3|(-2(-1x^2 + 3x - 2)^2 - 2(-1x^2 + 3x - 2) + 1)| + 2) + 1 between the vertical lines x = 0.1 and x = 2.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30.6", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1(2|(1cos(3\u03c0(-2(-1x^2 + 3x - 5)^2 + 3(-1x^2 + 3x - 5) + 3) + 3) + 2) + 3| - 1) + 5 and g(x) = -2|(1sin(2\u03c0(1(-2x - 4) + 1) - 3) + 2) - 3| - 1 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1|((-3(5(-2|(1cos(2\u03c0x + 1) - 3) + 3| + 1) - 5))/(1(5(-2|(1cos(2\u03c0x + 1) - 3) + 3| + 1) - 5)))| - 3 and g(x) = 1(2(-5(-5x^2 - 4x + 4) - 3)^2 + 5(-5(-5x^2 - 4x + 4) - 3) - 4)^2 + 4(2(-5(-5x^2 - 4x + 4) - 3)^2 + 5(-5(-5x^2 - 4x + 4) - 3) - 4) + 3 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": "18.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2cos(3\u03c0(-1|((1(1(1x^2 + 1x + 3)^2 - 4(1x^2 + 1x + 3) - 4) + 1)/(2(1(1x^2 + 1x + 3)^2 - 4(1x^2 + 1x + 3) - 4))) - 1| + 2) - 2) + 2 and g(x) = -2(-1sin(3\u03c0(-1|(3|x + 3| + 2) - 3| - 3) - 2) - 1) - 1 between the vertical lines x = -0.0 and x = 0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 5(-1(-2|(4((3x - 1)/(-3x - 3))) + 2| + 3) - 3)^2 + 1(-1(-2|(4((3x - 1)/(-3x - 3))) + 2| + 3) - 3) + 5 and g(x) = -5((3(-4((2x - 2)/(-2x + 3))^2 + 4((2x - 2)/(-2x + 3)) - 4) - 1)/(-2(-4((2x - 2)/(-2x + 3))^2 + 4((2x - 2)/(-2x + 3)) - 4) + 1)) + 2 from x = -4.8 to x = -0.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10181.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2|(3cos(2\u03c0(4(1(-4x^2 - 1x + 4) + 2) - 4)) - 2) - 1| and g(x) = 1(-3(-2(3|x + 2| - 3)^2 - 4(3|x + 2| - 3) + 2) + 5)^2 + 1(-3(-2(3|x + 2| - 3)^2 - 4(3|x + 2| - 3) + 2) + 5) 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 3((2((3(-2cos(2\u03c0(2x + 5) - 3) - 3) - 3)/(2(-2cos(2\u03c0(2x + 5) - 3) - 3) + 2)) + 2)/(-2((3(-2cos(2\u03c0(2x + 5) - 3) - 3) - 3)/(2(-2cos(2\u03c0(2x + 5) - 3) - 3) + 2)) - 3)) + 1 and g(x) = (3(1((1(3sin(1\u03c0x - 1) - 3) - 3)/(1(3sin(1\u03c0x - 1) - 3) + 3)) - 2) - 2)/(-2(1((1(3sin(1\u03c0x - 1) - 3) - 3)/(1(3sin(1\u03c0x - 1) - 3) + 3)) - 2)) between the vertical lines x = -1.4 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) = 2(-1(-5(3(3x)^2 - 5(3x)) - 4) - 4)^2 - 4(-1(-5(3(3x)^2 - 5(3x)) - 4) - 4) + 1 and g(x) = (-1(-1|((3(4x - 4) - 2)/(1(4x - 4) + 3)) - 3|) + 3)/(-3(-1|((3(4x - 4) - 2)/(1(4x - 4) + 3)) - 3|) + 1) from x = 0.6 to x = 0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2(4(2sin(2\u03c0(-3(3|x + 1| + 3)^2 + 1(3|x + 1| + 3) + 5) - 2) - 1)^2 + 2(2sin(2\u03c0(-3(3|x + 1| + 3)^2 + 1(3|x + 1| + 3) + 5) - 2) - 1)) + 2 and g(x) = (1((1(3|(2x^2 - 4x + 5) + 1| - 1))/(2(3|(2x^2 - 4x + 5) + 1| - 1) + 3)) - 3)/(2((1(3|(2x^2 - 4x + 5) + 1| - 1))/(2(3|(2x^2 - 4x + 5) + 1| - 1) + 3))) from x = 1.4 to x = 1.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 3(1(1|(-1cos(2\u03c0(-1x^2 - 4) + 2)) - 1| + 2)) - 2 and g(x) = 2|(3|(-1|((2x - 1)/(2x + 1)) - 3|)| - 2) - 3| - 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": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3(-1|((-3(5(3cos(3\u03c0x) - 2)) + 2)/(-3(5(3cos(3\u03c0x) - 2)) + 1))| - 2)^2 - 2(-1|((-3(5(3cos(3\u03c0x) - 2)) + 2)/(-3(5(3cos(3\u03c0x) - 2)) + 1))| - 2) + 3, g(x) = (-3(4(3|(-3|x + 1| + 2)| - 3) + 5) + 1)/(-2(4(3|(-3|x + 1| + 2)| - 3) + 5) - 1), 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": "10.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1|(3e^(-1((1((1(-1|x + 3| + 1) - 3)/(-1(-1|x + 3| + 1) - 3)) + 3)/(-1((1(-1|x + 3| + 1) - 3)/(-1(-1|x + 3| + 1) - 3)) - 3))) + 1) + 1| - 3, g(x) = 1(-3(4(-1x^2 + 4) + 3)^2 - 3(4(-1x^2 + 4) + 3) + 5)^2 + 2(-3(4(-1x^2 + 4) + 3)^2 - 3(4(-1x^2 + 4) + 3) + 5) - 2, x = 2.2, and x = 2.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.8", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2((1(2sin(1\u03c0((2(4x^2 + 3) + 3)/(-2(4x^2 + 3) - 2)) - 1) - 3) + 3)/(2(2sin(1\u03c0((2(4x^2 + 3) + 3)/(-2(4x^2 + 3) - 2)) - 1) - 3) + 3))^2 - 1((1(2sin(1\u03c0((2(4x^2 + 3) + 3)/(-2(4x^2 + 3) - 2)) - 1) - 3) + 3)/(2(2sin(1\u03c0((2(4x^2 + 3) + 3)/(-2(4x^2 + 3) - 2)) - 1) - 3) + 3)) + 1 and g(x) = -4(3(-2|((1x + 2)/(2x - 1)) - 3|) + 3)^2 - 5(3(-2|((1x + 2)/(2x - 1)) - 3|) + 3) - 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": "1.4", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3(-2cos(1\u03c0(1|((-1(-3|x + 2| - 2))/(-3(-3|x + 2| - 2) - 3)) + 1| - 2) - 3) - 2) + 5, g(x) = -1|(-2cos(3\u03c0(-4(3x^2 - 2x + 5) + 5) + 3) + 2)| + 3, 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-3(2(2|(3(1e^(-2x))^2 + 4(1e^(-2x)) - 1)|) - 3) - 3)/(-3(2(2|(3(1e^(-2x))^2 + 4(1e^(-2x)) - 1)|) - 3) - 1) and g(x) = -5((-2(-3sin(2\u03c0(-5x + 2) - 3)) - 1)/(1(-3sin(2\u03c0(-5x + 2) - 3))))^2 + 5((-2(-3sin(2\u03c0(-5x + 2) - 3)) - 1)/(1(-3sin(2\u03c0(-5x + 2) - 3)))) + 5 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": "5.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -4((-2(1|((1((-1x + 1)/(-3x - 3)))/(-2((-1x + 1)/(-3x - 3)) - 2)) + 2| - 1) + 1)/(-2(1|((1((-1x + 1)/(-3x - 3)))/(-2((-1x + 1)/(-3x - 3)) - 2)) + 2| - 1) - 3)) + 3 and g(x) = 3((1(-1cos(3\u03c0(3|x - 3|)) + 1) + 2)/(3(-1cos(3\u03c0(3|x - 3|)) + 1) + 3))^2 + 5((1(-1cos(3\u03c0(3|x - 3|)) + 1) + 2)/(3(-1cos(3\u03c0(3|x - 3|)) + 1) + 3)) - 1 from x = 3.8 to x = 3.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 3|((3((-1(4(-2x^2 - 4x - 3) + 2) + 3)/(-1(4(-2x^2 - 4x - 3) + 2))) - 2)/(2((-1(4(-2x^2 - 4x - 3) + 2) + 3)/(-1(4(-2x^2 - 4x - 3) + 2))) + 3))| - 3 and g(x) = 3(1|(3(-2|x| + 1)^2 - 4(-2|x| + 1) - 4) - 3| - 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3((-2(2|((-2(-4x^2 + 2x + 5) + 2)/(-1(-4x^2 + 2x + 5) - 3)) + 2| - 1) + 2)/(-2(2|((-2(-4x^2 + 2x + 5) + 2)/(-1(-4x^2 + 2x + 5) - 3)) + 2| - 1) + 3)) - 1 and g(x) = 3(1e^(-1(-3(5x - 2) - 2)) - 3) - 4 from x = -0.9 to x = 0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9.6", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (1((-1(-3cos(3\u03c0(3(2x^2 - 4x + 3)^2 - 2(2x^2 - 4x + 3) - 5) + 3) + 1) - 1)/(-2(-3cos(3\u03c0(3(2x^2 - 4x + 3)^2 - 2(2x^2 - 4x + 3) - 5) + 3) + 1) + 1)))/(-2((-1(-3cos(3\u03c0(3(2x^2 - 4x + 3)^2 - 2(2x^2 - 4x + 3) - 5) + 3) + 1) - 1)/(-2(-3cos(3\u03c0(3(2x^2 - 4x + 3)^2 - 2(2x^2 - 4x + 3) - 5) + 3) + 1) + 1)) - 1) and g(x) = 3|((-2(1|(1|x|)| - 3))/(2(1|(1|x|)| - 3) + 3)) - 2| - 3 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": "6.4", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3|(1(-2sin(2\u03c0(-1|(-5x^2 - 2x + 3) - 3| + 2)))^2 + 1(-2sin(2\u03c0(-1|(-5x^2 - 2x + 3) - 3| + 2)))) - 2| - 1 and g(x) = 4(-2e^(-1((1((2x + 2)/(-1x - 1)) + 2)/(2((2x + 2)/(-1x - 1)) - 1))) - 1) + 5 between the vertical lines x = 1.3 and x = 1.4000000000000001. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3|(-2|((-2((-3(-2x^2 - 4x + 3) + 2)/(-2(-2x^2 - 4x + 3) - 2)) - 1)/(2((-3(-2x^2 - 4x + 3) + 2)/(-2(-2x^2 - 4x + 3) - 2)) - 3))| - 2) + 3|, g(x) = 2(1(5(2x^2 + 1x - 3)^2 + 1(2x^2 + 1x - 3) - 3)^2 - 2(5(2x^2 + 1x - 3)^2 + 1(2x^2 + 1x - 3) - 3) + 1)^2 + 3(1(5(2x^2 + 1x - 3)^2 + 1(2x^2 + 1x - 3) - 3)^2 - 2(5(2x^2 + 1x - 3)^2 + 1(2x^2 + 1x - 3) - 3) + 1), x = 0.8, and x = 1.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "86.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (3(-2(-4((-1(-1x^2 + 4x + 2) - 2)/(-1(-1x^2 + 4x + 2) - 3))^2 + 2) + 5) - 2)/(-3(-2(-4((-1(-1x^2 + 4x + 2) - 2)/(-1(-1x^2 + 4x + 2) - 3))^2 + 2) + 5) + 1) and g(x) = -1sin(3\u03c0(-2|(1|(-5x^2 + 1x) - 2| + 1) + 2| + 2) - 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": "Determine the area of the region enclosed by the graphs of f(x) = -5((2(1((3(-3x - 2) + 2)/(-2(-3x - 2))) - 5) + 2)/(2(1((3(-3x - 2) + 2)/(-2(-3x - 2))) - 5) + 3)) - 5 and g(x) = -4(5((-2(-3|x + 3| + 2) + 3)/(-1(-3|x + 3| + 2) + 2))^2 + 1) - 4 between the vertical lines x = -2.9 and x = -2.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2|((-3(1((2((2x - 1)/(1x - 2)))/(3((2x - 1)/(1x - 2)) - 1)) + 1) - 1)/(2(1((2((2x - 1)/(1x - 2)))/(3((2x - 1)/(1x - 2)) - 1)) + 1) - 1))| - 3 and g(x) = 4((2(2|(-1|x - 2|) - 1|) + 1)/(-2(2|(-1|x - 2|) - 1|) + 3))^2 - 5((2(2|(-1|x - 2|) - 1|) + 1)/(-2(2|(-1|x - 2|) - 1|) + 3)) from x = 0.4 to x = 0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1(2|(-4(-2|(2x - 2) - 1| + 1)^2 - 1(-2|(2x - 2) - 1| + 1) + 2) - 2| + 1)^2 - 1(2|(-4(-2|(2x - 2) - 1| + 1)^2 - 1(-2|(2x - 2) - 1| + 1) + 2) - 2| + 1) + 2 and g(x) = (3(-3|(1|(-2x) + 1| - 1) + 3| + 2) + 2)/(-2(-3|(1|(-2x) + 1| - 1) + 3| + 2) + 3) between the vertical lines x = 1.2 and x = 1.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 5((-2(-2(2((1x + 3)/(3x))^2 - 1((1x + 3)/(3x)) - 4) - 4) - 1)/(-3(-2(2((1x + 3)/(3x))^2 - 1((1x + 3)/(3x)) - 4) - 4) + 1)) - 2 and g(x) = 4(-4(-1|(-2sin(2\u03c0x) + 3) - 1| + 3)^2 - 2) + 3 between the vertical lines x = -0.9 and x = 1.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "106.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1e^(2(1((3(-1|(-1x^2 + 4x + 3) - 2| + 2) - 3)/(-2(-1|(-1x^2 + 4x + 3) - 2| + 2) + 1)))) + 3 and g(x) = (-3((-1(3cos(1\u03c0(-2|x - 1| - 2) + 1) - 2) + 1)/(3(3cos(1\u03c0(-2|x - 1| - 2) + 1) - 2) + 1)) + 1)/(2((-1(3cos(1\u03c0(-2|x - 1| - 2) + 1) - 2) + 1)/(3(3cos(1\u03c0(-2|x - 1| - 2) + 1) - 2) + 1)) + 3) between the vertical lines x = -4.4 and x = -4.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-2((-1(1|(-3e^(1(1|x - 2| + 3)) + 3) - 2| - 3) - 2)/(-1(1|(-3e^(1(1|x - 2| + 3)) + 3) - 2| - 3))) + 1)/(-2((-1(1|(-3e^(1(1|x - 2| + 3)) + 3) - 2| - 3) - 2)/(-1(1|(-3e^(1(1|x - 2| + 3)) + 3) - 2| - 3))) + 1) and g(x) = (-2((-2(4((-1x + 2)/(-3x + 4))^2 - 2) + 2)/(2(4((-1x + 2)/(-3x + 4))^2 - 2))) + 3)/(1((-2(4((-1x + 2)/(-3x + 4))^2 - 2) + 2)/(2(4((-1x + 2)/(-3x + 4))^2 - 2)))) between the vertical lines x = 0.8 and x = 1.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7.9", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (1(-5(1(-1(-5x^2 + 4x - 2)^2 - 5(-5x^2 + 4x - 2) - 4) - 2)^2 - 4(1(-1(-5x^2 + 4x - 2)^2 - 5(-5x^2 + 4x - 2) - 4) - 2)))/(2(-5(1(-1(-5x^2 + 4x - 2)^2 - 5(-5x^2 + 4x - 2) - 4) - 2)^2 - 4(1(-1(-5x^2 + 4x - 2)^2 - 5(-5x^2 + 4x - 2) - 4) - 2)) + 2), g(x) = 2(3sin(3\u03c0(3(1|x + 1| + 3)^2 - 2(1|x + 1| + 3) - 1) + 1) - 2)^2 + 1(3sin(3\u03c0(3(1|x + 1| + 3)^2 - 2(1|x + 1| + 3) - 1) + 1) - 2) + 1, x = 0.9, and x = 1.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1(-1(2|(1((-1x - 3)/(1x))^2 - 5((-1x - 3)/(1x)) + 3) + 2|)) - 5, g(x) = -3cos(3\u03c0(4(2(-3|x + 3| - 3)) + 5) + 3) - 3, 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": "1.9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3|(-2|(-1|(-1(1e^(-1x) + 1)^2 + 2(1e^(-1x) + 1) - 4)| + 2) + 2| - 3) + 1| + 2 and g(x) = -3|(1|(2(-3sin(1\u03c0x - 3) - 2) - 3) + 2|) + 2| - 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": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2(4(1(3(2|x| - 3)^2 - 2(2|x| - 3) + 2) - 3)^2 - 5) + 1 and g(x) = -2|((1(-3(-3x^2 - 4x + 2)^2 - 5(-3x^2 - 4x + 2) - 1) + 1)/(3(-3(-3x^2 - 4x + 2)^2 - 5(-3x^2 - 4x + 2) - 1) + 1)) - 2| - 1 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2sin(1\u03c0((-2(3(-1|((1x + 2)/(1x)) - 3| - 1) - 5) + 3)/(3(3(-1|((1x + 2)/(1x)) - 3| - 1) - 5) + 1)) + 3) - 1 and g(x) = -1(3e^(-2(1(-5x + 1)^2 - 2(-5x + 1))))^2 - 1 between the vertical lines x = -0.2 and x = 0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "86.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (2((3(-3cos(2\u03c0((-1(-4x - 3) + 2)/(-2(-4x - 3) - 1)) - 1) + 1) - 2)/(3(-3cos(2\u03c0((-1(-4x - 3) + 2)/(-2(-4x - 3) - 1)) - 1) + 1) + 2)) + 1)/(1((3(-3cos(2\u03c0((-1(-4x - 3) + 2)/(-2(-4x - 3) - 1)) - 1) + 1) - 2)/(3(-3cos(2\u03c0((-1(-4x - 3) + 2)/(-2(-4x - 3) - 1)) - 1) + 1) + 2))) and g(x) = 1(2(1(-3sin(3\u03c0x) + 3) + 2) + 5)^2 - 5(2(1(-3sin(3\u03c0x) + 3) + 2) + 5) - 5 from x = -1.2 to x = 0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "213.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1|(1((-2(-1cos(1\u03c0((3x - 3)/(2x + 3)) - 2) - 2) - 1)/(1(-1cos(1\u03c0((3x - 3)/(2x + 3)) - 2) - 2) + 3)) + 2) - 3| and g(x) = (-1((1(1|(-1x^2 + 3x - 1) - 3| - 3) - 1)/(2(1|(-1x^2 + 3x - 1) - 3| - 3) + 3)) + 3)/(-3((1(1|(-1x^2 + 3x - 1) - 3| - 3) - 1)/(2(1|(-1x^2 + 3x - 1) - 3| - 3) + 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": "213.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -4(3|(-1((1(2x - 5) + 3)/(1(2x - 5) + 2))^2 + 2((1(2x - 5) + 3)/(1(2x - 5) + 2)) + 1) + 3| - 3) - 5, g(x) = 1|(2(-1|((1x - 1)/(2x + 2))| - 1)^2 - 3(-1|((1x - 1)/(2x + 2))| - 1) + 3) - 3|, 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": "8.9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1|((-2(-3|(-2cos(3\u03c0(-3x - 2) + 3) - 2) - 3| - 2) + 1)/(1(-3|(-2cos(3\u03c0(-3x - 2) + 3) - 2) - 3| - 2) - 2)) + 1| and g(x) = 2cos(2\u03c0(-1(1((2x - 2)/(2x - 3)) + 4)^2 - 2(1((2x - 2)/(2x - 3)) + 4)) + 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-2(-5((2(1(2x + 3)^2 + 3(2x + 3) + 3))/(1(1(2x + 3)^2 + 3(2x + 3) + 3))) + 5) - 3)/(-2(-5((2(1(2x + 3)^2 + 3(2x + 3) + 3))/(1(1(2x + 3)^2 + 3(2x + 3) + 3))) + 5) + 3) and g(x) = 3sin(3\u03c0(-2(1((-2x - 3)/(1x + 2)) + 1) + 4) + 2) - 2 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3|(1sin(2\u03c0(-2|(5(3x^2 + 5x - 5) - 1) + 1|) - 3) + 2) - 2| - 3 and g(x) = -3(1(2(1x)^2 - 2(1x) + 2)^2 - 3(2(1x)^2 - 2(1x) + 2) - 1) + 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -4(3|(4(3sin(3\u03c0(-3|x + 2|) - 2) - 3)^2 - 4(3sin(3\u03c0(-3|x + 2|) - 2) - 3) - 1) - 2| - 3) + 5 and g(x) = 2(1|(-2|(-4x^2 - 4x + 2) - 3| - 2) + 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": "18.5", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2sin(1\u03c0(-2|(2(4(-2x)^2 + 3(-2x) - 1)^2 - 1(4(-2x)^2 + 3(-2x) - 1) - 3) - 1| + 1) + 3) + 3, g(x) = (-1((-3((-1(2x^2 + 2x - 4) - 2)/(3(2x^2 + 2x - 4) + 1)) + 3)/(-2((-1(2x^2 + 2x - 4) - 2)/(3(2x^2 + 2x - 4) + 1)) - 2)) + 2)/(-1((-3((-1(2x^2 + 2x - 4) - 2)/(3(2x^2 + 2x - 4) + 1)) + 3)/(-2((-1(2x^2 + 2x - 4) - 2)/(3(2x^2 + 2x - 4) + 1)) - 2))), x = 2.5, 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-2(-1(2|((-3(-3x^2 + 4x + 4) + 1)/(-3(-3x^2 + 4x + 4) + 2)) + 3|) + 2) + 3)/(3(-1(2|((-3(-3x^2 + 4x + 4) + 1)/(-3(-3x^2 + 4x + 4) + 2)) + 3|) + 2) + 2), g(x) = -1(5(1(1|x| - 2) - 1) - 5)^2 - 3(5(1(1|x| - 2) - 1) - 5) + 5, x = -4.3, 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": "6.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-1(2|((3(5(1x^2 - 3x - 4) + 5) + 1)/(2(5(1x^2 - 3x - 4) + 5) - 1))| - 2) - 2)/(-3(2|((3(5(1x^2 - 3x - 4) + 5) + 1)/(2(5(1x^2 - 3x - 4) + 5) - 1))| - 2) + 4) and g(x) = 2(2cos(3\u03c0(1((-3x - 1)/(-2x - 3))^2 + 3((-3x - 1)/(-2x - 3)))) + 1) + 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1(-1|(-4(2(-3cos(3\u03c0x - 1) + 3) - 4)^2 + 1(2(-3cos(3\u03c0x - 1) + 3) - 4) - 1)| - 3) + 1 and g(x) = (-1(-3cos(3\u03c0(-1|(5x + 5) - 1| - 2) - 3) - 2) + 1)/(3(-3cos(3\u03c0(-1|(5x + 5) - 1| - 2) - 3) - 2) - 1) from x = 0.6 to x = 2.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "187.6", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1|(1(-2(1|(5x + 4) - 1| + 3)^2 + 4(1|(5x + 4) - 1| + 3) + 2) + 5) - 1| + 1 and g(x) = 5((-2(-5(-3|x| - 2)^2 - 2(-3|x| - 2) - 1) + 1)/(-2(-5(-3|x| - 2)^2 - 2(-3|x| - 2) - 1) + 3))^2 - 5((-2(-5(-3|x| - 2)^2 - 2(-3|x| - 2) - 1) + 1)/(-2(-5(-3|x| - 2)^2 - 2(-3|x| - 2) - 1) + 3)) - 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": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-2(2((-1(-2|((-2x - 2)/(-3x - 2)) + 1| - 3))/(2(-2|((-2x - 2)/(-3x - 2)) + 1| - 3))) - 4) - 1)/(-3(2((-1(-2|((-2x - 2)/(-3x - 2)) + 1| - 3))/(2(-2|((-2x - 2)/(-3x - 2)) + 1| - 3))) - 4) + 2) and g(x) = (-1(3(-2|(1|x - 3| + 2) - 3| + 3) - 5) - 3)/(2(3(-2|(1|x - 3| + 2) - 3| + 3) - 5)) between the vertical lines x = 1.1 and x = 2.9. 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": "Calculate the area enclosed between the functions f(x) = 2(-2sin(1\u03c0((-1(5((1x - 3)/(-2x + 3)) + 1) - 3)/(-3(5((1x - 3)/(-2x + 3)) + 1) + 4)) - 2)) and g(x) = 1sin(3\u03c0((3(-4(1x - 2) + 5) - 3)/(-3(-4(1x - 2) + 5) - 3))) + 2 from x = 2.9 to x = 3.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -3(-1|(-2|((2(-4x + 4) - 2)/(-3(-4x + 4))) - 1| + 3) - 3|) - 1, g(x) = -2|((-2(5(3x^2 + 1x)^2 - 2(3x^2 + 1x) + 4) + 3)/(2(5(3x^2 + 1x)^2 - 2(3x^2 + 1x) + 4) + 1)) + 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": "23.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-1(-4(2|(1cos(3\u03c0(3|x - 3| - 2) - 2) - 1) + 2|)^2 + 3(2|(1cos(3\u03c0(3|x - 3| - 2) - 2) - 1) + 2|) + 1) - 1)/(-1(-4(2|(1cos(3\u03c0(3|x - 3| - 2) - 2) - 1) + 2|)^2 + 3(2|(1cos(3\u03c0(3|x - 3| - 2) - 2) - 1) + 2|) + 1) - 2) and g(x) = 2cos(1\u03c0(-3|((-3((-2x - 3)/(-3x + 2)) + 3)/(3((-2x - 3)/(-3x + 2)) + 3)) - 2| + 3) - 3) + 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2|(1|((2((2(-3|x + 3| - 1) - 1)/(1(-3|x + 3| - 1) - 3)) + 2)/(-2((2(-3|x + 3| - 1) - 1)/(1(-3|x + 3| - 1) - 3)) + 3)) + 1| + 2) - 1| - 2, g(x) = (-2(3sin(2\u03c0(3(-1|x - 3| - 3) + 1) - 3)) + 2)/(2(3sin(2\u03c0(3(-1|x - 3| - 3) + 1) - 3)) + 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": "3.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (3(5(1|(-3(3cos(1\u03c0x - 2) - 1) + 4) + 1| - 1)^2 + 3(1|(-3(3cos(1\u03c0x - 2) - 1) + 4) + 1| - 1) - 1) - 2)/(3(5(1|(-3(3cos(1\u03c0x - 2) - 1) + 4) + 1| - 1)^2 + 3(1|(-3(3cos(1\u03c0x - 2) - 1) + 4) + 1| - 1) - 1) + 2) and g(x) = -1|(-2|(-1(-4x - 4) - 2) + 3|) + 3| + 1 between the vertical lines x = 2.8 and x = 4.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "75.6", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (2(1((-3(2cos(1\u03c0(-3|x + 3|))) - 2)/(2(2cos(1\u03c0(-3|x + 3|))) + 1))^2 - 3((-3(2cos(1\u03c0(-3|x + 3|))) - 2)/(2(2cos(1\u03c0(-3|x + 3|))) + 1))) + 3)/(-2(1((-3(2cos(1\u03c0(-3|x + 3|))) - 2)/(2(2cos(1\u03c0(-3|x + 3|))) + 1))^2 - 3((-3(2cos(1\u03c0(-3|x + 3|))) - 2)/(2(2cos(1\u03c0(-3|x + 3|))) + 1))) - 3) and g(x) = -3((-1(-3cos(3\u03c0((-2x - 2)/(-3x + 4)) - 3) - 1) - 3)/(2(-3cos(3\u03c0((-2x - 2)/(-3x + 4)) - 3) - 1) + 1)) + 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": "1.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -4(1((-1(5(2|x - 3| - 2) + 1) - 3)/(-2(5(2|x - 3| - 2) + 1) + 1))) + 5, g(x) = -3(2sin(3\u03c0(4(3x - 4) - 1) + 3) - 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": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1sin(3\u03c0(2(3|(3(3|x + 1| - 1)^2 + 5(3|x + 1| - 1) + 1) + 2|) + 3) - 2), g(x) = -3sin(3\u03c0(-1(-2(1|x - 1| - 3)^2 - 5(1|x - 1| - 3) - 1)^2 + 4(-2(1|x - 1| - 3)^2 - 5(1|x - 1| - 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": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1|(1(1(-3(2e^(1x) + 1)^2 - 5(2e^(1x) + 1)) + 2) + 2) - 1| + 3, g(x) = 3|(-1(2sin(1\u03c0(-5x^2 - 1x)) + 3)) - 3| + 2, x = -1.4, and x = -1.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.7", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 4(1(-2((2(-5x^2 - 4x) - 2)/(-2(-5x^2 - 4x) - 3)) - 2) + 3) + 1 and g(x) = (-3(4(2|(-2sin(1\u03c0x + 2) + 1) - 1| + 1)^2 + 4(2|(-2sin(1\u03c0x + 2) + 1) - 1| + 1) - 2) + 2)/(1(4(2|(-2sin(1\u03c0x + 2) + 1) - 1| + 1)^2 + 4(2|(-2sin(1\u03c0x + 2) + 1) - 1| + 1) - 2)) between the vertical lines x = -0.9 and x = 0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2|(5((1(3e^(-2((1x + 2)/(2x + 3))) + 2) - 2)/(1(3e^(-2((1x + 2)/(2x + 3))) + 2))) + 4) + 3| - 3 and g(x) = -2|(-2|((-3((-3x - 2)/(-2x)) + 3)/(-3((-3x - 2)/(-2x)) + 1)) + 2| + 1) - 2| between the vertical lines x = -0.9 and x = -0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "87.7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (1(-2sin(1\u03c0(5(2(-4x^2 - 2)^2 - 1(-4x^2 - 2) - 5)^2 - 4)) + 3) + 3)/(-2(-2sin(1\u03c0(5(2(-4x^2 - 2)^2 - 1(-4x^2 - 2) - 5)^2 - 4)) + 3) + 3) and g(x) = 2((-1((-2(-2|x - 2| + 2) + 3)/(1(-2|x - 2| + 2))))/(3((-2(-2|x - 2| + 2) + 3)/(1(-2|x - 2| + 2))) - 2))^2 - 1((-1((-2(-2|x - 2| + 2) + 3)/(1(-2|x - 2| + 2))))/(3((-2(-2|x - 2| + 2) + 3)/(1(-2|x - 2| + 2))) - 2)) + 4 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": "0.7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (1(-1cos(2\u03c0((2((2(-3|x - 2| - 3) + 1)/(-1(-3|x - 2| - 3) + 3)) + 3)/(-3((2(-3|x - 2| - 3) + 1)/(-1(-3|x - 2| - 3) + 3)) + 1)) + 2)) + 1)/(1(-1cos(2\u03c0((2((2(-3|x - 2| - 3) + 1)/(-1(-3|x - 2| - 3) + 3)) + 3)/(-3((2(-3|x - 2| - 3) + 1)/(-1(-3|x - 2| - 3) + 3)) + 1)) + 2)) + 2) and g(x) = -2(3(1|(-2|x + 1| + 3)| - 3) + 5) - 5 from x = 0.3 to x = 0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 5(4(3|((-1(-3|x + 2| + 3) + 3)/(1(-3|x + 2| + 3))) + 1|)^2 - 2(3|((-1(-3|x + 2| + 3) + 3)/(1(-3|x + 2| + 3))) + 1|) + 1)^2 + 1, g(x) = 1|(-5(-2(-2sin(3\u03c0x - 2) + 2)^2 - 5(-2sin(3\u03c0x - 2) + 2) + 2) + 5) - 1| - 1, x = 3.8, 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": "64.6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 5(1(-1e^(1((-3((2x - 2)/(3x - 1)) + 3)/(2((2x - 2)/(3x - 1)) - 1))) - 1)^2 + 3(-1e^(1((-3((2x - 2)/(3x - 1)) + 3)/(2((2x - 2)/(3x - 1)) - 1))) - 1) + 4)^2 - 2(1(-1e^(1((-3((2x - 2)/(3x - 1)) + 3)/(2((2x - 2)/(3x - 1)) - 1))) - 1)^2 + 3(-1e^(1((-3((2x - 2)/(3x - 1)) + 3)/(2((2x - 2)/(3x - 1)) - 1))) - 1) + 4) + 4 and g(x) = 1(1|(2((-1x - 3)/(-3x)) + 3) - 3| - 3) + 5 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": "88.7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1(-2(-3|(-3sin(3\u03c0((-1x + 1)/(3x - 2)) + 2) - 3) + 1| + 3)^2 - 2(-3|(-3sin(3\u03c0((-1x + 1)/(3x - 2)) + 2) - 3) + 1| + 3) + 2)^2 - 2(-2(-3|(-3sin(3\u03c0((-1x + 1)/(3x - 2)) + 2) - 3) + 1| + 3)^2 - 2(-3|(-3sin(3\u03c0((-1x + 1)/(3x - 2)) + 2) - 3) + 1| + 3) + 2) and g(x) = (1(2(2(2|x - 2|)^2 - 3(2|x - 2|) + 3)^2 - 4(2(2|x - 2|)^2 - 3(2|x - 2|) + 3)) + 1)/(1(2(2(2|x - 2|)^2 - 3(2|x - 2|) + 3)^2 - 4(2(2|x - 2|)^2 - 3(2|x - 2|) + 3))) from x = 2.3 to x = 2.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7.6", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3((2(-1|((2((-1x - 3)/(-1x - 1)) - 2)/(2((-1x - 3)/(-1x - 1)) + 2)) - 1| + 2) - 3)/(-2(-1|((2((-1x - 3)/(-1x - 1)) - 2)/(2((-1x - 3)/(-1x - 1)) + 2)) - 1| + 2) - 1)), g(x) = (2(-3(-1(1|x + 1| - 2)^2 + 5(1|x + 1| - 2))^2 - 5(-1(1|x + 1| - 2)^2 + 5(1|x + 1| - 2)) + 2) + 3)/(1(-3(-1(1|x + 1| - 2)^2 + 5(1|x + 1| - 2))^2 - 5(-1(1|x + 1| - 2)^2 + 5(1|x + 1| - 2)) + 2) + 2), x = -2.6, 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": "18.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2sin(3\u03c0(3((-1(-2|(-2x^2 + 3x - 4) + 3| - 3) + 1)/(3(-2|(-2x^2 + 3x - 4) + 3| - 3) - 1)) - 5) + 1) + 1, g(x) = -3e^(2(-3|((3(2|x| - 1) - 1)/(-2(2|x| - 1) - 2)) - 3| + 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": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (2(3sin(2\u03c0(1(-1(2|x + 2|) + 2)^2 + 1(-1(2|x + 2|) + 2) + 1) + 1)))/(2(3sin(2\u03c0(1(-1(2|x + 2|) + 2)^2 + 1(-1(2|x + 2|) + 2) + 1) + 1)) - 1), g(x) = 2((-1(-2cos(1\u03c0(-2|x + 3|)) - 1) - 2)/(1(-2cos(1\u03c0(-2|x + 3|)) - 1))) + 1, x = -4.1, 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (2(-4((-3(-1|(-3|x - 2| + 3) + 1| + 3) - 1)/(-1(-1|(-3|x - 2| + 3) + 1| + 3) + 2)) - 1) - 2)/(2(-4((-3(-1|(-3|x - 2| + 3) + 1| + 3) - 1)/(-1(-1|(-3|x - 2| + 3) + 1| + 3) + 2)) - 1)) and g(x) = 4(-2|(-5(-3sin(1\u03c0x - 1)) - 2) + 3| + 1)^2 - 3(-2|(-5(-3sin(1\u03c0x - 1)) - 2) + 3| + 1) + 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": "2.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1((3((3(-1|(1cos(2\u03c0x - 2) + 2)| + 1) - 1)/(3(-1|(1cos(2\u03c0x - 2) + 2)| + 1) + 3)) - 2)/(2((3(-1|(1cos(2\u03c0x - 2) + 2)| + 1) - 1)/(3(-1|(1cos(2\u03c0x - 2) + 2)| + 1) + 3)) - 3))^2 - 5((3((3(-1|(1cos(2\u03c0x - 2) + 2)| + 1) - 1)/(3(-1|(1cos(2\u03c0x - 2) + 2)| + 1) + 3)) - 2)/(2((3(-1|(1cos(2\u03c0x - 2) + 2)| + 1) - 1)/(3(-1|(1cos(2\u03c0x - 2) + 2)| + 1) + 3)) - 3)) - 2 and g(x) = -3|((-3((-1((-1x - 1)/(3x + 1)) + 2)/(2((-1x - 1)/(3x + 1)) - 3)) - 2)/(-3((-1((-1x - 1)/(3x + 1)) + 2)/(2((-1x - 1)/(3x + 1)) - 3)) + 4)) + 3| + 1 between the vertical lines x = 1.7 and x = 2.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1|((2(2sin(3\u03c0(-2|((3x + 1)/(1x + 2)) - 2| - 3) + 3)) + 3)/(3(2sin(3\u03c0(-2|((3x + 1)/(1x + 2)) - 2| - 3) + 3)) - 2)) - 1| - 1 and g(x) = (-3(4(-1(-3e^(2x) - 2) - 5) + 4))/(2(4(-1(-3e^(2x) - 2) - 5) + 4) - 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": "0.7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -5(-2(3((3(3sin(1\u03c0x - 2) - 1) + 1)/(2(3sin(1\u03c0x - 2) - 1) - 1)) - 1)^2 + 2(3((3(3sin(1\u03c0x - 2) - 1) + 1)/(2(3sin(1\u03c0x - 2) - 1) - 1)) - 1) + 2) - 5 and g(x) = -1|(-3(-4(5x^2 + 4x) - 1)^2 + 4(-4(5x^2 + 4x) - 1)) + 1| + 1 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": "0.9", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -4((-2(-3(-1|(3|x - 2| + 2) - 3|)^2 + 2(-1|(3|x - 2| + 2) - 3|)) + 1)/(-3(-3(-1|(3|x - 2| + 2) - 3|)^2 + 2(-1|(3|x - 2| + 2) - 3|)) - 3)) + 1 and g(x) = -1|(1e^(-1(5(-1x^2 + 2x + 4)^2 - 1(-1x^2 + 2x + 4))) - 2) - 2| - 3 between the vertical lines x = 1.8 and x = 2.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (2(1|((2(3e^(2(1x - 3)) - 2) - 2)/(-1(3e^(2(1x - 3)) - 2) + 2)) - 3|) - 1)/(3(1|((2(3e^(2(1x - 3)) - 2) - 2)/(-1(3e^(2(1x - 3)) - 2) + 2)) - 3|)) and g(x) = -1|((2((1(-5x - 3))/(-1(-5x - 3) + 2)) - 3)/(3((1(-5x - 3))/(-1(-5x - 3) + 2)) - 2)) - 1| + 1 between the vertical lines x = -1.0 and x = -0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3|(3(-1(2((3x + 1)/(2x - 1))^2 - 4((3x + 1)/(2x - 1)) + 1)^2 + 1(2((3x + 1)/(2x - 1))^2 - 4((3x + 1)/(2x - 1)) + 1) + 5) - 3) - 3| + 2 and g(x) = -5(-2((-3(-3sin(3\u03c0x + 1) + 3))/(-3(-3sin(3\u03c0x + 1) + 3) + 4))^2 + 2((-3(-3sin(3\u03c0x + 1) + 3))/(-3(-3sin(3\u03c0x + 1) + 3) + 4)) + 3)^2 + 3(-2((-3(-3sin(3\u03c0x + 1) + 3))/(-3(-3sin(3\u03c0x + 1) + 3) + 4))^2 + 2((-3(-3sin(3\u03c0x + 1) + 3))/(-3(-3sin(3\u03c0x + 1) + 3) + 4)) + 3) + 5 between the vertical lines x = 1.3 and x = 1.4000000000000001. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "55.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (1(2(2((1(-3|x - 3| + 1) - 2)/(1(-3|x - 3| + 1) - 3))^2 + 4((1(-3|x - 3| + 1) - 2)/(1(-3|x - 3| + 1) - 3)) - 1) + 2) - 1)/(-3(2(2((1(-3|x - 3| + 1) - 2)/(1(-3|x - 3| + 1) - 3))^2 + 4((1(-3|x - 3| + 1) - 2)/(1(-3|x - 3| + 1) - 3)) - 1) + 2) + 4) and g(x) = (-3(4(-2sin(2\u03c0(3|x + 2| - 3) - 2)) - 2) - 2)/(-2(4(-2sin(2\u03c0(3|x + 2| - 3) - 2)) - 2) + 3) from x = 3.0 to x = 3.1. 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(-3((2(3|x - 3| - 2) + 1)/(-2(3|x - 3| - 2) - 2))^2 + 2((2(3|x - 3| - 2) + 1)/(-2(3|x - 3| - 2) - 2)) + 1)^2 - 2(-3((2(3|x - 3| - 2) + 1)/(-2(3|x - 3| - 2) - 2))^2 + 2((2(3|x - 3| - 2) + 1)/(-2(3|x - 3| - 2) - 2)) + 1) - 1) - 3, g(x) = 1|((-2(-2(-1|x - 3| + 3)^2 + 2(-1|x - 3| + 3) + 5) - 2)/(-1(-2(-1|x - 3| + 3)^2 + 2(-1|x - 3| + 3) + 5) + 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": "2.6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2(-2e^(-1(2(-5((-2x + 2)/(-2x - 1)) - 2)^2 - 5(-5((-2x + 2)/(-2x - 1)) - 2) - 1)) - 2) + 5 and g(x) = 5(2|(-4(-1e^(1x) + 2)^2 - 3(-1e^(1x) + 2))| + 1) - 5 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": "33.4", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2(-2|(5((-3(-3x))/(2(-3x) + 2)) + 3)| + 2) - 2 and g(x) = (1((2(3|(-3|x - 3| - 1) - 1| + 1) + 1)/(-1(3|(-3|x - 3| - 1) - 1| + 1) - 2)) + 1)/(-1((2(3|(-3|x - 3| - 1) - 1| + 1) + 1)/(-1(3|(-3|x - 3| - 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": "Determine the area of the region enclosed by the graphs of f(x) = 2(1(-1sin(2\u03c0(-2|(-3x^2 + 2x + 1) + 2| - 3) + 1) + 3)^2 - 2(-1sin(2\u03c0(-2|(-3x^2 + 2x + 1) + 2| - 3) + 1) + 3) + 5)^2 - 1(1(-1sin(2\u03c0(-2|(-3x^2 + 2x + 1) + 2| - 3) + 1) + 3)^2 - 2(-1sin(2\u03c0(-2|(-3x^2 + 2x + 1) + 2| - 3) + 1) + 3) + 5) - 2 and g(x) = 1(4(-3|((1x - 1)/(1x)) + 2| + 1))^2 + 1(4(-3|((1x - 1)/(1x)) + 2| + 1)) 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": "18.9", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2e^(-2(1|(-3|(-4(-5x^2 - 4x + 4)^2 - 5(-5x^2 - 4x + 4) + 4) + 1| + 1)|)) + 2, g(x) = 1|(-2(3((1x - 1)/(3x))^2 + 4((1x - 1)/(3x)) + 5) + 5) - 1| - 1, x = 0.5, and x = 0.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 5(2|(-1|(2(4x - 2)^2 - 4(4x - 2) + 1) - 3| + 2) - 2| - 1) + 3 and g(x) = -1(4(1(3sin(1\u03c0x + 2) - 1) + 1) - 1) + 2 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": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3(1e^(-1(2|(-3|(-3x^2 + 3x + 4) - 2| - 1) + 1| - 3)))^2 - 1(1e^(-1(2|(-3|(-3x^2 + 3x + 4) - 2| - 1) + 1| - 3))) + 2, g(x) = (3(-5(-1(1|x + 2| + 3)) + 4))/(1(-5(-1(1|x + 2| + 3)) + 4)), x = 1.4, 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": "33.6", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-2(1(-4(-2((-3x + 2)/(-3x + 4))^2 + 2((-3x + 2)/(-3x + 4)) + 5)^2 + 2(-2((-3x + 2)/(-3x + 4))^2 + 2((-3x + 2)/(-3x + 4)) + 5) + 2) + 1) + 2)/(1(1(-4(-2((-3x + 2)/(-3x + 4))^2 + 2((-3x + 2)/(-3x + 4)) + 5)^2 + 2(-2((-3x + 2)/(-3x + 4))^2 + 2((-3x + 2)/(-3x + 4)) + 5) + 2) + 1) + 1), g(x) = 1(-3cos(3\u03c0((3(-3x + 1) + 2)/(-2(-3x + 1) + 3)) - 2) - 3) + 4, x = 1.0, 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": "4.6", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3|((-3(2((2(1x^2 - 5x + 3) - 3)/(2(1x^2 - 5x + 3) + 1))^2 - 4((2(1x^2 - 5x + 3) - 3)/(2(1x^2 - 5x + 3) + 1)) - 1) + 3)/(3(2((2(1x^2 - 5x + 3) - 3)/(2(1x^2 - 5x + 3) + 1))^2 - 4((2(1x^2 - 5x + 3) - 3)/(2(1x^2 - 5x + 3) + 1)) - 1) + 1)) + 2| - 1, g(x) = (3((-3(-5(4x) + 1) + 1)/(2(-5(4x) + 1) + 3)) + 2)/(-1((-3(-5(4x) + 1) + 1)/(2(-5(4x) + 1) + 3)) + 3), x = 3.2, and x = 4.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-1(-3(-4(1(3sin(1\u03c0x - 3) + 1)^2 + 4(3sin(1\u03c0x - 3) + 1) + 1) + 2) - 4) + 3)/(-3(-3(-4(1(3sin(1\u03c0x - 3) + 1)^2 + 4(3sin(1\u03c0x - 3) + 1) + 1) + 2) - 4) - 1) and g(x) = 1(3(-3sin(1\u03c0(-1|x + 2| + 3) + 2) - 3)^2 - 1(-3sin(1\u03c0(-1|x + 2| + 3) + 2) - 3)) - 5 between the vertical lines x = -1.6 and x = -0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "78.7", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2|(3(-1((-2((3x + 3)/(-1x + 3)))/(-2((3x + 3)/(-1x + 3)) + 3))^2 + 3((-2((3x + 3)/(-1x + 3)))/(-2((3x + 3)/(-1x + 3)) + 3)) + 3)^2 - 3(-1((-2((3x + 3)/(-1x + 3)))/(-2((3x + 3)/(-1x + 3)) + 3))^2 + 3((-2((3x + 3)/(-1x + 3)))/(-2((3x + 3)/(-1x + 3)) + 3)) + 3) - 2) - 3|, g(x) = 1|(2(-2cos(2\u03c0(-3x^2 + 5x) - 3) - 3)^2 + 3(-2cos(2\u03c0(-3x^2 + 5x) - 3) - 3) + 5) - 3| - 2, x = -0.4, and x = -0.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2(-2|(3(2|(-1x + 3) - 1| - 2) + 2) + 3| - 1)^2 + 1(-2|(3(2|(-1x + 3) - 1| - 2) + 2) + 3| - 1) + 2, g(x) = 2|(-1|(3(3x - 3)^2 + 3(3x - 3) + 2) + 1| + 2) - 3| + 1, x = 1.6, 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": "110.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (2(-3|(2(-5(-3x - 4)^2 + 1(-3x - 4) - 2)^2 + 3(-5(-3x - 4)^2 + 1(-3x - 4) - 2) + 5)| + 3) - 3)/(-1(-3|(2(-5(-3x - 4)^2 + 1(-3x - 4) - 2)^2 + 3(-5(-3x - 4)^2 + 1(-3x - 4) - 2) + 5)| + 3) + 2) and g(x) = (1(-1|(2cos(2\u03c0(-3|x - 2|) + 1) - 1) - 2| + 3) + 3)/(2(-1|(2cos(2\u03c0(-3|x - 2|) + 1) - 1) - 2| + 3) + 2) between the vertical lines x = -1.2 and x = -0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-2(2(-1((-3((-2x + 3)/(3x + 1)) + 1)/(2((-2x + 3)/(3x + 1)) + 1))^2 - 3((-3((-2x + 3)/(3x + 1)) + 1)/(2((-2x + 3)/(3x + 1)) + 1)) + 1)^2 - 3(-1((-3((-2x + 3)/(3x + 1)) + 1)/(2((-2x + 3)/(3x + 1)) + 1))^2 - 3((-3((-2x + 3)/(3x + 1)) + 1)/(2((-2x + 3)/(3x + 1)) + 1)) + 1) - 2) + 1)/(1(2(-1((-3((-2x + 3)/(3x + 1)) + 1)/(2((-2x + 3)/(3x + 1)) + 1))^2 - 3((-3((-2x + 3)/(3x + 1)) + 1)/(2((-2x + 3)/(3x + 1)) + 1)) + 1)^2 - 3(-1((-3((-2x + 3)/(3x + 1)) + 1)/(2((-2x + 3)/(3x + 1)) + 1))^2 - 3((-3((-2x + 3)/(3x + 1)) + 1)/(2((-2x + 3)/(3x + 1)) + 1)) + 1) - 2) - 3), g(x) = 1|((1(-3|((3x - 3)/(-3x - 3)) + 3| - 2) - 3)/(-1(-3|((3x - 3)/(-3x - 3)) + 3| - 2) - 1)) + 3| - 1, x = -1.8, 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) = 3|(1(-5(1cos(3\u03c0(3|x + 3| - 1) - 3) - 3) + 3) - 4)| + 3 and g(x) = 2(1|(3|(-1x + 5) - 2| + 1) + 3| - 1)^2 - 2(1|(3|(-1x + 5) - 2| + 1) + 3| - 1) + 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": "0.7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2((-3(1(4(2|x + 2| - 3) + 5) - 4) + 3)/(-2(1(4(2|x + 2| - 3) + 5) - 4) + 3))^2 + 2((-3(1(4(2|x + 2| - 3) + 5) - 4) + 3)/(-2(1(4(2|x + 2| - 3) + 5) - 4) + 3)) - 3 and g(x) = -2|(4(1(-5x^2 + 3) + 4) + 2) + 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": "4.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (2(5(-3|(3|(1e^(-1x) - 2)|) + 3| - 3)^2 - 1) + 1)/(-3(5(-3|(3|(1e^(-1x) - 2)|) + 3| - 3)^2 - 1) + 4) and g(x) = (2((2((1(1x^2 - 5x + 4))/(1(1x^2 - 5x + 4) + 1)) + 1)/(3((1(1x^2 - 5x + 4))/(1(1x^2 - 5x + 4) + 1)) + 2)) + 1)/(-2((2((1(1x^2 - 5x + 4))/(1(1x^2 - 5x + 4) + 1)) + 1)/(3((1(1x^2 - 5x + 4))/(1(1x^2 - 5x + 4) + 1)) + 2)) - 3) between the vertical lines x = 1.2 and x = 3.8. 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(1|(-5(3e^(1(-2|x| + 3)) + 1) + 2) + 3| - 1) + 3 and g(x) = (2(-1(-2sin(2\u03c0(-3x^2 + 4x - 4) + 1))^2 + 3(-2sin(2\u03c0(-3x^2 + 4x - 4) + 1)) - 5) - 1)/(3(-1(-2sin(2\u03c0(-3x^2 + 4x - 4) + 1))^2 + 3(-2sin(2\u03c0(-3x^2 + 4x - 4) + 1)) - 5) + 3) 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": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1cos(1\u03c0((1(2|(-2|(-1|x| + 3)| - 3) - 3| + 2) + 2)/(-3(2|(-2|(-1|x| + 3)| - 3) - 3| + 2) - 2)) - 2) + 2 and g(x) = 5(-1(2(-3x - 2) + 2)^2 + 4) + 4 between the vertical lines x = -0.7 and x = 0.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10.9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1|((-3((3(-1|(1e^(1x) - 3) - 2| + 1) - 3)/(-2(-1|(1e^(1x) - 3) - 2| + 1) + 3)) + 2)/(3((3(-1|(1e^(1x) - 3) - 2| + 1) - 3)/(-2(-1|(1e^(1x) - 3) - 2| + 1) + 3)) + 3)) + 3| - 3 and g(x) = 2(5(-2|(-5x^2 + 2x + 3) - 3| + 1)^2 + 5(-2|(-5x^2 + 2x + 3) - 3| + 1) - 1) + 3 from x = 0.6 to x = 0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2|(1|(-5((2(-1sin(2\u03c0x + 3) - 1) - 1)/(2(-1sin(2\u03c0x + 3) - 1) + 2))^2 - 1((2(-1sin(2\u03c0x + 3) - 1) - 1)/(2(-1sin(2\u03c0x + 3) - 1) + 2)) - 1) + 2|) - 1| - 3 and g(x) = 3sin(2\u03c0((1(-2(5x^2 + 1x - 1)^2 - 4(5x^2 + 1x - 1) + 1) + 2)/(1(-2(5x^2 + 1x - 1)^2 - 4(5x^2 + 1x - 1) + 1) + 1)) - 1) - 1 between the vertical lines x = -4.6 and x = -4.5. Round 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) = -2sin(1\u03c0(2|((1(3|(1x^2 + 3x - 3) + 3| - 1) + 3)/(-3(3|(1x^2 + 3x - 3) + 3| - 1) + 4)) + 3| + 1) - 1) - 1, g(x) = 1(3(-2|(2|x - 1|) - 1| + 3)^2 - 3(-2|(2|x - 1|) - 1| + 3) - 1) - 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": "0.7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1|(-1(-3sin(1\u03c0(4(4x^2 - 2x + 2)^2 + 2(4x^2 - 2x + 2) + 4)) - 3)^2) + 1| + 1 and g(x) = (-1(5(2|(2|x - 3| - 3) + 2| - 2) + 4) + 3)/(2(5(2|(2|x - 3| - 3) + 2| - 2) + 4) - 3) from x = 2.1 to x = 2.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9.7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-1(-3((-1(1(1sin(1\u03c0x + 3) - 1) + 4) + 3)/(-1(1(1sin(1\u03c0x + 3) - 1) + 4))) - 4) - 2)/(-1(-3((-1(1(1sin(1\u03c0x + 3) - 1) + 4) + 3)/(-1(1(1sin(1\u03c0x + 3) - 1) + 4))) - 4) + 3) and g(x) = (-3((-1(-1|(3x + 4) - 3| - 3) + 3)/(2(-1|(3x + 4) - 3| - 3) + 1)) - 3)/(1((-1(-1|(3x + 4) - 3| - 3) + 3)/(2(-1|(3x + 4) - 3| - 3) + 1))) from x = -0.9 to x = 0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -4((1(-3(-2(1x + 1) - 1) - 5) - 2)/(-1(-3(-2(1x + 1) - 1) - 5) + 2)) - 3 and g(x) = -5(-1(-3(1|x| - 1) + 1) - 1) - 1 between the vertical lines x = -1.5 and x = 1.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2|(-2|(1(1(-1x^2 + 2x) - 3) + 2) + 3| + 2)| + 2 and g(x) = 5((-1(-5(2|x + 1| - 3) - 5) + 2)/(3(-5(2|x + 1| - 3) - 5) + 3)) + 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3(3cos(3\u03c0(-4(-3|((-3x + 3)/(-3x - 2)) - 2| + 1)^2 + 1(-3|((-3x + 3)/(-3x - 2)) - 2| + 1) + 2) + 1) - 2) - 2 and g(x) = (-3((2(1(-2x^2 - 5x + 5)^2 + 3(-2x^2 - 5x + 5) - 1) + 1)/(2(1(-2x^2 - 5x + 5)^2 + 3(-2x^2 - 5x + 5) - 1) - 1)) + 3)/(3((2(1(-2x^2 - 5x + 5)^2 + 3(-2x^2 - 5x + 5) - 1) + 1)/(2(1(-2x^2 - 5x + 5)^2 + 3(-2x^2 - 5x + 5) - 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": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1(-1(-1cos(1\u03c0((1(3|x + 3| + 2) - 2)/(-3(3|x + 3| + 2) - 2))) + 2)^2 + 1(-1cos(1\u03c0((1(3|x + 3| + 2) - 2)/(-3(3|x + 3| + 2) - 2))) + 2) + 3) - 4, g(x) = 3sin(2\u03c0(3(-4(3|x - 3| + 2)^2 - 1)^2 + 3(-4(3|x - 3| + 2)^2 - 1) - 5) - 3) - 3, 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": "Calculate the area enclosed between the functions f(x) = (-1(3|(5((-2(-2|x| + 2) - 3)/(-2(-2|x| + 2) + 1)) - 1) - 1|))/(1(3|(5((-2(-2|x| + 2) - 3)/(-2(-2|x| + 2) + 1)) - 1) - 1|) - 3) and g(x) = 4(-3(-1sin(3\u03c0(-1x^2 - 4) - 2) + 3) - 3) - 2 from x = -3.3 to x = -2.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "75.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3(-2(1|((1(-2x + 4) + 3)/(-3(-2x + 4) - 3)) + 3|))^2 - 4(-2(1|((1(-2x + 4) + 3)/(-3(-2x + 4) - 3)) + 3|)) - 1 and g(x) = 1(-1e^(1(5(-3x - 1)^2 - 4(-3x - 1) + 2)) - 3) + 3 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": "23.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3|((2(-2(-1|(3x) + 3| - 2)^2 + 5(-1|(3x) + 3| - 2) - 2) - 1)/(2(-2(-1|(3x) + 3| - 2)^2 + 5(-1|(3x) + 3| - 2) - 2) + 3)) + 2| + 1 and g(x) = 5(4(-4((2x + 3)/(-1x + 2))^2 + 2((2x + 3)/(-1x + 2)) + 5) - 4) between the vertical lines x = -4.0 and x = -0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "215.8", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2|(4(-1cos(1\u03c0((2(3|x + 2| + 3) - 3)/(-3(3|x + 2| + 3))) - 2) - 3) + 3) + 1| + 2, g(x) = 2|(3(4(1x) - 1) - 4) - 1| - 2, x = 0.1, 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": "7.8", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-3((-2(4(-1(1sin(1\u03c0x) - 1) + 5)^2 - 4(-1(1sin(1\u03c0x) - 1) + 5)) + 3)/(-2(4(-1(1sin(1\u03c0x) - 1) + 5)^2 - 4(-1(1sin(1\u03c0x) - 1) + 5)) + 3)) + 1)/(2((-2(4(-1(1sin(1\u03c0x) - 1) + 5)^2 - 4(-1(1sin(1\u03c0x) - 1) + 5)) + 3)/(-2(4(-1(1sin(1\u03c0x) - 1) + 5)^2 - 4(-1(1sin(1\u03c0x) - 1) + 5)) + 3)) - 3), g(x) = 3(-1sin(1\u03c0(-4(-3x - 2)) - 1) - 2)^2 - 1(-1sin(1\u03c0(-4(-3x - 2)) - 1) - 2) - 5, x = 2.8, and x = 2.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2(2cos(3\u03c0((-2(-1|(-1x - 4)| - 2) - 2)/(-1(-1|(-1x - 4)| - 2) - 2)) + 3) + 3)^2 - 5(2cos(3\u03c0((-2(-1|(-1x - 4)| - 2) - 2)/(-1(-1|(-1x - 4)| - 2) - 2)) + 3) + 3) - 2 and g(x) = 3sin(2\u03c0(3|(4((-2x + 3)/(3x + 1))^2 + 5((-2x + 3)/(3x + 1)) + 4) + 2| - 1) + 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2((-1(-4((3((1x + 1)/(-1x + 3)))/(3((1x + 1)/(-1x + 3)) - 2)) - 4) + 1)/(3(-4((3((1x + 1)/(-1x + 3)))/(3((1x + 1)/(-1x + 3)) - 2)) - 4) - 2))^2 - 4((-1(-4((3((1x + 1)/(-1x + 3)))/(3((1x + 1)/(-1x + 3)) - 2)) - 4) + 1)/(3(-4((3((1x + 1)/(-1x + 3)))/(3((1x + 1)/(-1x + 3)) - 2)) - 4) - 2)) - 5, g(x) = -5(2|(4(1x) - 1) - 3| - 3) - 2, 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": "7.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1|(1|(-2|(2|(-1x^2 - 2x + 3) - 2| - 3) - 3| - 2) - 1| - 3) - 1| - 2 and g(x) = 1(1|((-3(1|x| - 2) - 1)/(-1(1|x| - 2) - 3)) + 1| - 1)^2 + 3(1|((-3(1|x| - 2) - 1)/(-1(1|x| - 2) - 3)) + 1| - 1) - 4 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) = -3cos(2\u03c0(2|(-2|(-1|(1x^2 - 2x + 3) - 3|) + 2| - 3)| + 2) - 2) and g(x) = -5(-1|(2|(1x^2 - 2) + 1| - 1) - 3| + 3)^2 + 2(-1|(2|(1x^2 - 2) + 1| - 1) - 3| + 3) + 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": "Calculate the area enclosed between the functions f(x) = -1|(1((-1(4((2x - 1)/(2x + 3))^2 + 4((2x - 1)/(2x + 3)) + 4) - 1)/(2(4((2x - 1)/(2x + 3))^2 + 4((2x - 1)/(2x + 3)) + 4) - 1))^2 - 4((-1(4((2x - 1)/(2x + 3))^2 + 4((2x - 1)/(2x + 3)) + 4) - 1)/(2(4((2x - 1)/(2x + 3))^2 + 4((2x - 1)/(2x + 3)) + 4) - 1)) + 3) - 3| + 3 and g(x) = -1|(-3(-3((3x + 3)/(-1x + 2))^2 + 1((3x + 3)/(-1x + 2)) + 3)^2 + 5(-3((3x + 3)/(-1x + 2))^2 + 1((3x + 3)/(-1x + 2)) + 3) + 4) + 3| + 1 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-2(1|(-1(1|(2x^2 + 2x + 2) + 1| + 3) + 4) - 3| + 1) - 3)/(-1(1|(-1(1|(2x^2 + 2x + 2) + 1| + 3) + 4) - 3| + 1)) and g(x) = (-1(-1(3((-3x)/(1x + 1))^2 - 3((-3x)/(1x + 1)) + 1) + 3) + 2)/(2(-1(3((-3x)/(1x + 1))^2 - 3((-3x)/(1x + 1)) + 1) + 3)) 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": "3.8", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-2(-2(-3sin(3\u03c0((-2(1|x + 2|) - 1)/(2(1|x + 2|) + 3))) - 1)^2 - 4(-3sin(3\u03c0((-2(1|x + 2|) - 1)/(2(1|x + 2|) + 3))) - 1) + 5) - 2)/(-2(-2(-3sin(3\u03c0((-2(1|x + 2|) - 1)/(2(1|x + 2|) + 3))) - 1)^2 - 4(-3sin(3\u03c0((-2(1|x + 2|) - 1)/(2(1|x + 2|) + 3))) - 1) + 5) - 1) and g(x) = 4(-3(3(-2e^(2x) + 1)^2 - 1(-2e^(2x) + 1) - 1)^2 + 2(3(-2e^(2x) + 1)^2 - 1(-2e^(2x) + 1) - 1) + 3) between the vertical lines x = -3.0 and x = -1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-1(-2(-3sin(2\u03c0((2(-2x - 5) + 3)/(1(-2x - 5))) + 1) - 2) + 2) - 3)/(-2(-2(-3sin(2\u03c0((2(-2x - 5) + 3)/(1(-2x - 5))) + 1) - 2) + 2) + 1) and g(x) = 2|(2|(-3|((2x - 1)/(1x)) - 3| - 2) - 2|) + 1| + 1 between the vertical lines x = -1.9 and x = -1.5. 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": "Calculate the area enclosed between the functions f(x) = -3((2((3(4(2x - 1) - 4) - 3)/(-3(4(2x - 1) - 4))) + 3)/(2((3(4(2x - 1) - 4) - 3)/(-3(4(2x - 1) - 4))) + 2))^2 + 1((2((3(4(2x - 1) - 4) - 3)/(-3(4(2x - 1) - 4))) + 3)/(2((3(4(2x - 1) - 4) - 3)/(-3(4(2x - 1) - 4))) + 2)) - 1 and g(x) = (-2(2(1e^(-1(5x + 4)))^2 - 5(1e^(-1(5x + 4))) - 4) - 1)/(1(2(1e^(-1(5x + 4)))^2 - 5(1e^(-1(5x + 4))) - 4) - 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": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2(1|((3(-2sin(1\u03c0(-3|x + 2| + 3) - 3) + 1) - 1)/(1(-2sin(1\u03c0(-3|x + 2| + 3) - 3) + 1) + 3)) + 3| - 1)^2 - 3(1|((3(-2sin(1\u03c0(-3|x + 2| + 3) - 3) + 1) - 1)/(1(-2sin(1\u03c0(-3|x + 2| + 3) - 3) + 1) + 3)) + 3| - 1) - 1, g(x) = 4(-1|(2cos(1\u03c0((-3x + 1)/(1x + 3)) + 3) - 1)| + 2)^2 - 5(-1|(2cos(1\u03c0((-3x + 1)/(1x + 3)) + 3) - 1)| + 2) - 2, x = -4.5, 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": "12.9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -5(2(5((1(-1x^2 - 3x + 4) - 1)/(1(-1x^2 - 3x + 4) + 1))^2 + 4((1(-1x^2 - 3x + 4) - 1)/(1(-1x^2 - 3x + 4) + 1)) + 2)^2 - 5(5((1(-1x^2 - 3x + 4) - 1)/(1(-1x^2 - 3x + 4) + 1))^2 + 4((1(-1x^2 - 3x + 4) - 1)/(1(-1x^2 - 3x + 4) + 1)) + 2) + 2)^2 + 1(2(5((1(-1x^2 - 3x + 4) - 1)/(1(-1x^2 - 3x + 4) + 1))^2 + 4((1(-1x^2 - 3x + 4) - 1)/(1(-1x^2 - 3x + 4) + 1)) + 2)^2 - 5(5((1(-1x^2 - 3x + 4) - 1)/(1(-1x^2 - 3x + 4) + 1))^2 + 4((1(-1x^2 - 3x + 4) - 1)/(1(-1x^2 - 3x + 4) + 1)) + 2) + 2) - 5 and g(x) = -3|(-1(3cos(2\u03c0(-1x^2 - 2x - 2) - 3) - 3) + 4) - 2| + 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": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -3(2(-2|(3|((-3x + 2)/(2x + 2)) - 3|) - 1| + 2) + 1)^2 - 4(2(-2|(3|((-3x + 2)/(2x + 2)) - 3|) - 1| + 2) + 1), g(x) = (2(-1((2(1x^2 + 3) - 3)/(1(1x^2 + 3) - 2)) + 3))/(-1(-1((2(1x^2 + 3) - 3)/(1(1x^2 + 3) - 2)) + 3) - 3), x = -0.5, 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": "7.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1|((-2(-2|(-1(-3x^2 + 2x) - 1) + 2| - 3) + 2)/(2(-2|(-1(-3x^2 + 2x) - 1) + 2| - 3) + 1)) - 2| - 3, g(x) = -1|(-3|((2(3|x - 2| - 2) + 1)/(1(3|x - 2| - 2) - 3))| + 3) + 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": "8.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3|(3sin(1\u03c0(3|(3(-5x^2 - 2x - 4)^2 - 2(-5x^2 - 2x - 4) + 4) + 2| - 2) - 3) - 3) - 3| + 3 and g(x) = -1|(2(1(-1x^2 + 3x + 3) + 3)) + 2| + 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": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-1(3|((1(-5(-1x^2 - 5x - 2) + 5) - 1)/(3(-5(-1x^2 - 5x - 2) + 5) + 1)) - 1| + 3) - 3)/(2(3|((1(-5(-1x^2 - 5x - 2) + 5) - 1)/(3(-5(-1x^2 - 5x - 2) + 5) + 1)) - 1| + 3) - 1), g(x) = 3|((2((-1(-2sin(2\u03c0x - 3)) - 1)/(-3(-2sin(2\u03c0x - 3)) + 4)) + 1)/(-2((-1(-2sin(2\u03c0x - 3)) - 1)/(-3(-2sin(2\u03c0x - 3)) + 4)) + 3)) + 2| - 2, x = 3.1, 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": "1.7", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 4(-3e^(-1(-2((-1(1|x - 1| - 2) + 3)/(2(1|x - 1| - 2) - 1)) + 4)) + 1) - 5 and g(x) = -3cos(2\u03c0(1(1|(-2|x| - 1) + 2| + 1)^2 + 2(1|(-2|x| - 1) + 2| + 1) + 5) + 3) - 2 between the vertical lines x = -4.5 and x = -4.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1|((-1(-3cos(3\u03c0(-1(5x + 5) - 5) - 1) + 3) - 2)/(1(-3cos(3\u03c0(-1(5x + 5) - 5) - 1) + 3) - 2)) + 1| - 1 and g(x) = (-2((-3(2sin(3\u03c0(-1|x + 2| - 2) - 3) + 2))/(2(2sin(3\u03c0(-1|x + 2| - 2) - 3) + 2) - 1)))/(-1((-3(2sin(3\u03c0(-1|x + 2| - 2) - 3) + 2))/(2(2sin(3\u03c0(-1|x + 2| - 2) - 3) + 2) - 1)) - 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": "1.4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -4((3(1|((-2((-1x + 3)/(-1x - 2)) + 2)/(-1((-1x + 3)/(-1x - 2)) + 3)) - 2| + 3) + 2)/(1(1|((-2((-1x + 3)/(-1x - 2)) + 2)/(-1((-1x + 3)/(-1x - 2)) + 3)) - 2| + 3) + 3))^2 - 1 and g(x) = (-3(-1(2(2x) - 2)^2 + 3(2(2x) - 2)) + 3)/(2(-1(2(2x) - 2)^2 + 3(2(2x) - 2)) + 3) from x = 0.4 to x = 1.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19.7", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3((-1((-2((-1(2sin(2\u03c0x) + 1) + 2)/(1(2sin(2\u03c0x) + 1) - 2)) + 2)/(1((-1(2sin(2\u03c0x) + 1) + 2)/(1(2sin(2\u03c0x) + 1) - 2)) + 2)) - 2)/(1((-2((-1(2sin(2\u03c0x) + 1) + 2)/(1(2sin(2\u03c0x) + 1) - 2)) + 2)/(1((-1(2sin(2\u03c0x) + 1) + 2)/(1(2sin(2\u03c0x) + 1) - 2)) + 2)))) - 3, g(x) = -1|(-3(3|(-1x) - 2|) + 4)|, x = -3.3, 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": "11.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2|(2e^(2(-3((-1(4x - 2))/(-2(4x - 2) + 3))^2 + 5((-1(4x - 2))/(-2(4x - 2) + 3)) - 2)) + 3) - 2| + 1 and g(x) = -5(3sin(2\u03c0(-4(-3|x| - 2) + 3) - 2) - 3)^2 + 5(3sin(2\u03c0(-4(-3|x| - 2) + 3) - 2) - 3) - 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": "9.9", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (1(-5(2cos(1\u03c0(3|(-2x^2 + 1x + 5) - 2| - 2) - 1) + 3) + 4) - 2)/(-3(-5(2cos(1\u03c0(3|(-2x^2 + 1x + 5) - 2| - 2) - 1) + 3) + 4) - 2), g(x) = -2|(-5(1(-3|x - 1| + 1)^2 + 2(-3|x - 1| + 1) - 3) - 4) - 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": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1|(-4(4((-3(-2e^(-2x) + 2) + 2)/(-3(-2e^(-2x) + 2) + 2)) + 5) + 2) - 3| - 2 and g(x) = 1(-3|(3cos(3\u03c0(-1x - 2) + 3)) + 1| - 3)^2 + 2(-3|(3cos(3\u03c0(-1x - 2) + 3)) + 1| - 3) - 1 between the vertical lines x = -0.5 and x = -0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28.7", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 5(-3sin(1\u03c0(-3|(-2|(-3|x + 2|) - 1| - 2) - 3| - 1) + 1) - 2)^2 + 3(-3sin(1\u03c0(-3|(-2|(-3|x + 2|) - 1| - 2) - 3| - 1) + 1) - 2) - 5, g(x) = 2cos(1\u03c0((-1((2(-3x^2 - 4x + 1) + 2)/(-3(-3x^2 - 4x + 1) - 3)) + 3)/(1((2(-3x^2 - 4x + 1) + 2)/(-3(-3x^2 - 4x + 1) - 3)) + 3)) - 2) - 1, x = 4.9, and x = 5.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1|((2((-3(-5(-1sin(2\u03c0x - 2) + 2) - 3) - 2)/(-3(-5(-1sin(2\u03c0x - 2) + 2) - 3) - 3)) + 1)/(-1((-3(-5(-1sin(2\u03c0x - 2) + 2) - 3) - 2)/(-3(-5(-1sin(2\u03c0x - 2) + 2) - 3) - 3)) + 2)) + 2| + 1 and g(x) = 2((-3(-3sin(2\u03c0(-3|x - 2| + 3)) + 1) - 3)/(3(-3sin(2\u03c0(-3|x - 2| + 3)) + 1))) + 3 between the vertical lines x = -0.7 and x = -0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-2((2(-4(2|(5x^2 - 3) + 2| + 1)^2 + 3(2|(5x^2 - 3) + 2| + 1) + 3))/(-2(-4(2|(5x^2 - 3) + 2| + 1)^2 + 3(2|(5x^2 - 3) + 2| + 1) + 3) + 3)))/(-2((2(-4(2|(5x^2 - 3) + 2| + 1)^2 + 3(2|(5x^2 - 3) + 2| + 1) + 3))/(-2(-4(2|(5x^2 - 3) + 2| + 1)^2 + 3(2|(5x^2 - 3) + 2| + 1) + 3) + 3)) - 1) and g(x) = -3(-1sin(1\u03c0((-3((2x - 2)/(-3x + 4)))/(-1((2x - 2)/(-3x + 4)) - 2)) - 3) - 1) - 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": "0.9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3|((-3((-2(-1((-2x + 3)/(2x + 3)) + 1) + 1)/(-3(-1((-2x + 3)/(2x + 3)) + 1) - 1)) - 2)/(1((-2(-1((-2x + 3)/(2x + 3)) + 1) + 1)/(-3(-1((-2x + 3)/(2x + 3)) + 1) - 1)) - 3))| - 1 and g(x) = -1|(-3(4(-1x^2 - 3x + 4)^2 + 3(-1x^2 - 3x + 4) + 2) - 1) + 1| - 2 from x = -0.3 to x = -0.19999999999999998. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29.5", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1|(-1cos(3\u03c0(3((-1(-1x - 1) + 2)/(-3(-1x - 1) + 4))^2 - 2((-1(-1x - 1) + 2)/(-3(-1x - 1) + 4)) - 1) - 2) - 3)| + 3, g(x) = (1(-1(-3cos(1\u03c0(-4x^2 - 5x + 3) - 1))^2 - 2(-3cos(1\u03c0(-4x^2 - 5x + 3) - 1)) + 2) + 2)/(2(-1(-3cos(1\u03c0(-4x^2 - 5x + 3) - 1))^2 - 2(-3cos(1\u03c0(-4x^2 - 5x + 3) - 1)) + 2) + 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": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1|((3(-4(1((-1x + 2)/(-2x))^2 + 4((-1x + 2)/(-2x)) + 1)^2 - 5(1((-1x + 2)/(-2x))^2 + 4((-1x + 2)/(-2x)) + 1) + 1) + 3)/(1(-4(1((-1x + 2)/(-2x))^2 + 4((-1x + 2)/(-2x)) + 1)^2 - 5(1((-1x + 2)/(-2x))^2 + 4((-1x + 2)/(-2x)) + 1) + 1) + 2)) - 2|, g(x) = (-3(-1(5(3x^2 + 2x + 4)^2 - 5(3x^2 + 2x + 4) + 1) + 1) + 3)/(3(-1(5(3x^2 + 2x + 4)^2 - 5(3x^2 + 2x + 4) + 1) + 1) - 1), 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": "1.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2|(-5((1(-2((2x)/(2x))^2 + 2((2x)/(2x)) + 4) - 2)/(1(-2((2x)/(2x))^2 + 2((2x)/(2x)) + 4) - 2))^2) - 1| and g(x) = (-1(-2(-3cos(1\u03c0(1|x - 2| + 2) - 1) + 1) + 4) + 2)/(2(-2(-3cos(1\u03c0(1|x - 2| + 2) - 1) + 1) + 4) + 1) from x = -3.7 to x = -3.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10.4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 5((1(4(-3(-3e^(2x) - 3)^2 - 1(-3e^(2x) - 3))^2 - 1(-3(-3e^(2x) - 3)^2 - 1(-3e^(2x) - 3)) - 5) - 1)/(3(4(-3(-3e^(2x) - 3)^2 - 1(-3e^(2x) - 3))^2 - 1(-3(-3e^(2x) - 3)^2 - 1(-3e^(2x) - 3)) - 5) + 1))^2 - 2((1(4(-3(-3e^(2x) - 3)^2 - 1(-3e^(2x) - 3))^2 - 1(-3(-3e^(2x) - 3)^2 - 1(-3e^(2x) - 3)) - 5) - 1)/(3(4(-3(-3e^(2x) - 3)^2 - 1(-3e^(2x) - 3))^2 - 1(-3(-3e^(2x) - 3)^2 - 1(-3e^(2x) - 3)) - 5) + 1)) and g(x) = 2(4(-2(-3x^2 - 1x + 5)^2 + 2(-3x^2 - 1x + 5) + 2)^2 - 5) + 1 from x = 1.0 to x = 1.2. 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": "Find the area of the region bounded by the curves f(x) = -5(-1(-2(1(-3|x + 3| - 2) + 4)^2 + 4(1(-3|x + 3| - 2) + 4)) - 2) + 3, g(x) = 2|(2sin(3\u03c0(2|(-2|x + 1| + 2) + 3| - 1) - 1) - 1) - 3| - 3, x = -2.3, 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1(-2(1|(3((1x)/(1x + 3)) + 5)| + 2)^2 - 4(1|(3((1x)/(1x + 3)) + 5)| + 2) + 4) - 2, g(x) = -3|(3|(-1cos(1\u03c0(-1x - 2) + 3) - 1) - 1| + 2)| - 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -5((3(3|((3(4x^2 - 1x - 3) + 1)/(1(4x^2 - 1x - 3))) + 3| - 3) - 1)/(-3(3|((3(4x^2 - 1x - 3) + 1)/(1(4x^2 - 1x - 3))) + 3| - 3) + 4)) - 2, g(x) = (2(2cos(2\u03c0(3(-3x - 1) - 3) - 1) + 3))/(-2(2cos(2\u03c0(3(-3x - 1) - 3) - 1) + 3) + 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": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2(-4(2(2|(-2e^(1x) + 2) - 1| - 1)^2 - 3(2|(-2e^(1x) + 2) - 1| - 1) + 3) + 5)^2 - 3(-4(2(2|(-2e^(1x) + 2) - 1| - 1)^2 - 3(2|(-2e^(1x) + 2) - 1| - 1) + 3) + 5) + 1 and g(x) = -1(5((-2(-2|x + 2| + 2) + 2)/(-2(-2|x + 2| + 2) + 3)) + 4)^2 - 5(5((-2(-2|x + 2| + 2) + 2)/(-2(-2|x + 2| + 2) + 3)) + 4) - 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": "35.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1(1sin(2\u03c0(-5(4(2|x + 1| + 2) + 5) - 3) + 1) + 3) + 4 and g(x) = 3|(-2(3|(1x^2 + 2x + 1)| - 3)^2 + 3(3|(1x^2 + 2x + 1)| - 3) + 3)| - 1 from x = 0.3 to x = 0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2(3|((1(5(2|x + 3| + 1)^2 - 5(2|x + 3| + 1)))/(3(5(2|x + 3| + 1)^2 - 5(2|x + 3| + 1)) - 1)) - 3| + 3) + 4 and g(x) = -1(-2(-2(1x^2 + 1x + 2) + 4)^2 - 4(-2(1x^2 + 1x + 2) + 4) + 1)^2 + 4(-2(-2(1x^2 + 1x + 2) + 4)^2 - 4(-2(1x^2 + 1x + 2) + 4) + 1) - 5 from x = -1.8 to x = 0.8. 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": "Determine the area of the region enclosed by the graphs of f(x) = 3(-3cos(1\u03c0(4(-5((3x + 2)/(-3x - 3)) - 4) + 5)) - 2) + 3 and g(x) = (3(2(5(3|x - 2| - 2) - 1)^2 - 1(5(3|x - 2| - 2) - 1) - 2))/(3(2(5(3|x - 2| - 2) - 1)^2 - 1(5(3|x - 2| - 2) - 1) - 2) + 1) 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": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2|(-2((1(1|(1x + 4) - 2| + 3) - 3)/(2(1|(1x + 4) - 2| + 3) + 2)) - 3) - 1| + 1 and g(x) = (-2(4((-1((3x)/(-3x + 2)) + 3)/(2((3x)/(-3x + 2)) + 1))^2 - 4) + 3)/(3(4((-1((3x)/(-3x + 2)) + 3)/(2((3x)/(-3x + 2)) + 1))^2 - 4) - 1) between the vertical lines x = 0.3 and x = 0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2sin(1\u03c0(4((3(2(2|x| + 1)^2 - 4(2|x| + 1) + 4) + 2)/(-2(2(2|x| + 1)^2 - 4(2|x| + 1) + 4) - 1)) + 2)) - 1, g(x) = -1|(-4(1|((1x + 1)/(3x)) - 2| - 1) - 1) + 2|, x = 0.2, and x = 0.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3|(3(2cos(1\u03c0((2(-4x^2))/(3(-4x^2) + 1))) - 2) + 3) - 3| + 2 and g(x) = 1|(-1|(2sin(3\u03c0(-2|x| - 3) + 2) + 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": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-1(3(-2(2(-2x + 5) - 5) + 5)^2 + 5))/(1(3(-2(2(-2x + 5) - 5) + 5)^2 + 5) + 3), g(x) = -3|(4((3(4x^2 - 2x - 4) + 1)/(-2(4x^2 - 2x - 4) - 2)) - 1) - 3| + 3, x = 1.2, and x = 1.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-3(-1sin(2\u03c0(-4(1|(-1|x + 2| + 2) + 1| + 3)^2 + 3(1|(-1|x + 2| + 2) + 1| + 3)) - 1) - 1) + 3)/(1(-1sin(2\u03c0(-4(1|(-1|x + 2| + 2) + 1| + 3)^2 + 3(1|(-1|x + 2| + 2) + 1| + 3)) - 1) - 1) + 1) and g(x) = 1(-2cos(1\u03c0((-1(-5x^2 - 5x - 2))/(-2(-5x^2 - 5x - 2) - 3)) + 1) - 2)^2 + 2(-2cos(1\u03c0((-1(-5x^2 - 5x - 2))/(-2(-5x^2 - 5x - 2) - 3)) + 1) - 2) - 2 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": "2.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (2((3(2(1((1x + 3)/(3x + 1)))^2 - 4(1((1x + 3)/(3x + 1))) + 1) + 3)/(1(2(1((1x + 3)/(3x + 1)))^2 - 4(1((1x + 3)/(3x + 1))) + 1) + 1)))/(2((3(2(1((1x + 3)/(3x + 1)))^2 - 4(1((1x + 3)/(3x + 1))) + 1) + 3)/(1(2(1((1x + 3)/(3x + 1)))^2 - 4(1((1x + 3)/(3x + 1))) + 1) + 1)) - 1) and g(x) = 2((-1((3(-3sin(3\u03c0x) - 2) + 1)/(1(-3sin(3\u03c0x) - 2))) + 2)/(-2((3(-3sin(3\u03c0x) - 2) + 1)/(1(-3sin(3\u03c0x) - 2))) - 1)) + 1 between the vertical lines x = -4.4 and x = -4.0. 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) = -3sin(2\u03c0(-2(1(5(-3x^2 + 3x + 4)^2 + 5(-3x^2 + 3x + 4) - 1)^2 + 2(5(-3x^2 + 3x + 4)^2 + 5(-3x^2 + 3x + 4) - 1) + 5)^2 + 1(1(5(-3x^2 + 3x + 4)^2 + 5(-3x^2 + 3x + 4) - 1)^2 + 2(5(-3x^2 + 3x + 4)^2 + 5(-3x^2 + 3x + 4) - 1) + 5) - 2) - 2) - 2 and g(x) = -2|((1(2e^(1(-3|x| - 2)) - 2) + 3)/(-3(2e^(1(-3|x| - 2)) - 2) - 2)) - 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) = -5((1((1(-1cos(1\u03c0(4x^2 + 4x + 4) + 3) + 2) + 3)/(-1(-1cos(1\u03c0(4x^2 + 4x + 4) + 3) + 2) + 2)) - 3)/(-2((1(-1cos(1\u03c0(4x^2 + 4x + 4) + 3) + 2) + 3)/(-1(-1cos(1\u03c0(4x^2 + 4x + 4) + 3) + 2) + 2)) - 2))^2 + 3((1((1(-1cos(1\u03c0(4x^2 + 4x + 4) + 3) + 2) + 3)/(-1(-1cos(1\u03c0(4x^2 + 4x + 4) + 3) + 2) + 2)) - 3)/(-2((1(-1cos(1\u03c0(4x^2 + 4x + 4) + 3) + 2) + 3)/(-1(-1cos(1\u03c0(4x^2 + 4x + 4) + 3) + 2) + 2)) - 2)) + 1, g(x) = -1|(-5(4(5x^2 - 2x - 3) + 5) + 3) - 3| - 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-2(2|((3(-1|(1sin(2\u03c0x - 1) + 2)| - 1) - 1)/(1(-1|(1sin(2\u03c0x - 1) + 2)| - 1))) + 3|) - 2)/(2(2|((3(-1|(1sin(2\u03c0x - 1) + 2)| - 1) - 1)/(1(-1|(1sin(2\u03c0x - 1) + 2)| - 1))) + 3|) + 2), g(x) = -2(1(-3cos(3\u03c0(-2|x + 3| + 1) - 3) - 2)^2 + 3(-3cos(3\u03c0(-2|x + 3| + 1) - 3) - 2) + 4) + 3, 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": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2(4((1(1|(-1sin(1\u03c0x + 1) + 3) + 2| + 3) - 2)/(-3(1|(-1sin(1\u03c0x + 1) + 3) + 2| + 3) - 2))) + 4 and g(x) = 3|((-2(1|(-5x^2 + 3x + 5) + 1| - 2) + 1)/(3(1|(-5x^2 + 3x + 5) + 1| - 2) + 1))| - 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": "5.9", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -4(-3|(-3sin(3\u03c0((3(-1|x| + 1) + 2)/(1(-1|x| + 1) - 3)) + 3) + 2) + 1| + 3) + 5, g(x) = 3(5(-3(-2|x + 3|) - 4)^2 + 3(-3(-2|x + 3|) - 4) + 5) + 2, x = -3.6, 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": "1.9", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (1(-4((-2(-2(1|x| - 2) + 1) - 1)/(3(-2(1|x| - 2) + 1) - 2))^2 - 5((-2(-2(1|x| - 2) + 1) - 1)/(3(-2(1|x| - 2) + 1) - 2)) - 1) + 3)/(-1(-4((-2(-2(1|x| - 2) + 1) - 1)/(3(-2(1|x| - 2) + 1) - 2))^2 - 5((-2(-2(1|x| - 2) + 1) - 1)/(3(-2(1|x| - 2) + 1) - 2)) - 1)) and g(x) = 2(4((3((1x + 3)/(-1x + 2)) - 3)/(1((1x + 3)/(-1x + 2)) - 2))^2 - 4((3((1x + 3)/(-1x + 2)) - 3)/(1((1x + 3)/(-1x + 2)) - 2)) - 3) + 3 between the vertical lines x = 1.0 and x = 3.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "161.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3(-1(-1cos(1\u03c0(2|((-2x + 2)/(-2x + 3)) + 3|) + 2) - 3) - 5)^2 + 1 and g(x) = -5(-1sin(1\u03c0(1(-4x^2 + 1x + 5)^2 + 2(-4x^2 + 1x + 5) + 2)) + 3)^2 + 2(-1sin(1\u03c0(1(-4x^2 + 1x + 5)^2 + 2(-4x^2 + 1x + 5) + 2)) + 3) - 4 from x = 3.3 to x = 3.4. 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((1(-3(1(2|x + 1| - 3) - 1)^2 + 2(1(2|x + 1| - 3) - 1) - 3) + 2)/(1(-3(1(2|x + 1| - 3) - 1)^2 + 2(1(2|x + 1| - 3) - 1) - 3) - 3))^2 - 2((1(-3(1(2|x + 1| - 3) - 1)^2 + 2(1(2|x + 1| - 3) - 1) - 3) + 2)/(1(-3(1(2|x + 1| - 3) - 1)^2 + 2(1(2|x + 1| - 3) - 1) - 3) - 3)) + 3 and g(x) = -4(-1(-5(-2cos(1\u03c0x + 3))^2 - 3(-2cos(1\u03c0x + 3))) - 2) + 1 between the vertical lines x = -1.3 and x = -0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18.8", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-1(-1(3cos(3\u03c0(2((-2x)/(3x + 3)) + 3) + 1))) + 3)/(-1(-1(3cos(3\u03c0(2((-2x)/(3x + 3)) + 3) + 1))) - 2), g(x) = -1|(2((2(-5x^2 + 2x - 5) - 1)/(2(-5x^2 + 2x - 5) - 1)) - 5) + 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": "0.9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-1(3|(1(1((-3x - 2)/(3x - 2))^2 + 5((-3x - 2)/(3x - 2)) - 3)^2 + 4(1((-3x - 2)/(3x - 2))^2 + 5((-3x - 2)/(3x - 2)) - 3) - 3)| - 2))/(-3(3|(1(1((-3x - 2)/(3x - 2))^2 + 5((-3x - 2)/(3x - 2)) - 3)^2 + 4(1((-3x - 2)/(3x - 2))^2 + 5((-3x - 2)/(3x - 2)) - 3) - 3)| - 2) - 3) and g(x) = -2(-3|(4((-3x - 1)/(-3x))^2 + 2((-3x - 1)/(-3x))) - 3| + 1) + 2 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((-3((3(-1|(1|x - 3| - 3) - 1| + 1) + 1)/(1(-1|(1|x - 3| - 3) - 1| + 1) + 3)) - 1)/(3((3(-1|(1|x - 3| - 3) - 1| + 1) + 1)/(1(-1|(1|x - 3| - 3) - 1| + 1) + 3)) + 2)) - 3)/(1((-3((3(-1|(1|x - 3| - 3) - 1| + 1) + 1)/(1(-1|(1|x - 3| - 3) - 1| + 1) + 3)) - 1)/(3((3(-1|(1|x - 3| - 3) - 1| + 1) + 1)/(1(-1|(1|x - 3| - 3) - 1| + 1) + 3)) + 2)) - 3) and g(x) = -1|(-4(-3|(-1x^2 - 5x) - 1| + 3)^2 - 5(-3|(-1x^2 - 5x) - 1| + 3)) + 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": "0.9", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -3(1(1(-3|(-4x - 2) + 3|)^2 + 4(-3|(-4x - 2) + 3|) - 1) - 5) + 5, g(x) = 5(-4(-3(3sin(2\u03c0x + 3) - 1) + 3) - 3)^2 + 4, 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": "10.8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-2(3sin(3\u03c0((2(1(1x - 1)^2 - 4(1x - 1) + 3) - 3)/(2(1(1x - 1)^2 - 4(1x - 1) + 3) - 1)) - 2) + 1) - 1)/(-3(3sin(3\u03c0((2(1(1x - 1)^2 - 4(1x - 1) + 3) - 3)/(2(1(1x - 1)^2 - 4(1x - 1) + 3) - 1)) - 2) + 1) + 1) and g(x) = (-3(-1(2(3cos(1\u03c0x + 2) + 2)^2 + 3(3cos(1\u03c0x + 2) + 2) + 3)^2 + 4(2(3cos(1\u03c0x + 2) + 2)^2 + 3(3cos(1\u03c0x + 2) + 2) + 3) - 3))/(1(-1(2(3cos(1\u03c0x + 2) + 2)^2 + 3(3cos(1\u03c0x + 2) + 2) + 3)^2 + 4(2(3cos(1\u03c0x + 2) + 2)^2 + 3(3cos(1\u03c0x + 2) + 2) + 3) - 3)) from x = 3.9 to x = 4.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2((1(2sin(2\u03c0(3|((-1x + 1)/(-1x - 1)) + 3| - 2) + 2) + 3) - 1)/(-1(2sin(2\u03c0(3|((-1x + 1)/(-1x - 1)) + 3| - 2) + 2) + 3))) and g(x) = 2cos(3\u03c0((2(-4(-2x + 4) - 5) - 2)/(-2(-4(-2x + 4) - 5) - 2)) - 3) + 3 from x = 2.4 to x = 3.3. 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) = -4(-5((2(2((2x)/(2x - 1)) + 2) + 2)/(-2(2((2x)/(2x - 1)) + 2) + 3)) - 4) + 5 and g(x) = 2cos(3\u03c0(1(2(1|x + 1| - 2)^2 + 3(1|x + 1| - 2) - 3)^2 - 5(2(1|x + 1| - 2)^2 + 3(1|x + 1| - 2) - 3) - 4)) 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1(1(5(-2(3x)^2 - 3(3x) + 5)^2 - 5(-2(3x)^2 - 3(3x) + 5) - 3)^2 + 1(5(-2(3x)^2 - 3(3x) + 5)^2 - 5(-2(3x)^2 - 3(3x) + 5) - 3) - 4) + 5 and g(x) = (-2(4(5(5x^2 + 2x + 3)^2 - 4(5x^2 + 2x + 3) + 3)^2 + 3(5(5x^2 + 2x + 3)^2 - 4(5x^2 + 2x + 3) + 3) + 1) + 2)/(-2(4(5(5x^2 + 2x + 3)^2 - 4(5x^2 + 2x + 3) + 3)^2 + 3(5(5x^2 + 2x + 3)^2 - 4(5x^2 + 2x + 3) + 3) + 1) + 3) between the vertical lines x = -0.8 and x = -0.7000000000000001. 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": "Calculate the area enclosed between the functions f(x) = (-1(-2|(-1|(-4(3|x - 1| - 2)^2 - 4(3|x - 1| - 2) + 3) - 2|) + 2| + 2) + 2)/(-3(-2|(-1|(-4(3|x - 1| - 2)^2 - 4(3|x - 1| - 2) + 3) - 2|) + 2| + 2) - 3) and g(x) = (3(3|(3|((2x - 2)/(-1x + 2)) - 1|) + 1| - 1) + 1)/(1(3|(3|((2x - 2)/(-1x + 2)) - 1|) + 1| - 1)) from x = 1.8 to x = 1.9. 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|(-1(-3e^(-2(-3|(-5x^2 + 3x + 5) + 3| + 3)) + 2) - 3) - 3| and g(x) = 1(4(1(-1x^2 + 2)^2 - 4(-1x^2 + 2) - 1)^2 - 5(1(-1x^2 + 2)^2 - 4(-1x^2 + 2) - 1) + 4) + 2 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": "16.6", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 4((2(-2((2(-4x^2 - 1x + 4) + 2)/(3(-4x^2 - 1x + 4) + 1))^2 + 5((2(-4x^2 - 1x + 4) + 2)/(3(-4x^2 - 1x + 4) + 1)) + 1) - 2)/(-3(-2((2(-4x^2 - 1x + 4) + 2)/(3(-4x^2 - 1x + 4) + 1))^2 + 5((2(-4x^2 - 1x + 4) + 2)/(3(-4x^2 - 1x + 4) + 1)) + 1) + 4))^2 + 1((2(-2((2(-4x^2 - 1x + 4) + 2)/(3(-4x^2 - 1x + 4) + 1))^2 + 5((2(-4x^2 - 1x + 4) + 2)/(3(-4x^2 - 1x + 4) + 1)) + 1) - 2)/(-3(-2((2(-4x^2 - 1x + 4) + 2)/(3(-4x^2 - 1x + 4) + 1))^2 + 5((2(-4x^2 - 1x + 4) + 2)/(3(-4x^2 - 1x + 4) + 1)) + 1) + 4)) - 3, g(x) = 1(-3|((3((-1x - 2)/(1x + 3)) - 3)/(1((-1x - 2)/(1x + 3)))) - 2| + 1)^2 + 1(-3|((3((-1x - 2)/(1x + 3)) - 3)/(1((-1x - 2)/(1x + 3)))) - 2| + 1) - 2, x = -2.9, and x = -2.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2|((2((-1(-4(-5x^2 + 5) + 1) - 3)/(2(-4(-5x^2 + 5) + 1) + 3)) + 3)/(2((-1(-4(-5x^2 + 5) + 1) - 3)/(2(-4(-5x^2 + 5) + 1) + 3)) + 3)) + 3| + 3 and g(x) = 2|(2((3(2|x - 2| - 1) + 3)/(3(2|x - 2| - 1) - 2))^2 + 5((3(2|x - 2| - 1) + 3)/(3(2|x - 2| - 1) - 2)) + 5) + 2| + 1 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": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2|((3(1|((-1(2cos(2\u03c0x + 2) - 3) - 1)/(-1(2cos(2\u03c0x + 2) - 3) + 2)) - 1| + 2) - 3)/(-2(1|((-1(2cos(2\u03c0x + 2) - 3) - 1)/(-1(2cos(2\u03c0x + 2) - 3) + 2)) - 1| + 2) - 2)) - 1| + 1, g(x) = 1|(5((3(2|x - 1| - 2))/(-3(2|x - 1| - 2) - 3)) - 3) + 2| - 2, x = 0.3, 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": "141.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-1((3(3(3(-1x^2 - 4x - 5) + 5) + 5))/(2(3(3(-1x^2 - 4x - 5) + 5) + 5) + 3)) - 1)/(2((3(3(3(-1x^2 - 4x - 5) + 5) + 5))/(2(3(3(-1x^2 - 4x - 5) + 5) + 5) + 3)) - 3), g(x) = (-1(-1(1cos(1\u03c0(1x^2 + 5x - 1) - 2) - 2)^2 + 2(1cos(1\u03c0(1x^2 + 5x - 1) - 2) - 2) + 2) + 2)/(1(-1(1cos(1\u03c0(1x^2 + 5x - 1) - 2) - 2)^2 + 2(1cos(1\u03c0(1x^2 + 5x - 1) - 2) - 2) + 2)), x = -3.2, 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": "13.9", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1|((-2(-1|(-3|(-3x + 3) - 1| - 3) + 3| - 2))/(-1(-1|(-3|(-3x + 3) - 1| - 3) + 3| - 2) - 2)) - 2| and g(x) = -3(2cos(1\u03c0(-5((-2x - 3)/(1x))) - 1)) + 1 between the vertical lines x = -1.6 and x = -1.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1(1(3|((1((-3x + 3)/(2x + 1)) - 1)/(-1((-3x + 3)/(2x + 1)) - 1)) - 2| + 1) - 4)^2 - 2(1(3|((1((-3x + 3)/(2x + 1)) - 1)/(-1((-3x + 3)/(2x + 1)) - 1)) - 2| + 1) - 4) + 4 and g(x) = 1|((-2((1(-1|x|) - 2)/(-1(-1|x|) - 3)) - 2)/(1((1(-1|x|) - 2)/(-1(-1|x|) - 3))))| from x = 0.6 to x = 0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3(-3(-1(2|(-1x^2 - 5x + 5) + 1| - 1) + 2)^2 + 4(-1(2|(-1x^2 - 5x + 5) + 1| - 1) + 2) + 1) + 4 and g(x) = -2e^(1(1(-3(4x - 2) - 3))) + 1 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": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2((1(-4(1((1x - 1)/(2x - 3)) + 2)^2 - 4(1((1x - 1)/(2x - 3)) + 2) + 2) - 2)/(1(-4(1((1x - 1)/(2x - 3)) + 2)^2 - 4(1((1x - 1)/(2x - 3)) + 2) + 2) + 1))^2 - 3((1(-4(1((1x - 1)/(2x - 3)) + 2)^2 - 4(1((1x - 1)/(2x - 3)) + 2) + 2) - 2)/(1(-4(1((1x - 1)/(2x - 3)) + 2)^2 - 4(1((1x - 1)/(2x - 3)) + 2) + 2) + 1)) - 1 and g(x) = (3(2((2(2|x + 3| + 1) + 1)/(-1(2|x + 3| + 1) - 3))^2) - 2)/(2(2((2(2|x + 3| + 1) + 1)/(-1(2|x + 3| + 1) - 3))^2) + 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": "15.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1|(-3(2((1(-2sin(1\u03c0x - 1)) - 1)/(3(-2sin(1\u03c0x - 1)) - 1)) + 5) - 5) + 3| - 2 and g(x) = 1(4(-5(-4x)^2 + 2(-4x) - 1)^2 - 2(-5(-4x)^2 + 2(-4x) - 1) - 4) + 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": "2.9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 3cos(2\u03c0(-3|((2(2|((2x)/(-2x - 2)) + 1| - 3) - 1)/(1(2|((2x)/(-2x - 2)) + 1| - 3) - 3)) + 3| + 3) - 1) + 1 and g(x) = 5(1|((-3(-2|x - 2|))/(3(-2|x - 2|) + 1)) - 2| - 3)^2 + 1(1|((-3(-2|x - 2|))/(3(-2|x - 2|) + 1)) - 2| - 3) - 1 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": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (3(2(-2|(2cos(2\u03c0(2|x + 2| + 3) - 2) + 1)| - 1) - 3) - 2)/(-1(2(-2|(2cos(2\u03c0(2|x + 2| + 3) - 2) + 1)| - 1) - 3) - 1) and g(x) = 5(-4(-2(1|x - 2| - 2)) - 1) + 5 from x = 0.1 to x = 3.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "145.9", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2|(-2|(1((-1(1x^2 - 4x - 2) - 2)/(-1(1x^2 - 4x - 2) - 2))) - 1| - 2) - 3|, g(x) = -2|(2|(-4(-3sin(3\u03c0x - 1) - 1)^2 - 5(-3sin(3\u03c0x - 1) - 1) + 4) + 1| - 1) - 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": "4.8", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2|(-1sin(3\u03c0(1(1|(5x - 4) + 3| - 3) + 1) + 3) - 3) + 2| and g(x) = -3e^(-2(3|(4(1|x - 1| + 3) + 5) + 1| - 2)) - 1 between the vertical lines x = -0.3 and x = -0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 5(3|(-2|(1(-5x^2 - 4x + 5)^2 + 3(-5x^2 - 4x + 5)) - 3| - 1) + 2| - 3)^2 + 2(3|(-2|(1(-5x^2 - 4x + 5)^2 + 3(-5x^2 - 4x + 5)) - 3| - 1) + 2| - 3) and g(x) = 1cos(3\u03c0((1(-3|(2x - 5) - 2| - 3) - 1)/(1(-3|(2x - 5) - 2| - 3))) + 2) 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": "87.4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1(5((1(3(-2|x - 2|) + 5) - 3)/(1(3(-2|x - 2|) + 5) + 1)) - 5) + 3 and g(x) = -3sin(1\u03c0(-2(-3((1x + 1)/(-2x + 1)) - 3) - 2) - 1) from x = 1.6 to x = 1.7000000000000002. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3cos(1\u03c0(-4(-4(1(1x - 4)^2 - 3(1x - 4) + 2) - 1)^2 - 2(-4(1(1x - 4)^2 - 3(1x - 4) + 2) - 1) - 1)) + 2, g(x) = (-1((-2(2(1x - 2) - 1) + 3)/(-3(2(1x - 2) - 1) + 2)) + 2)/(-2((-2(2(1x - 2) - 1) + 3)/(-3(2(1x - 2) - 1) + 2)) - 3), 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (1(5((-1((-2(-3cos(2\u03c0x + 2) + 1) + 1)/(2(-3cos(2\u03c0x + 2) + 1) + 1)) - 2)/(-1((-2(-3cos(2\u03c0x + 2) + 1) + 1)/(2(-3cos(2\u03c0x + 2) + 1) + 1)) - 3))) - 2)/(2(5((-1((-2(-3cos(2\u03c0x + 2) + 1) + 1)/(2(-3cos(2\u03c0x + 2) + 1) + 1)) - 2)/(-1((-2(-3cos(2\u03c0x + 2) + 1) + 1)/(2(-3cos(2\u03c0x + 2) + 1) + 1)) - 3))) + 3) and g(x) = 1(4(1((3x + 3)/(1x)) + 2)^2 + 4(1((3x + 3)/(1x)) + 2) - 2) - 1 from x = -0.7 to x = -0.5. 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": "Determine the area of the region enclosed by the graphs of f(x) = (-2((-2(2|(2cos(3\u03c0(-2x + 3) - 3)) - 3| - 3) + 1)/(-2(2|(2cos(3\u03c0(-2x + 3) - 3)) - 3| - 3) - 3)) - 1)/(-3((-2(2|(2cos(3\u03c0(-2x + 3) - 3)) - 3| - 3) + 1)/(-2(2|(2cos(3\u03c0(-2x + 3) - 3)) - 3| - 3) - 3)) - 3) and g(x) = 1|(-3sin(1\u03c0(-1(-5x + 2)^2 + 5) + 3) - 1) - 1| + 3 between the vertical lines x = -0.0 and x = 0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2|(-2(-1|(1(-1x^2 + 2x - 4)^2 - 1(-1x^2 + 2x - 4) - 4) - 3| + 3)^2 - 2(-1|(1(-1x^2 + 2x - 4)^2 - 1(-1x^2 + 2x - 4) - 4) - 3| + 3) - 5)| and g(x) = -2|(3|(-4((-2x + 3)/(-2x - 3)) + 4) + 3| + 2) + 3| + 1 from x = 0.4 to x = 1.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2sin(3\u03c0(3(1|(3|(-1x^2 + 1x - 1) + 1| - 1)|)^2 - 2(1|(3|(-1x^2 + 1x - 1) + 1| - 1)|) - 1) + 3) and g(x) = (-1((3((1(-5x - 1) + 1)/(1(-5x - 1) - 2)) - 1)/(2((1(-5x - 1) + 1)/(1(-5x - 1) - 2)) - 1)))/(-2((3((1(-5x - 1) + 1)/(1(-5x - 1) - 2)) - 1)/(2((1(-5x - 1) + 1)/(1(-5x - 1) - 2)) - 1)) - 3) between the vertical lines x = -2.7 and x = -2.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1((-1(-4(-3e^(-1(-4x + 3)) + 2) + 1) - 2)/(2(-4(-3e^(-1(-4x + 3)) + 2) + 1) + 2)) + 3 and g(x) = (3(3|(-1cos(1\u03c0(-1|x + 2| - 3)) + 3) - 3| - 3))/(-1(3|(-1cos(1\u03c0(-1|x + 2| - 3)) + 3) - 3| - 3) - 3) between the vertical lines x = 1.4 and x = 1.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "44.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1|(-3((-3(-4(-2|x - 3| + 3) + 5) + 2)/(-2(-4(-2|x - 3| + 3) + 5) + 3))^2 - 2((-3(-4(-2|x - 3| + 3) + 5) + 2)/(-2(-4(-2|x - 3| + 3) + 5) + 3)) - 4)| and g(x) = 5((2((1((-1x)/(-3x)) - 1)/(-1((-1x)/(-3x)) - 1)) - 1)/(-1((1((-1x)/(-3x)) - 1)/(-1((-1x)/(-3x)) - 1)) + 3))^2 + 3((2((1((-1x)/(-3x)) - 1)/(-1((-1x)/(-3x)) - 1)) - 1)/(-1((1((-1x)/(-3x)) - 1)/(-1((-1x)/(-3x)) - 1)) + 3)) + 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2((2((2(3|(1x - 2) - 1| - 2) + 2)/(-1(3|(1x - 2) - 1| - 2) + 2)) + 3)/(3((2(3|(1x - 2) - 1| - 2) + 2)/(-1(3|(1x - 2) - 1| - 2) + 2)) + 1)) + 3 and g(x) = (-3(-2e^(1(-1(2|x| + 3)^2 + 4(2|x| + 3) + 2)) + 1) - 1)/(-2(-2e^(1(-1(2|x| + 3)^2 + 4(2|x| + 3) + 2)) + 1) - 1) from x = -0.8 to x = 0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1((3(5(1(-5x + 5)^2 - 2(-5x + 5) + 4) + 5))/(-2(5(1(-5x + 5)^2 - 2(-5x + 5) + 4) + 5) + 3)) - 1 and g(x) = -5(-5(2(-1x^2 - 5x) + 2)^2 - 3(2(-1x^2 - 5x) + 2))^2 - 4(-5(2(-1x^2 - 5x) + 2)^2 - 3(2(-1x^2 - 5x) + 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": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1|(2(-2e^(1((-2(-3x^2 + 4) - 1)/(-3(-3x^2 + 4) - 3))) + 1)^2 + 3(-2e^(1((-2(-3x^2 + 4) - 1)/(-3(-3x^2 + 4) - 3))) + 1) - 5) + 2| - 3, g(x) = -2|(4((3(-2x - 2) + 3)/(2(-2x - 2) - 1))^2 - 5((3(-2x - 2) + 3)/(2(-2x - 2) - 1)) - 3) - 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": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-3((3(-3(3|((-3x + 3)/(2x - 1))|) + 5) - 3)/(-1(-3(3|((-3x + 3)/(2x - 1))|) + 5) + 3)))/(-2((3(-3(3|((-3x + 3)/(2x - 1))|) + 5) - 3)/(-1(-3(3|((-3x + 3)/(2x - 1))|) + 5) + 3)) - 1) and g(x) = (2(-2cos(2\u03c0(4(1x + 2) + 4) + 3) + 3) + 2)/(-1(-2cos(2\u03c0(4(1x + 2) + 4) + 3) + 3) + 2) between the vertical lines x = 0.9 and x = 1.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6.9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -4(-3e^(-1(3(-4(2x - 2) + 5)^2 - 5(-4(2x - 2) + 5) - 3)) - 1) - 5 and g(x) = -5(-2(3|(-3x + 4) - 3| - 1)^2 - 2(3|(-3x + 4) - 3| - 1) + 2)^2 - 3(-2(3|(-3x + 4) - 3| - 1)^2 - 2(3|(-3x + 4) - 3| - 1) + 2) + 1 from x = 0.2 to x = 0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (1(-4(-3cos(3\u03c0((1(-1|x + 3| - 3) - 2)/(-1(-1|x + 3| - 3) - 2)) - 3) - 3)) - 1)/(-1(-4(-3cos(3\u03c0((1(-1|x + 3| - 3) - 2)/(-1(-1|x + 3| - 3) - 2)) - 3) - 3))) and g(x) = 1|(-3|(2|(2x^2 - 5x - 5) - 2| + 2) - 2| + 2) - 1| - 2 from x = -3.7 to x = -3.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "82.6", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2|((-1((2(1(-2|x - 1|) + 4) - 3)/(-2(1(-2|x - 1|) + 4) + 3)) + 3)/(-3((2(1(-2|x - 1|) + 4) - 3)/(-2(1(-2|x - 1|) + 4) + 3)) - 1)) + 1| + 1 and g(x) = -2|(-3cos(1\u03c0(-5(3x - 5)^2 - 1(3x - 5)) - 1) + 2) + 3| + 2 between the vertical lines x = -3.7 and x = -3.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -5((1((3(-3(4x - 1)^2 + 1(4x - 1) + 2) + 2)/(-3(-3(4x - 1)^2 + 1(4x - 1) + 2) + 1)) - 3)/(2((3(-3(4x - 1)^2 + 1(4x - 1) + 2) + 2)/(-3(-3(4x - 1)^2 + 1(4x - 1) + 2) + 1)) - 1)) - 4, g(x) = 4(1(1(2|x - 1| + 2) - 3)^2 + 3(1(2|x - 1| + 2) - 3) - 1)^2 + 2(1(1(2|x - 1| + 2) - 3)^2 + 3(1(2|x - 1| + 2) - 3) - 1) - 5, x = 0.1, and x = 0.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -5((-3(1(3|(-1x - 3) + 3|)^2 + 5(3|(-1x - 3) + 3|) + 3))/(2(1(3|(-1x - 3) + 3|)^2 + 5(3|(-1x - 3) + 3|) + 3) - 3)) + 1 and g(x) = 1(2|(-2|(1cos(2\u03c0x - 2) + 2) - 1| + 2) - 3|)^2 + 1(2|(-2|(1cos(2\u03c0x - 2) + 2) - 1| + 2) - 3|) - 4 from x = -4.1 to x = -3.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38.6", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-3(-1((2(2|(-3|x + 3| + 3) + 3| - 3) + 3)/(3(2|(-3|x + 3| + 3) + 3| - 3)))^2 + 3((2(2|(-3|x + 3| + 3) + 3| - 3) + 3)/(3(2|(-3|x + 3| + 3) + 3| - 3))) - 5))/(1(-1((2(2|(-3|x + 3| + 3) + 3| - 3) + 3)/(3(2|(-3|x + 3| + 3) + 3| - 3)))^2 + 3((2(2|(-3|x + 3| + 3) + 3| - 3) + 3)/(3(2|(-3|x + 3| + 3) + 3| - 3))) - 5) - 2), g(x) = -4((-2(2|(1x^2 - 4x + 3)|))/(2(2|(1x^2 - 4x + 3)|) - 1)) + 4, x = 2.9, 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": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-2(-3(-3(-3e^(2(-1x - 2)) + 3)^2 - 4(-3e^(2(-1x - 2)) + 3)) + 2) + 2)/(-1(-3(-3(-3e^(2(-1x - 2)) + 3)^2 - 4(-3e^(2(-1x - 2)) + 3)) + 2) + 2) and g(x) = (-2(4(-5(2x - 1)^2 + 3(2x - 1) + 5) - 4) + 2)/(3(4(-5(2x - 1)^2 + 3(2x - 1) + 5) - 4) - 2) between the vertical lines x = -2.2 and x = -2.0. 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": "Determine the area of the region enclosed by the graphs of f(x) = 2e^(-1(2((-3(1(-2|x + 2| - 1) + 4) - 1)/(-3(1(-2|x + 2| - 1) + 4)))^2 + 1((-3(1(-2|x + 2| - 1) + 4) - 1)/(-3(1(-2|x + 2| - 1) + 4))) - 4)) + 1 and g(x) = 2(-1(-5(-2x + 1) - 3)^2 + 1(-5(-2x + 1) - 3) + 3)^2 - 2(-1(-5(-2x + 1) - 3)^2 + 1(-5(-2x + 1) - 3) + 3) - 3 between the vertical lines x = 0.6 and x = 0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.9", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-3(5((2(1sin(2\u03c0(3x^2 - 5x + 1) - 3) + 1) + 3)/(-2(1sin(2\u03c0(3x^2 - 5x + 1) - 3) + 1) + 3))^2 + 3((2(1sin(2\u03c0(3x^2 - 5x + 1) - 3) + 1) + 3)/(-2(1sin(2\u03c0(3x^2 - 5x + 1) - 3) + 1) + 3)) + 2) + 3)/(3(5((2(1sin(2\u03c0(3x^2 - 5x + 1) - 3) + 1) + 3)/(-2(1sin(2\u03c0(3x^2 - 5x + 1) - 3) + 1) + 3))^2 + 3((2(1sin(2\u03c0(3x^2 - 5x + 1) - 3) + 1) + 3)/(-2(1sin(2\u03c0(3x^2 - 5x + 1) - 3) + 1) + 3)) + 2) + 1), g(x) = 4(1e^(1(1((-3x + 2)/(-3x)))) - 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": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-1(-1(-4(-3(-2|x + 3| - 1)^2 + 3(-2|x + 3| - 1)))^2 - 4(-4(-3(-2|x + 3| - 1)^2 + 3(-2|x + 3| - 1))) - 2) - 2)/(-1(-1(-4(-3(-2|x + 3| - 1)^2 + 3(-2|x + 3| - 1)))^2 - 4(-4(-3(-2|x + 3| - 1)^2 + 3(-2|x + 3| - 1))) - 2)), g(x) = (1(2|(-1(2sin(2\u03c0x - 3) + 2)^2 - 2(2sin(2\u03c0x - 3) + 2) + 4) - 2| - 3) + 2)/(-1(2|(-1(2sin(2\u03c0x - 3) + 2)^2 - 2(2sin(2\u03c0x - 3) + 2) + 4) - 2| - 3) - 3), x = 3.1, and x = 3.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-2((-1(-1((-1(-5x^2 - 5x + 2) + 2)/(-3(-5x^2 - 5x + 2) - 1))) - 2)/(3(-1((-1(-5x^2 - 5x + 2) + 2)/(-3(-5x^2 - 5x + 2) - 1))) + 3)))/(-1((-1(-1((-1(-5x^2 - 5x + 2) + 2)/(-3(-5x^2 - 5x + 2) - 1))) - 2)/(3(-1((-1(-5x^2 - 5x + 2) + 2)/(-3(-5x^2 - 5x + 2) - 1))) + 3)) + 3) and g(x) = 3|((-2(-2|((1x)/(3x + 1)) + 3| + 1) + 2)/(-1(-2|((1x)/(3x + 1)) + 3| + 1) - 2)) + 2| + 1 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": "35.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -4(5(4(-4(1cos(1\u03c0x) + 1)^2 + 5(1cos(1\u03c0x) + 1) + 2)^2 - 3(-4(1cos(1\u03c0x) + 1)^2 + 5(1cos(1\u03c0x) + 1) + 2) - 3) - 1) + 5 and g(x) = 1(-5((1((-3x - 3)/(1x - 3)) - 2)/(-1((-3x - 3)/(1x - 3)) + 2))^2 + 4((1((-3x - 3)/(1x - 3)) - 2)/(-1((-3x - 3)/(1x - 3)) + 2)) + 3) - 1 from x = 3.6 to x = 3.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.8", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1|((-2(-1(-2|(2x + 3) - 2| + 3)^2 + 2(-2|(2x + 3) - 2| + 3) - 4))/(2(-1(-2|(2x + 3) - 2| + 3)^2 + 2(-2|(2x + 3) - 2| + 3) - 4) + 3)) - 1|, g(x) = 2cos(1\u03c0(5(2|(2x + 3) + 3| - 2)^2 + 2(2|(2x + 3) + 3| - 2) - 2) - 1) + 3, 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2|(1(3(1|(2sin(1\u03c0x - 3) + 1) - 2|)^2 + 5(1|(2sin(1\u03c0x - 3) + 1) - 2|))^2 + 5) + 1| - 1 and g(x) = -3|(-3(-3((1x + 3)/(2x)) + 4)^2 + 4(-3((1x + 3)/(2x)) + 4) + 4)| - 2 between the vertical lines x = -3.0 and x = -2.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17.8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2(-2|(-4((-3(5x - 5) - 1)/(3(5x - 5) - 1))^2 - 2((-3(5x - 5) - 1)/(3(5x - 5) - 1)) + 3)| + 2)^2 + 3(-2|(-4((-3(5x - 5) - 1)/(3(5x - 5) - 1))^2 - 2((-3(5x - 5) - 1)/(3(5x - 5) - 1)) + 3)| + 2) + 1 and g(x) = (-2(2sin(1\u03c0(-1|(-3x - 3) - 2| - 1) + 1)) - 3)/(-2(2sin(1\u03c0(-1|(-3x - 3) - 2| - 1) + 1)) - 1) from x = -0.9 to 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": "Calculate the area enclosed between the functions f(x) = -2(-1((2(-3(-1|x - 1| + 2)^2 - 5(-1|x - 1| + 2) - 1) - 3)/(2(-3(-1|x - 1| + 2)^2 - 5(-1|x - 1| + 2) - 1) - 1))^2 + 3((2(-3(-1|x - 1| + 2)^2 - 5(-1|x - 1| + 2) - 1) - 3)/(2(-3(-1|x - 1| + 2)^2 - 5(-1|x - 1| + 2) - 1) - 1)) - 3) - 5 and g(x) = -1(2(-2cos(3\u03c0(-5x + 5) - 2) + 1) + 2)^2 - 1(2(-2cos(3\u03c0(-5x + 5) - 2) + 1) + 2) + 5 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": "2.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 5(2(-1(5(1sin(2\u03c0x) + 2)^2 - 1(1sin(2\u03c0x) + 2) - 5) + 2)^2 - 3(-1(5(1sin(2\u03c0x) + 2)^2 - 1(1sin(2\u03c0x) + 2) - 5) + 2) - 1)^2 + 5(2(-1(5(1sin(2\u03c0x) + 2)^2 - 1(1sin(2\u03c0x) + 2) - 5) + 2)^2 - 3(-1(5(1sin(2\u03c0x) + 2)^2 - 1(1sin(2\u03c0x) + 2) - 5) + 2) - 1) + 1, g(x) = 3|(2((1((2x + 3)/(-1x - 3)) + 3)/(-3((2x + 3)/(-1x - 3)))) + 5) - 2| + 3, x = -4.2, and x = -4.1000000000000005. 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": "Calculate the area enclosed between the functions f(x) = -1|(1(1|(3(-1e^(-1x) + 1)^2 - 3(-1e^(-1x) + 1) + 4) + 2| - 3) + 5) + 2| - 3 and g(x) = -3|((-2(-3|(1e^(1x) + 3) - 3| + 3) - 1)/(1(-3|(1e^(1x) + 3) - 3| + 3) + 1)) + 3| - 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": "32.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 4(3|(1|(4(-2cos(3\u03c0x + 2) - 2) + 4)| + 3) + 2|)^2 - 4(3|(1|(4(-2cos(3\u03c0x + 2) - 2) + 4)| + 3) + 2|) + 3 and g(x) = 2((2(4((-3x + 3)/(2x + 3)) + 3) - 2)/(1(4((-3x + 3)/(2x + 3)) + 3)))^2 + 4((2(4((-3x + 3)/(2x + 3)) + 3) - 2)/(1(4((-3x + 3)/(2x + 3)) + 3))) - 3 from x = 3.4 to x = 3.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -5(-3(1|((2(4x + 1) - 3)/(3(4x + 1))) - 2| - 3) - 4) - 5 and g(x) = (-2(2|(4(-1sin(3\u03c0x + 1) + 3)^2 + 3) - 3| + 3) + 3)/(-3(2|(4(-1sin(3\u03c0x + 1) + 3)^2 + 3) - 3| + 3) - 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": "176.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2(-3|(-3(-2(-1x^2 + 5x - 1)^2 + 3(-1x^2 + 5x - 1) + 2) + 5)| - 1)^2 + 4(-3|(-3(-2(-1x^2 + 5x - 1)^2 + 3(-1x^2 + 5x - 1) + 2) + 5)| - 1) - 2 and g(x) = (2(1((1(3cos(1\u03c0x + 1) + 2))/(2(3cos(1\u03c0x + 1) + 2) - 1)) - 3) - 1)/(2(1((1(3cos(1\u03c0x + 1) + 2))/(2(3cos(1\u03c0x + 1) + 2) - 1)) - 3) - 1) 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": "4.7", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3|((-3(-3|(2cos(3\u03c0((-2x + 3)/(-2x - 3)) - 3) - 1) - 1| + 2) + 2)/(-2(-3|(2cos(3\u03c0((-2x + 3)/(-2x - 3)) - 3) - 1) - 1| + 2))) - 1| + 3, g(x) = 3((3(-1sin(3\u03c0(-1x^2 + 1x - 1) - 1) - 3) - 1)/(2(-1sin(3\u03c0(-1x^2 + 1x - 1) - 1) - 3) + 3)) - 4, x = -1.8, and x = -1.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1|(-3|((2((2(-2|x - 3| - 2) - 1)/(1(-2|x - 3| - 2))))/(1((2(-2|x - 3| - 2) - 1)/(1(-2|x - 3| - 2))) + 2)) - 1| - 1) - 3| - 1 and g(x) = (3(-1sin(1\u03c0(3|(-4x^2 - 5x - 3) - 3| + 3) - 1) + 1) - 2)/(-2(-1sin(1\u03c0(3|(-4x^2 - 5x - 3) - 3| + 3) - 1) + 1)) 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": "91.7", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1(1|(-2(-2(-1|x + 3| + 1)^2 + 4(-1|x + 3| + 1) + 2) - 4) + 2| + 3) + 5 and g(x) = (1(3sin(3\u03c0(-2|((2x - 2)/(-3x + 2)) - 1| - 1)) + 3))/(-1(3sin(3\u03c0(-2|((2x - 2)/(-3x + 2)) - 1| - 1)) + 3)) between the vertical lines x = -4.8 and x = -4.3. 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": "Determine the area of the region enclosed by the graphs of f(x) = (1((-1((-1(3cos(3\u03c0((-3x)/(2x - 1)) - 1) + 3) + 2)/(1(3cos(3\u03c0((-3x)/(2x - 1)) - 1) + 3) - 3)) + 3)/(1((-1(3cos(3\u03c0((-3x)/(2x - 1)) - 1) + 3) + 2)/(1(3cos(3\u03c0((-3x)/(2x - 1)) - 1) + 3) - 3)) - 2)) - 1)/(-3((-1((-1(3cos(3\u03c0((-3x)/(2x - 1)) - 1) + 3) + 2)/(1(3cos(3\u03c0((-3x)/(2x - 1)) - 1) + 3) - 3)) + 3)/(1((-1(3cos(3\u03c0((-3x)/(2x - 1)) - 1) + 3) + 2)/(1(3cos(3\u03c0((-3x)/(2x - 1)) - 1) + 3) - 3)) - 2))) and g(x) = (3(2e^(1(-2|(1x^2 - 3x + 4) - 3| + 2)) - 3))/(3(2e^(1(-2|(1x^2 - 3x + 4) - 3| + 2)) - 3) - 2) between the vertical lines x = 2.9 and x = 3.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.4", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1|(-2|(2(5(1x^2 + 3x + 3)^2 + 1(1x^2 + 3x + 3) - 2) - 4)| + 1) - 1| and g(x) = 2e^(-1(-3|((1(-2x^2 + 3x - 3) + 1)/(1(-2x^2 + 3x - 3) + 2)) - 3| - 2)) + 2 between the vertical lines x = 0.0 and x = 0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "52.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3((-3(-1(-2|(4x^2 + 4x + 5) - 1| + 1)) - 3)/(-1(-1(-2|(4x^2 + 4x + 5) - 1| + 1)) + 2))^2 + 4((-3(-1(-2|(4x^2 + 4x + 5) - 1| + 1)) - 3)/(-1(-1(-2|(4x^2 + 4x + 5) - 1| + 1)) + 2)) - 3 and g(x) = -5(1(2(-3cos(2\u03c0x + 2) - 2) + 3) - 4)^2 - 2(1(2(-3cos(2\u03c0x + 2) - 2) + 3) - 4) + 1 between the vertical lines x = -2.0 and x = -1.6. 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(-4(-2e^(1x) - 2)^2 - 2(-2e^(1x) - 2) - 3)^2 + 2(-4(-2e^(1x) - 2)^2 - 2(-2e^(1x) - 2) - 3) + 2)^2 - 2(1(-4(-2e^(1x) - 2)^2 - 2(-2e^(1x) - 2) - 3)^2 + 2(-4(-2e^(1x) - 2)^2 - 2(-2e^(1x) - 2) - 3) + 2) + 3) - 2)/(3(1(1(-4(-2e^(1x) - 2)^2 - 2(-2e^(1x) - 2) - 3)^2 + 2(-4(-2e^(1x) - 2)^2 - 2(-2e^(1x) - 2) - 3) + 2)^2 - 2(1(-4(-2e^(1x) - 2)^2 - 2(-2e^(1x) - 2) - 3)^2 + 2(-4(-2e^(1x) - 2)^2 - 2(-2e^(1x) - 2) - 3) + 2) + 3) - 2), g(x) = -1e^(1(4(-5((1x - 1)/(2x - 1))^2 + 4((1x - 1)/(2x - 1)) + 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": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1cos(3\u03c0(-2|(5(-5((-2x - 2)/(1x + 2))^2 - 4((-2x - 2)/(1x + 2)) - 2)^2 + 2(-5((-2x - 2)/(1x + 2))^2 - 4((-2x - 2)/(1x + 2)) - 2) - 5) + 3| + 3) + 1) + 3 and g(x) = 1(3e^(-1(1(-1x^2 + 1x + 4) - 4)) + 3) - 5 from x = 1.3 to 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": "Calculate the area enclosed between the functions f(x) = -5(-2cos(1\u03c0((-1((2(-1|x + 3| + 2) + 1)/(1(-1|x + 3| + 2) - 3)) + 2)/(2((2(-1|x + 3| + 2) + 1)/(1(-1|x + 3| + 2) - 3)) - 1)) - 2) - 1) - 4 and g(x) = (-2(4(-1|(-1|x + 3| - 3) - 3| + 3) - 1))/(-2(4(-1|(-1|x + 3| - 3) - 3| + 3) - 1) - 3) 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": "0.7", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-1(2(4(4(-3|x + 2| + 2)^2 - 5(-3|x + 2| + 2) + 1)^2 - 1) - 2))/(-1(2(4(4(-3|x + 2| + 2)^2 - 5(-3|x + 2| + 2) + 1)^2 - 1) - 2) - 2) and g(x) = -1(1|(-5((-2x)/(2x - 3))^2 + 4((-2x)/(2x - 3)) - 5) - 1| - 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": "3.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -4(-5(-1((-2(3x^2 + 1) - 1)/(-3(3x^2 + 1) + 1))) + 5) + 5 and g(x) = -1|((-3((1(1x^2 - 5x + 4) - 2)/(1(1x^2 - 5x + 4))) - 3)/(-2((1(1x^2 - 5x + 4) - 2)/(1(1x^2 - 5x + 4))) + 1)) - 2| - 1 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": "148.5", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -4(1|((3(-3(-2e^(-2x) - 2)^2 + 5(-2e^(-2x) - 2) + 3))/(-1(-3(-2e^(-2x) - 2)^2 + 5(-2e^(-2x) - 2) + 3) + 3)) + 3| + 1)^2 + 4(1|((3(-3(-2e^(-2x) - 2)^2 + 5(-2e^(-2x) - 2) + 3))/(-1(-3(-2e^(-2x) - 2)^2 + 5(-2e^(-2x) - 2) + 3) + 3)) + 3| + 1) + 3, g(x) = 2|(2|(3cos(2\u03c0(4x - 5) - 2) - 3) + 2| - 3) - 2| + 1, x = -3.6, and x = -3.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -4(-1(1(-1(3cos(1\u03c0x + 2) - 1)^2 - 4(3cos(1\u03c0x + 2) - 1) - 1) + 1)^2 + 2(1(-1(3cos(1\u03c0x + 2) - 1)^2 - 4(3cos(1\u03c0x + 2) - 1) - 1) + 1) - 2)^2 + 5(-1(1(-1(3cos(1\u03c0x + 2) - 1)^2 - 4(3cos(1\u03c0x + 2) - 1) - 1) + 1)^2 + 2(1(-1(3cos(1\u03c0x + 2) - 1)^2 - 4(3cos(1\u03c0x + 2) - 1) - 1) + 1) - 2) - 4, g(x) = -2(4(3((2x - 2)/(-2x - 3))^2 + 5((2x - 2)/(-2x - 3)) + 3) - 1) + 3, 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": "61.7", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (1(3(-1(1cos(3\u03c0(1|x| - 3) - 3) + 2) - 4) + 5) - 3)/(3(3(-1(1cos(3\u03c0(1|x| - 3) - 3) + 2) - 4) + 5) + 2), g(x) = -1|(1(-2cos(2\u03c0((1x + 1)/(3x - 2)) - 2) - 1)^2 - 5(-2cos(2\u03c0((1x + 1)/(3x - 2)) - 2) - 1) + 3) - 3| + 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": "0.7", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1|(-3(-1(-2sin(3\u03c0(2|x + 2| + 2) - 3) - 1)^2 + 5(-2sin(3\u03c0(2|x + 2| + 2) - 3) - 1) + 4)^2 + 3) + 2| - 3 and g(x) = (3(-4((-2(-3sin(2\u03c0x - 3) + 2) - 2)/(1(-3sin(2\u03c0x - 3) + 2))) + 2) + 1)/(2(-4((-2(-3sin(2\u03c0x - 3) + 2) - 2)/(1(-3sin(2\u03c0x - 3) + 2))) + 2) - 3) 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": "23.4", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (1(-3|(-3|((-3(1|x - 1| + 1) - 3)/(-1(1|x - 1| + 1) + 2)) + 2| + 1)|) - 3)/(-2(-3|(-3|((-3(1|x - 1| + 1) - 3)/(-1(1|x - 1| + 1) + 2)) + 2| + 1)|) + 1) and g(x) = 1|(-3((-3(2cos(3\u03c0x - 2) + 3) + 3)/(1(2cos(3\u03c0x - 2) + 3) - 2))^2 + 2((-3(2cos(3\u03c0x - 2) + 3) + 3)/(1(2cos(3\u03c0x - 2) + 3) - 2)) + 5) + 3| - 1 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": "208.7", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (3(5(-3|((-2(1|x - 1| + 2) - 2)/(3(1|x - 1| + 2) - 2))| - 2) - 1) + 1)/(-2(5(-3|((-2(1|x - 1| + 2) - 2)/(3(1|x - 1| + 2) - 2))| - 2) - 1) + 3), g(x) = (-2(-1(-2cos(1\u03c0(-2x^2 - 5x + 1) + 2) + 1) + 1) - 3)/(-1(-1(-2cos(1\u03c0(-2x^2 - 5x + 1) + 2) + 1) + 1) + 2), x = -4.3, and x = -4.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (3(2(-1|(-1cos(3\u03c0(1x^2 + 4x + 3) - 2)) - 2| - 2)^2 + 1) - 3)/(3(2(-1|(-1cos(3\u03c0(1x^2 + 4x + 3) - 2)) - 2| - 2)^2 + 1) + 1) and g(x) = 4((1(2(2x + 2) + 2) - 1)/(1(2(2x + 2) + 2) - 2))^2 - 1((1(2(2x + 2) + 2) - 1)/(1(2(2x + 2) + 2) - 2)) from x = -1.7 to 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) = 2|((-3(-5(-1((-2x + 1)/(2x + 2)) - 4)^2 + 4(-1((-2x + 1)/(2x + 2)) - 4) + 1) + 3)/(-3(-5(-1((-2x + 1)/(2x + 2)) - 4)^2 + 4(-1((-2x + 1)/(2x + 2)) - 4) + 1) + 2)) - 3| - 3 and g(x) = 1((2(2|(-2x^2 - 4x + 2) + 3| + 3) - 2)/(-1(2|(-2x^2 - 4x + 2) + 3| + 3) - 1))^2 + 4((2(2|(-2x^2 - 4x + 2) + 3| + 3) - 2)/(-1(2|(-2x^2 - 4x + 2) + 3| + 3) - 1)) + 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": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-2(-5(-1|(2(3cos(3\u03c0x) - 1)^2)| + 3)^2 + 1(-1|(2(3cos(3\u03c0x) - 1)^2)| + 3) + 3) - 1)/(3(-5(-1|(2(3cos(3\u03c0x) - 1)^2)| + 3)^2 + 1(-1|(2(3cos(3\u03c0x) - 1)^2)| + 3) + 3) - 2) and g(x) = 1(-1(3(-2x + 3)^2 - 3(-2x + 3) + 5)^2 + 4(3(-2x + 3)^2 - 3(-2x + 3) + 5) + 4) + 4 from x = 0.9 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": "Determine the area of the region enclosed by the graphs of f(x) = (3(-3(2|(5(1cos(3\u03c0x + 2) + 2) - 2) + 2| + 2) - 1) + 1)/(2(-3(2|(5(1cos(3\u03c0x + 2) + 2) - 2) + 2| + 2) - 1) - 1) and g(x) = 4(-3(4((1x - 1)/(3x)) - 4) - 5)^2 - 1(-3(4((1x - 1)/(3x)) - 4) - 5) between the vertical lines x = -1.8 and x = -1.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.7", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1(1(-4(2sin(2\u03c0(3x^2 + 3x - 3) + 1) - 1)^2 - 2(2sin(2\u03c0(3x^2 + 3x - 3) + 1) - 1) + 5)^2 + 1(-4(2sin(2\u03c0(3x^2 + 3x - 3) + 1) - 1)^2 - 2(2sin(2\u03c0(3x^2 + 3x - 3) + 1) - 1) + 5) + 2) + 3 and g(x) = 2|(-1(-1|(3x^2 + 2x + 3) - 1| - 3)^2 - 4(-1|(3x^2 + 2x + 3) - 1| - 3) + 3) + 2| - 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": "1.9", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-2(3|(3|(5((2x + 3)/(-1x + 3)) + 1) + 2| - 3)| + 3) + 1)/(-1(3|(3|(5((2x + 3)/(-1x + 3)) + 1) + 2| - 3)| + 3)), g(x) = 3|(1((3(-3|x| - 2) - 2)/(3(-3|x| - 2) + 1)) - 2) - 1| - 3, x = -0.4, and x = 0.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-1(2|(3|(2|(-1sin(1\u03c0x + 1) - 1) + 1| + 3) + 1| + 1) + 3| + 3) - 2)/(1(2|(3|(2|(-1sin(1\u03c0x + 1) - 1) + 1| + 3) + 1| + 1) + 3| + 3)) and g(x) = (3(5(2cos(1\u03c0(-3x^2 - 4x + 5) - 3) + 1) - 5) - 3)/(2(5(2cos(1\u03c0(-3x^2 - 4x + 5) - 3) + 1) - 5) - 1) between the vertical lines x = 1.3 and x = 1.8. 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(5(1(2x^2 + 1x + 3) - 4)^2 - 3(1(2x^2 + 1x + 3) - 4) + 2) + 3)/(-2(5(1(2x^2 + 1x + 3) - 4)^2 - 3(1(2x^2 + 1x + 3) - 4) + 2) - 2)) + 3)/(-1((-1(5(1(2x^2 + 1x + 3) - 4)^2 - 3(1(2x^2 + 1x + 3) - 4) + 2) + 3)/(-2(5(1(2x^2 + 1x + 3) - 4)^2 - 3(1(2x^2 + 1x + 3) - 4) + 2) - 2))) and g(x) = -2|(1((-1((1x - 1)/(-1x + 3)))/(2((1x - 1)/(-1x + 3)) - 3)) + 5) - 1| + 3 from x = 2.2 to x = 3.0. 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) = 2|(5(2e^(1(-1|(-2|x + 3| + 1) + 3| + 2)) - 2) - 3)| - 1 and g(x) = (3(5(1(-1sin(3\u03c0x - 1) - 1)^2 - 4(-1sin(3\u03c0x - 1) - 1) - 3)^2 - 5(1(-1sin(3\u03c0x - 1) - 1)^2 - 4(-1sin(3\u03c0x - 1) - 1) - 3) - 2) + 3)/(1(5(1(-1sin(3\u03c0x - 1) - 1)^2 - 4(-1sin(3\u03c0x - 1) - 1) - 3)^2 - 5(1(-1sin(3\u03c0x - 1) - 1)^2 - 4(-1sin(3\u03c0x - 1) - 1) - 3) - 2)) from x = -0.2 to x = -0.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2(1|(4(2(3|x - 1| - 3)^2 - 1(3|x - 1| - 3) - 2)^2 - 5(2(3|x - 1| - 3)^2 - 1(3|x - 1| - 3) - 2) + 5) - 1| - 1)^2 + 2(1|(4(2(3|x - 1| - 3)^2 - 1(3|x - 1| - 3) - 2)^2 - 5(2(3|x - 1| - 3)^2 - 1(3|x - 1| - 3) - 2) + 5) - 1| - 1) - 2 and g(x) = 3(4(-1|(3sin(2\u03c0x - 3) + 2) - 2| - 3)^2 + 2(-1|(3sin(2\u03c0x - 3) + 2) - 2| - 3) - 4) + 5 between the vertical lines x = 1.6 and x = 1.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "61.9", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 3sin(3\u03c0(1(5(-3(3|x|) + 4)^2 + 5(-3(3|x|) + 4) - 4) + 4) - 1) - 2 and g(x) = (1(2(-1|((2x - 1)/(-2x - 3)) + 1| - 2)) - 2)/(2(2(-1|((2x - 1)/(-2x - 3)) + 1| - 2)) + 2) between the vertical lines x = -4.4 and x = -4.3. 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) = -2|(2(-2cos(2\u03c0((-1(-1x^2 + 1x - 1))/(-3(-1x^2 + 1x - 1) - 3)) - 3)) + 5)| and g(x) = (-2(-3sin(3\u03c0(-2|(-5x^2 - 5x + 2) - 3| + 1) + 2) - 1) + 2)/(-3(-3sin(3\u03c0(-2|(-5x^2 - 5x + 2) - 3| + 1) + 2) - 1) + 2) from x = -3.5 to x = -3.4. 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": "Calculate the area enclosed between the functions f(x) = -4(-3sin(1\u03c0(2((-1((2x - 2)/(-3x)) + 2)/(3((2x - 2)/(-3x)) + 3))^2 + 2((-1((2x - 2)/(-3x)) + 2)/(3((2x - 2)/(-3x)) + 3)) - 3) - 2))^2 + 1(-3sin(1\u03c0(2((-1((2x - 2)/(-3x)) + 2)/(3((2x - 2)/(-3x)) + 3))^2 + 2((-1((2x - 2)/(-3x)) + 2)/(3((2x - 2)/(-3x)) + 3)) - 3) - 2)) + 3 and g(x) = 2sin(2\u03c0(2|((-2(2|x + 2| - 1) - 3)/(-1(2|x + 2| - 1) - 2)) + 2| + 3) - 3) - 3 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": "1.7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (2(2sin(1\u03c0(1(-1|(2x^2 + 2x - 3) - 2| + 1) - 4) - 1) + 2) + 1)/(2(2sin(1\u03c0(1(-1|(2x^2 + 2x - 3) - 2| + 1) - 4) - 1) + 2) - 1) and g(x) = (1(3sin(1\u03c0(4(-2|x - 3| + 2) + 5)) - 2) + 2)/(3(3sin(1\u03c0(4(-2|x - 3| + 2) + 5)) - 2) + 1) from x = -3.3 to x = -3.1999999999999997. 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) = 4((-1((-3(3(-5x + 4)^2 - 5(-5x + 4)) + 2)/(1(3(-5x + 4)^2 - 5(-5x + 4)) - 2)) - 2)/(-1((-3(3(-5x + 4)^2 - 5(-5x + 4)) + 2)/(1(3(-5x + 4)^2 - 5(-5x + 4)) - 2)) + 3)) - 2 and g(x) = -1(2|(2(3x^2 - 5x + 3)^2 + 2(3x^2 - 5x + 3) + 4) - 3| - 2) + 2 from x = 0.4 to x = 0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.8", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3|(-1(-4(1(1sin(2\u03c0x + 3) - 3)^2 + 4(1sin(2\u03c0x + 3) - 3) - 3) + 2) + 2) + 2| - 1 and g(x) = -5(-1(2|(2e^(1x) - 3) - 2| + 3) + 5)^2 + 2 between the vertical lines x = 0.3 and x = 1.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "53.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -3e^(2((-3(-3|((1((-2x - 2)/(3x + 2)))/(2((-2x - 2)/(3x + 2)) - 1)) + 1| - 1) - 1)/(3(-3|((1((-2x - 2)/(3x + 2)))/(2((-2x - 2)/(3x + 2)) - 1)) + 1| - 1) + 2))) + 1, g(x) = 3cos(1\u03c0(2|((2(2x^2 - 3x + 4) - 2)/(3(2x^2 - 3x + 4) + 3)) - 1| - 1) + 2) + 1, x = -1.2, 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": "6.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1|((2(3|(4(1x^2 - 2x + 3) + 5) - 1|) + 2)/(-1(3|(4(1x^2 - 2x + 3) + 5) - 1|) + 2)) + 1| + 1 and g(x) = (-1((-1(3sin(3\u03c0(-2|x + 1| - 1) + 1) - 1) + 1)/(2(3sin(3\u03c0(-2|x + 1| - 1) + 1) - 1) - 1)))/(2((-1(3sin(3\u03c0(-2|x + 1| - 1) + 1) - 1) + 1)/(2(3sin(3\u03c0(-2|x + 1| - 1) + 1) - 1) - 1)) - 1) between the vertical lines x = 1.8 and 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": "Calculate the area enclosed between the functions f(x) = 1cos(3\u03c0(-2|(-3(-5((1x)/(-1x - 2)) + 5) + 4) + 1| + 2) + 2) + 3 and g(x) = 2|(1e^(2((2((1x + 2)/(2x - 1)) - 3)/(-2((1x + 2)/(2x - 1))))) + 1) - 2| + 2 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -5(4(3(3((-1x + 1)/(-1x - 1)) - 1)^2 + 2(3((-1x + 1)/(-1x - 1)) - 1) - 1)^2 - 1(3(3((-1x + 1)/(-1x - 1)) - 1)^2 + 2(3((-1x + 1)/(-1x - 1)) - 1) - 1) - 5) + 4 and g(x) = -5(-2|(-3|(-1cos(3\u03c0x + 1) + 3)| + 2) + 3| + 3)^2 + 3(-2|(-3|(-1cos(3\u03c0x + 1) + 3)| + 2) + 3| + 3) + 5 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": "151.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3|(-1|((2(-4(-5x^2 - 3x)^2 + 4(-5x^2 - 3x) - 5) - 2)/(-1(-4(-5x^2 - 3x)^2 + 4(-5x^2 - 3x) - 5) + 2)) - 3|) - 1| - 1 and g(x) = 5(-2(-1(3x^2 + 2x + 2)^2 + 2(3x^2 + 2x + 2) + 1) - 5) + 3 from x = -0.9 to x = 0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1cos(3\u03c0(1((2(-5(-4x + 3)^2 - 4(-4x + 3) + 1) - 1)/(3(-5(-4x + 3)^2 - 4(-4x + 3) + 1) - 2))^2 - 5((2(-5(-4x + 3)^2 - 4(-4x + 3) + 1) - 1)/(3(-5(-4x + 3)^2 - 4(-4x + 3) + 1) - 2)) - 1) - 3) + 3 and g(x) = -1(-2((1(-1|x + 2| + 2))/(-1(-1|x + 2| + 2) + 2)) + 5) + 2 between the vertical lines x = -2.5 and x = -1.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "179.6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-1(3cos(3\u03c0(-5(2((-3x - 1)/(-1x + 2)) - 1)^2 - 3(2((-3x - 1)/(-1x + 2)) - 1) + 5) + 3) - 1) + 1)/(-1(3cos(3\u03c0(-5(2((-3x - 1)/(-1x + 2)) - 1)^2 - 3(2((-3x - 1)/(-1x + 2)) - 1) + 5) + 3) - 1) + 2) and g(x) = -5(-4(1(-1x^2 + 5x - 3) + 3) - 2)^2 + 2(-4(1(-1x^2 + 5x - 3) + 3) - 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": "4.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3(-3(-1|(3|(-3sin(1\u03c0x + 2) - 2) - 2| - 1) - 1| + 2) - 2) and g(x) = -2|((2((-3(-1e^(1x) - 3) + 3)/(-1(-1e^(1x) - 3) + 3)))/(-1((-3(-1e^(1x) - 3) + 3)/(-1(-1e^(1x) - 3) + 3)) + 3)) + 1| - 3 between the vertical lines x = -0.9 and x = 0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "113.6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3(1|(-3(3cos(1\u03c0(3|x - 2| + 3) + 3) - 1)^2 - 5(3cos(1\u03c0(3|x - 2| + 3) + 3) - 1) - 3)| - 3) - 3 and g(x) = 4((-1(-2sin(3\u03c0((-1x - 3)/(2x + 3)) - 1) - 1) - 2)/(-2(-2sin(3\u03c0((-1x - 3)/(2x + 3)) - 1) - 1) - 1)) - 3 from x = -3.2 to x = -2.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (2(-2|(2(-3sin(1\u03c0(-5x - 5) - 2) - 2)^2 + 3(-3sin(1\u03c0(-5x - 5) - 2) - 2) + 4) - 1| + 2) - 2)/(-1(-2|(2(-3sin(1\u03c0(-5x - 5) - 2) - 2)^2 + 3(-3sin(1\u03c0(-5x - 5) - 2) - 2) + 4) - 1| + 2) + 2) and g(x) = -3cos(3\u03c0(4((-1((1x - 3)/(2x - 1)) - 2)/(3((1x - 3)/(2x - 1)) - 2))^2 + 1)) between the vertical lines x = -3.8 and x = -3.6999999999999997. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1sin(1\u03c0(2|(3(4(-4x^2 + 3x + 1) - 1)^2 - 1(4(-4x^2 + 3x + 1) - 1) + 1)| - 1) + 2) + 1 and g(x) = (3((2(-5(2cos(2\u03c0x + 3) - 1) + 3) + 3)/(-1(-5(2cos(2\u03c0x + 3) - 1) + 3) + 2)) - 2)/(-2((2(-5(2cos(2\u03c0x + 3) - 1) + 3) + 3)/(-1(-5(2cos(2\u03c0x + 3) - 1) + 3) + 2)) + 3) from x = -1.4 to 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": "Determine the area of the region enclosed by the graphs of f(x) = (-3(-3(-1(-3|((3x - 2)/(2x - 1))| - 1) - 2)^2 + 1(-1(-3|((3x - 2)/(2x - 1))| - 1) - 2) + 5) - 1)/(-2(-3(-1(-3|((3x - 2)/(2x - 1))| - 1) - 2)^2 + 1(-1(-3|((3x - 2)/(2x - 1))| - 1) - 2) + 5) - 1) and g(x) = -4(-4(-1e^(-1((-1x - 2)/(3x + 2))) + 3)^2 - 5(-1e^(-1((-1x - 2)/(3x + 2))) + 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": "6.4", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3(-1((-3(-2((-1x - 3)/(-1x + 2))) - 1)/(-2(-2((-1x - 3)/(-1x + 2))) + 1)) - 1) + 2 and g(x) = -4(-3|(-2|(-3|x + 1| + 3) - 1|) + 3| - 1) - 4 between the vertical lines x = -1.7 and x = -1.4. 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) = (-3(1((-3(1|(-2|x - 3| - 1) + 2| - 1) - 3)/(-2(1|(-2|x - 3| - 1) + 2| - 1) + 3))) + 2)/(-1(1((-3(1|(-2|x - 3| - 1) + 2| - 1) - 3)/(-2(1|(-2|x - 3| - 1) + 2| - 1) + 3))) + 2), g(x) = (-3(-2(2|(-2|x + 3| + 3) + 3|) + 2) - 2)/(-2(-2(2|(-2|x + 3| + 3) + 3|) + 2) - 3), x = 2.9, 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": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -4(2sin(1\u03c0((2(4(-1|x + 3| + 1) - 2) - 1)/(-3(4(-1|x + 3| + 1) - 2) + 2)) - 2) + 2)^2 + 2 and g(x) = 2(-2|(-3sin(3\u03c0(1x + 1)) + 2) + 3| - 3) - 3 from x = -2.6 to x = -2.4. 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) = 5(1|(-1|(-3|(5x^2 + 2x + 1) - 3| + 2) + 1| - 3) - 2| - 3)^2 - 5(1|(-1|(-3|(5x^2 + 2x + 1) - 3| + 2) + 1| - 3) - 2| - 3) and g(x) = 1e^(2(-3|(1|(-3|x| + 2) + 2| - 1) - 2| + 2)) + 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": "2.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-3(-3sin(3\u03c0((2((2(-1|x - 1| + 3) - 3)/(-3(-1|x - 1| + 3) + 4)))/(-1((2(-1|x - 1| + 3) - 3)/(-3(-1|x - 1| + 3) + 4)) - 1)) + 2) + 3) - 1)/(-2(-3sin(3\u03c0((2((2(-1|x - 1| + 3) - 3)/(-3(-1|x - 1| + 3) + 4)))/(-1((2(-1|x - 1| + 3) - 3)/(-3(-1|x - 1| + 3) + 4)) - 1)) + 2) + 3) + 3) and g(x) = -3((2(2(-4x)) + 2)/(3(2(-4x)) - 2))^2 + 4((2(2(-4x)) + 2)/(3(2(-4x)) - 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": "1.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1(2((-1(1(4x^2 - 1x + 5) - 4) - 2)/(2(1(4x^2 - 1x + 5) - 4) - 1))^2 + 2((-1(1(4x^2 - 1x + 5) - 4) - 2)/(2(1(4x^2 - 1x + 5) - 4) - 1)) - 3)^2 - 4(2((-1(1(4x^2 - 1x + 5) - 4) - 2)/(2(1(4x^2 - 1x + 5) - 4) - 1))^2 + 2((-1(1(4x^2 - 1x + 5) - 4) - 2)/(2(1(4x^2 - 1x + 5) - 4) - 1)) - 3) - 5, g(x) = (1(-1|(-3((-2x + 2)/(-2x + 3))^2 + 3((-2x + 2)/(-2x + 3)) + 5) - 3| + 3) + 2)/(-1(-1|(-3((-2x + 2)/(-2x + 3))^2 + 3((-2x + 2)/(-2x + 3)) + 5) - 3| + 3) + 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": "22.6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1cos(1\u03c0(-5(3(-1(1|x + 3| + 3)^2 + 3(1|x + 3| + 3) + 2) + 1) - 4) + 1) + 2 and g(x) = (3(-1|(-2sin(3\u03c0(-3x^2 + 4x + 3) + 2) + 2) + 1| - 1) - 3)/(1(-1|(-2sin(3\u03c0(-3x^2 + 4x + 3) + 2) + 2) + 1| - 1) - 2) 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-2(-1(2(2(2|x - 3| + 1) + 2)^2 + 1(2(2|x - 3| + 1) + 2))^2 - 5(2(2(2|x - 3| + 1) + 2)^2 + 1(2(2|x - 3| + 1) + 2)) - 3) - 1)/(-2(-1(2(2(2|x - 3| + 1) + 2)^2 + 1(2(2|x - 3| + 1) + 2))^2 - 5(2(2(2|x - 3| + 1) + 2)^2 + 1(2(2|x - 3| + 1) + 2)) - 3) - 1), g(x) = 1(-3(-3(-1x^2 + 5x - 5)^2 + 3(-1x^2 + 5x - 5) + 5) + 1)^2 - 3, x = 3.9, and x = 4.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (2(-5(2|(-2(1|x - 2| + 2) + 4) - 3| + 2)^2 - 4(2|(-2(1|x - 2| + 2) + 4) - 3| + 2) + 3) + 2)/(2(-5(2|(-2(1|x - 2| + 2) + 4) - 3| + 2)^2 - 4(2|(-2(1|x - 2| + 2) + 4) - 3| + 2) + 3) + 3), g(x) = 3cos(2\u03c0(3(2|(3x^2 + 3x) + 2| + 3)^2 + 2(2|(3x^2 + 3x) + 2| + 3) - 4) + 3) + 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-1(1((-1(2|(-2cos(3\u03c0x) - 3) + 3| + 2) + 1)/(2(2|(-2cos(3\u03c0x) - 3) + 3| + 2) + 1))^2 + 4((-1(2|(-2cos(3\u03c0x) - 3) + 3| + 2) + 1)/(2(2|(-2cos(3\u03c0x) - 3) + 3| + 2) + 1)) - 3))/(1(1((-1(2|(-2cos(3\u03c0x) - 3) + 3| + 2) + 1)/(2(2|(-2cos(3\u03c0x) - 3) + 3| + 2) + 1))^2 + 4((-1(2|(-2cos(3\u03c0x) - 3) + 3| + 2) + 1)/(2(2|(-2cos(3\u03c0x) - 3) + 3| + 2) + 1)) - 3)), g(x) = 1(-2sin(2\u03c0((-2(-3|x - 3| + 1) - 1)/(3(-3|x - 3| + 1) - 2)) - 2) - 1)^2 - 3(-2sin(2\u03c0((-2(-3|x - 3| + 1) - 1)/(3(-3|x - 3| + 1) - 2)) - 2) - 1) - 1, x = 3.1, and x = 3.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-1((3(1(-2cos(2\u03c0(-4x^2 - 5x - 4) - 1) + 2)^2 + 2(-2cos(2\u03c0(-4x^2 - 5x - 4) - 1) + 2)) + 3)/(1(1(-2cos(2\u03c0(-4x^2 - 5x - 4) - 1) + 2)^2 + 2(-2cos(2\u03c0(-4x^2 - 5x - 4) - 1) + 2)) - 3)) + 1)/(1((3(1(-2cos(2\u03c0(-4x^2 - 5x - 4) - 1) + 2)^2 + 2(-2cos(2\u03c0(-4x^2 - 5x - 4) - 1) + 2)) + 3)/(1(1(-2cos(2\u03c0(-4x^2 - 5x - 4) - 1) + 2)^2 + 2(-2cos(2\u03c0(-4x^2 - 5x - 4) - 1) + 2)) - 3)) + 2), g(x) = (-1((1(-3|(-2x^2 - 4x + 2) + 1|) + 2)/(2(-3|(-2x^2 - 4x + 2) + 1|) - 1)) + 1)/(-2((1(-3|(-2x^2 - 4x + 2) + 1|) + 2)/(2(-3|(-2x^2 - 4x + 2) + 1|) - 1)) - 2), x = -2.7, and x = -2.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1(5(1|(1(1x - 2) + 2) - 1| + 1) - 2)^2 + 3(5(1|(1(1x - 2) + 2) - 1| + 1) - 2) + 1 and g(x) = 3|(1(-4(2cos(2\u03c0x + 1) + 1)^2 - 5(2cos(2\u03c0x + 1) + 1) + 5) - 2) + 2| + 3 from x = 1.1 to x = 1.7. 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": "Determine the area of the region enclosed by the graphs of f(x) = 3sin(2\u03c0((2((1(-1(-5x^2 + 5) + 1) - 3)/(-3(-1(-5x^2 + 5) + 1) + 4)) + 3)/(-2((1(-1(-5x^2 + 5) + 1) - 3)/(-3(-1(-5x^2 + 5) + 1) + 4)) - 3)) - 2) - 2 and g(x) = -1|(-4(-3(-1x - 2) - 4)^2 - 4(-3(-1x - 2) - 4)) - 1| - 1 between the vertical lines x = -1.2 and x = -0.5. 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": "Determine the area of the region enclosed by the graphs of f(x) = 1|((-1(2|((-2((3x + 3)/(-1x + 2)) - 1)/(1((3x + 3)/(-1x + 2)) + 1)) + 1| - 1) - 3)/(2(2|((-2((3x + 3)/(-1x + 2)) - 1)/(1((3x + 3)/(-1x + 2)) + 1)) + 1| - 1))) - 2| - 2 and g(x) = (2(-1e^(-2((3(3|x - 2|) + 3)/(2(3|x - 2|) + 3))) - 3) + 1)/(-2(-1e^(-2((3(3|x - 2|) + 3)/(2(3|x - 2|) + 3))) - 3) - 1) between the vertical lines x = -1.2 and x = -1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-1(1(5((-2(2|x| - 2) - 2)/(1(2|x| - 2) + 2)) - 2) + 3) - 3)/(-1(1(5((-2(2|x| - 2) - 2)/(1(2|x| - 2) + 2)) - 2) + 3) - 2) and g(x) = (2(-1|(-3|(-3x + 3) - 2|) - 2| + 1) - 3)/(-1(-1|(-3|(-3x + 3) - 2|) - 2| + 1) - 2) from x = -0.7 to x = 0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -5((-1(-4((-1(1x^2 + 3x - 2) - 1)/(2(1x^2 + 3x - 2) - 1))^2 - 5((-1(1x^2 + 3x - 2) - 1)/(2(1x^2 + 3x - 2) - 1)) + 3))/(-1(-4((-1(1x^2 + 3x - 2) - 1)/(2(1x^2 + 3x - 2) - 1))^2 - 5((-1(1x^2 + 3x - 2) - 1)/(2(1x^2 + 3x - 2) - 1)) + 3) - 3))^2 + 4, g(x) = (-1(-1(1cos(2\u03c0(1x^2 - 4) + 1) - 1)^2 + 4(1cos(2\u03c0(1x^2 - 4) + 1) - 1) + 1) - 2)/(2(-1(1cos(2\u03c0(1x^2 - 4) + 1) - 1)^2 + 4(1cos(2\u03c0(1x^2 - 4) + 1) - 1) + 1) - 1), x = -4.1, 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": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 5(-2|((-3(-1|(-2cos(2\u03c0x + 3) + 1) - 1| + 1) + 2)/(-2(-1|(-2cos(2\u03c0x + 3) + 1) - 1| + 1) - 3)) - 1| - 3) + 2 and g(x) = (1(2cos(2\u03c0(-5(2|x + 1| - 2) - 1) + 3)) + 3)/(-3(2cos(2\u03c0(-5(2|x + 1| - 2) - 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": "3.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (2(2(-1|((2(2x^2 - 1x + 4) + 1)/(2(2x^2 - 1x + 4) - 1)) - 2| - 2)^2 - 2(-1|((2(2x^2 - 1x + 4) + 1)/(2(2x^2 - 1x + 4) - 1)) - 2| - 2) - 2) + 2)/(2(2(-1|((2(2x^2 - 1x + 4) + 1)/(2(2x^2 - 1x + 4) - 1)) - 2| - 2)^2 - 2(-1|((2(2x^2 - 1x + 4) + 1)/(2(2x^2 - 1x + 4) - 1)) - 2| - 2) - 2) - 3) and g(x) = (-1(5((-2(3cos(2\u03c0x - 3) + 3) + 3)/(-1(3cos(2\u03c0x - 3) + 3) - 1))^2 + 5((-2(3cos(2\u03c0x - 3) + 3) + 3)/(-1(3cos(2\u03c0x - 3) + 3) - 1))) + 2)/(2(5((-2(3cos(2\u03c0x - 3) + 3) + 3)/(-1(3cos(2\u03c0x - 3) + 3) - 1))^2 + 5((-2(3cos(2\u03c0x - 3) + 3) + 3)/(-1(3cos(2\u03c0x - 3) + 3) - 1))) + 2) between the vertical lines x = -4.9 and x = -4.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (1(2(2|((-3(-1|x + 2| + 2) + 3)/(2(-1|x + 2| + 2) - 3)) + 1| + 1)^2 + 1(2|((-3(-1|x + 2| + 2) + 3)/(2(-1|x + 2| + 2) - 3)) + 1| + 1) - 5))/(-1(2(2|((-3(-1|x + 2| + 2) + 3)/(2(-1|x + 2| + 2) - 3)) + 1| + 1)^2 + 1(2|((-3(-1|x + 2| + 2) + 3)/(2(-1|x + 2| + 2) - 3)) + 1| + 1) - 5)), g(x) = -2cos(1\u03c0(1(2|(-3x - 4) - 1| - 1) + 4) - 3) - 1, x = 2.7, and x = 2.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2sin(1\u03c0(-2(-3(-3(5x)^2 + 5(5x) + 4)^2 - 2(-3(5x)^2 + 5(5x) + 4) + 3)) - 2) and g(x) = (-1((-2(-5(-1|x - 3| + 1)^2 + 1(-1|x - 3| + 1) + 5) + 2)/(-2(-5(-1|x - 3| + 1)^2 + 1(-1|x - 3| + 1) + 5) - 1)) + 1)/(2((-2(-5(-1|x - 3| + 1)^2 + 1(-1|x - 3| + 1) + 5) + 2)/(-2(-5(-1|x - 3| + 1)^2 + 1(-1|x - 3| + 1) + 5) - 1)) + 1) between the vertical lines x = 0.0 and x = 0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-1(-1(2(4((2x + 3)/(-3x - 2))^2 + 5((2x + 3)/(-3x - 2)) + 1) - 5) - 2))/(3(-1(2(4((2x + 3)/(-3x - 2))^2 + 5((2x + 3)/(-3x - 2)) + 1) - 5) - 2) + 3), g(x) = 1|(3sin(2\u03c0(-1|(1x + 5) - 3| - 1) - 3) - 1) - 3| - 1, x = -1.3, and x = 0.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -4(2((-3(2cos(2\u03c0(-2|x - 3| - 2)) + 1) + 3)/(-3(2cos(2\u03c0(-2|x - 3| - 2)) + 1) - 3))^2 + 3((-3(2cos(2\u03c0(-2|x - 3| - 2)) + 1) + 3)/(-3(2cos(2\u03c0(-2|x - 3| - 2)) + 1) - 3)))^2 - 3(2((-3(2cos(2\u03c0(-2|x - 3| - 2)) + 1) + 3)/(-3(2cos(2\u03c0(-2|x - 3| - 2)) + 1) - 3))^2 + 3((-3(2cos(2\u03c0(-2|x - 3| - 2)) + 1) + 3)/(-3(2cos(2\u03c0(-2|x - 3| - 2)) + 1) - 3))) and g(x) = -1(-2e^(2(-3(1x^2 + 4x - 1) - 3)) - 2)^2 + 3(-2e^(2(-3(1x^2 + 4x - 1) - 3)) - 2) - 1 between the vertical lines x = -4.4 and x = -4.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2((3(5(2(2|x + 1| + 2)^2 - 3(2|x + 1| + 2) - 3)^2 - 1(2(2|x + 1| + 2)^2 - 3(2|x + 1| + 2) - 3)) + 1)/(3(5(2(2|x + 1| + 2)^2 - 3(2|x + 1| + 2) - 3)^2 - 1(2(2|x + 1| + 2)^2 - 3(2|x + 1| + 2) - 3)) + 1)) + 1 and g(x) = 3(-2((-3(-2x^2 + 5x - 1) + 1)/(-2(-2x^2 + 5x - 1) + 3)) + 2) - 2 between the vertical lines x = -0.0 and x = 2.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "178.7", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-2(1(-5(3(1cos(2\u03c0x) + 2)^2 - 5(1cos(2\u03c0x) + 2) + 3)^2 + 2(3(1cos(2\u03c0x) + 2)^2 - 5(1cos(2\u03c0x) + 2) + 3) + 4)) - 3)/(-3(1(-5(3(1cos(2\u03c0x) + 2)^2 - 5(1cos(2\u03c0x) + 2) + 3)^2 + 2(3(1cos(2\u03c0x) + 2)^2 - 5(1cos(2\u03c0x) + 2) + 3) + 4)) - 3), g(x) = (1(-5(-2sin(2\u03c0(1|x + 2| + 2)) + 3)^2 + 4(-2sin(2\u03c0(1|x + 2| + 2)) + 3) - 3) - 3)/(-2(-5(-2sin(2\u03c0(1|x + 2| + 2)) + 3)^2 + 4(-2sin(2\u03c0(1|x + 2| + 2)) + 3) - 3) - 2), x = 2.4, 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1|((2(1(-2(-4x - 2)^2 + 4(-4x - 2) + 1) - 5) - 1)/(3(1(-2(-4x - 2)^2 + 4(-4x - 2) + 1) - 5))) - 3| - 2 and g(x) = -1|(-2|(1|(-2|x - 2| - 3) + 3| - 2) - 2| - 3) + 2| + 2 between the vertical lines x = -1.3 and x = 1.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 3(-3(-1(-2|(-2x^2 - 1x + 2) + 3|)^2 - 5(-2|(-2x^2 - 1x + 2) + 3|) + 5)^2 + 4(-1(-2|(-2x^2 - 1x + 2) + 3|)^2 - 5(-2|(-2x^2 - 1x + 2) + 3|) + 5)) - 2 and g(x) = -4((-1(-2|(-2x - 3) + 3| - 1) - 2)/(2(-2|(-2x - 3) + 3| - 1) - 1))^2 - 2((-1(-2|(-2x - 3) + 3| - 1) - 2)/(2(-2|(-2x - 3) + 3| - 1) - 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": "5.7", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 5(1(-1e^(-1(5(-3|x - 1| + 2) - 4)) + 3) + 2) - 4, g(x) = (1(-4(-2|(2|x - 2| + 1) + 1| - 1)^2 + 2(-2|(2|x - 2| + 1) + 1| - 1) + 1) + 1)/(-2(-4(-2|(2|x - 2| + 1) + 1| - 1)^2 + 2(-2|(2|x - 2| + 1) + 1| - 1) + 1) + 3), x = 0.5, and x = 1.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 4((-2((1(2|((-2x - 2)/(1x)) + 1| - 2) + 3)/(1(2|((-2x - 2)/(1x)) + 1| - 2) - 2)) - 3)/(-2((1(2|((-2x - 2)/(1x)) + 1| - 2) + 3)/(1(2|((-2x - 2)/(1x)) + 1| - 2) - 2)) - 2))^2 + 4((-2((1(2|((-2x - 2)/(1x)) + 1| - 2) + 3)/(1(2|((-2x - 2)/(1x)) + 1| - 2) - 2)) - 3)/(-2((1(2|((-2x - 2)/(1x)) + 1| - 2) + 3)/(1(2|((-2x - 2)/(1x)) + 1| - 2) - 2)) - 2)) + 1 and g(x) = 2(1|(1|(1x + 4) + 3| + 3)| + 3) + 1 between the vertical lines x = -2.6 and x = -1.5. 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) = -4(2cos(1\u03c0((-1((-2(-5x + 2) + 3)/(3(-5x + 2) - 2)) + 3)/(-2((-2(-5x + 2) + 3)/(3(-5x + 2) - 2)) - 1)) - 1) - 3)^2 + 2(2cos(1\u03c0((-1((-2(-5x + 2) + 3)/(3(-5x + 2) - 2)) + 3)/(-2((-2(-5x + 2) + 3)/(3(-5x + 2) - 2)) - 1)) - 1) - 3) - 5, g(x) = -5(-2e^(2(-3|(4x^2 - 3x) - 3| + 2)) - 3)^2 - 3(-2e^(2(-3|(4x^2 - 3x) - 3| + 2)) - 3) + 4, 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": "3.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1(2(-1|((3(-2x^2 - 4) - 1)/(1(-2x^2 - 4))) - 1| + 3)^2 + 5(-1|((3(-2x^2 - 4) - 1)/(1(-2x^2 - 4))) - 1| + 3) - 4)^2 - 3(2(-1|((3(-2x^2 - 4) - 1)/(1(-2x^2 - 4))) - 1| + 3)^2 + 5(-1|((3(-2x^2 - 4) - 1)/(1(-2x^2 - 4))) - 1| + 3) - 4) + 5 and g(x) = -1((-1(5(3x^2 - 2) - 2) + 1)/(3(5(3x^2 - 2) - 2) + 2)) + 4 from x = -0.9 to x = 0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 3|((3(-2(-1(-2|x - 3| + 1) + 3) + 1) + 1)/(-1(-2(-1(-2|x - 3| + 1) + 3) + 1) + 3)) + 1| + 1 and g(x) = 1(3|(4((2x - 3)/(2x)) + 4) + 2| - 2) + 4 from x = 0.5 to 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": "Find the area of the region bounded by the curves f(x) = (-1(-2|((2(5(-2|x - 3| + 1) - 3) - 3)/(-3(5(-2|x - 3| + 1) - 3) - 3)) - 2| - 2) + 3)/(-3(-2|((2(5(-2|x - 3| + 1) - 3) - 3)/(-3(5(-2|x - 3| + 1) - 3) - 3)) - 2| - 2) + 2), g(x) = (-2(-1(2(1sin(1\u03c0x - 1) + 3) - 2)^2 + 4(2(1sin(1\u03c0x - 1) + 3) - 2) - 1) + 1)/(-1(-1(2(1sin(1\u03c0x - 1) + 3) - 2)^2 + 4(2(1sin(1\u03c0x - 1) + 3) - 2) - 1) + 2), x = 1.4, 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": "13.8", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2|(-2|((-2(-3|(-1e^(1x) - 2) + 3|) + 2)/(-3(-3|(-1e^(1x) - 2) + 3|))) + 3| + 1) + 3| + 3 and g(x) = -2cos(3\u03c0(5((2(1x - 1) + 2)/(2(1x - 1) - 1))^2 - 2((2(1x - 1) + 2)/(2(1x - 1) - 1)) + 1) - 2) - 3 between the vertical lines x = 2.9 and x = 3.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 3|((-1(-1(1(2x)^2 - 2(2x) + 4)^2 + 4(1(2x)^2 - 2(2x) + 4) - 5) + 3)/(1(-1(1(2x)^2 - 2(2x) + 4)^2 + 4(1(2x)^2 - 2(2x) + 4) - 5) - 3)) + 1| - 1 and g(x) = -3(-3(-1(1|x - 1| - 3))) + 3 from x = -2.4 to x = 4.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "106.8", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-2(-3sin(1\u03c0((2(-2(3|x - 3| - 3) + 3) - 2)/(-1(-2(3|x - 3| - 3) + 3) + 3)) - 1)) - 2)/(-2(-3sin(1\u03c0((2(-2(3|x - 3| - 3) + 3) - 2)/(-1(-2(3|x - 3| - 3) + 3) + 3)) - 1)) + 3), g(x) = -3|((-2(4(-1x - 4)^2 + 2(-1x - 4)) + 3)/(-2(4(-1x - 4)^2 + 2(-1x - 4)) + 3)) - 3|, x = 2.2, and x = 2.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1e^(-1((3(-2(2(-2|x - 1| - 3) + 3)^2 - 1(2(-2|x - 1| - 3) + 3) - 3) + 2)/(-3(-2(2(-2|x - 1| - 3) + 3)^2 - 1(2(-2|x - 1| - 3) + 3) - 3)))) - 2 and g(x) = (3(5(-1(-2x - 2) + 4)^2 + 2(-1(-2x - 2) + 4) - 4) + 1)/(-1(5(-1(-2x - 2) + 4)^2 + 2(-1(-2x - 2) + 4) - 4) + 2) from x = -3.8 to x = -2.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 4(3(-1|(-2cos(1\u03c0((3x + 1)/(2x - 3)) - 3) - 2)| + 1)^2 + 4(-1|(-2cos(1\u03c0((3x + 1)/(2x - 3)) - 3) - 2)| + 1) + 1)^2 - 4(3(-1|(-2cos(1\u03c0((3x + 1)/(2x - 3)) - 3) - 2)| + 1)^2 + 4(-1|(-2cos(1\u03c0((3x + 1)/(2x - 3)) - 3) - 2)| + 1) + 1) - 5, g(x) = -2cos(2\u03c0(-3(4((-1x - 1)/(-1x + 2)))^2 - 5(4((-1x - 1)/(-1x + 2))) + 2) - 2) + 3, 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": "22.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3((-1(-5(-5(-3sin(2\u03c0x) - 1)^2 - 4(-3sin(2\u03c0x) - 1) + 3) - 5) - 1)/(-1(-5(-5(-3sin(2\u03c0x) - 1)^2 - 4(-3sin(2\u03c0x) - 1) + 3) - 5) - 3))^2 + 2((-1(-5(-5(-3sin(2\u03c0x) - 1)^2 - 4(-3sin(2\u03c0x) - 1) + 3) - 5) - 1)/(-1(-5(-5(-3sin(2\u03c0x) - 1)^2 - 4(-3sin(2\u03c0x) - 1) + 3) - 5) - 3)) + 2 and g(x) = (-3(-1|((-2(-2|x + 3|) - 1)/(3(-2|x + 3|))) + 3| - 3) - 3)/(-2(-1|((-2(-2|x + 3|) - 1)/(3(-2|x + 3|))) + 3| - 3)) between the vertical lines x = 1.6 and x = 1.7000000000000002. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2(-1(-1|(-5(-1|x - 1| + 3)^2 - 2(-1|x - 1| + 3) + 1) + 2| - 1) - 3) + 2 and g(x) = -4(2(-3(3cos(2\u03c0x + 2) + 3)^2 - 3(3cos(2\u03c0x + 2) + 3) + 1) + 1) + 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": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1((-1((3(-2|((3x - 1)/(-2x + 3)) + 1| + 2) - 2)/(2(-2|((3x - 1)/(-2x + 3)) + 1| + 2) - 3)) + 1)/(3((3(-2|((3x - 1)/(-2x + 3)) + 1| + 2) - 2)/(2(-2|((3x - 1)/(-2x + 3)) + 1| + 2) - 3))))^2 - 3((-1((3(-2|((3x - 1)/(-2x + 3)) + 1| + 2) - 2)/(2(-2|((3x - 1)/(-2x + 3)) + 1| + 2) - 3)) + 1)/(3((3(-2|((3x - 1)/(-2x + 3)) + 1| + 2) - 2)/(2(-2|((3x - 1)/(-2x + 3)) + 1| + 2) - 3)))) and g(x) = (3(5(5((1x - 2)/(-2x + 1))^2 + 1((1x - 2)/(-2x + 1)) - 5)^2 - 2(5((1x - 2)/(-2x + 1))^2 + 1((1x - 2)/(-2x + 1)) - 5) - 1) + 3)/(3(5(5((1x - 2)/(-2x + 1))^2 + 1((1x - 2)/(-2x + 1)) - 5)^2 - 2(5((1x - 2)/(-2x + 1))^2 + 1((1x - 2)/(-2x + 1)) - 5) - 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": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2sin(3\u03c0(-4(1|(-1|(-1|x| + 3) + 2| + 1) + 1| - 2)^2 - 4(1|(-1|(-1|x| + 3) + 2| + 1) + 1| - 2) + 5) - 1) - 1 and g(x) = 1cos(1\u03c0(5((2(-5x + 5) - 1)/(-2(-5x + 5) + 3)) + 2) + 2) + 1 between the vertical lines x = -1.8 and x = -1.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-2((2(-2|((-3(1|x - 2|) - 3)/(1(1|x - 2|) - 2)) + 1| + 2) + 2)/(3(-2|((-3(1|x - 2|) - 3)/(1(1|x - 2|) - 2)) + 1| + 2))) + 1)/(-3((2(-2|((-3(1|x - 2|) - 3)/(1(1|x - 2|) - 2)) + 1| + 2) + 2)/(3(-2|((-3(1|x - 2|) - 3)/(1(1|x - 2|) - 2)) + 1| + 2)))), g(x) = -4(-2sin(1\u03c0(-3|((-3x - 3)/(-2x + 3)) + 3| - 3) - 2) + 2)^2 - 3(-2sin(1\u03c0(-3|((-3x - 3)/(-2x + 3)) + 3| - 3) - 2) + 2) + 1, x = 1.8, and x = 1.9000000000000001. 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": "Determine the area of the region enclosed by the graphs of f(x) = 4(1(2((-2(-3|x|) - 3)/(-3(-3|x|) + 4))^2 - 5((-2(-3|x|) - 3)/(-3(-3|x|) + 4)) - 3) - 1) + 1 and g(x) = (3(3(2|((2x - 1)/(2x - 1)) + 3| + 3) + 5) - 2)/(-1(3(2|((2x - 1)/(2x - 1)) + 3| + 3) + 5) + 3) between the vertical lines x = -0.1 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": "Calculate the area enclosed between the functions f(x) = 3(-1|(1(3cos(1\u03c0((1x + 3)/(-1x - 2)) + 3))^2 + 1(3cos(1\u03c0((1x + 3)/(-1x - 2)) + 3))) - 3| + 2)^2 + 5(-1|(1(3cos(1\u03c0((1x + 3)/(-1x - 2)) + 3))^2 + 1(3cos(1\u03c0((1x + 3)/(-1x - 2)) + 3))) - 3| + 2) - 1 and g(x) = (2(-2|(5(1cos(2\u03c0x + 2) - 1) - 5) - 2| - 3) - 3)/(-2(-2|(5(1cos(2\u03c0x + 2) - 1) - 5) - 2| - 3) + 3) 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": "Determine the area of the region enclosed by the graphs of f(x) = 4((2(4((-3(-2x^2 + 4x + 5) + 2)/(-1(-2x^2 + 4x + 5))) + 3) - 2)/(2(4((-3(-2x^2 + 4x + 5) + 2)/(-1(-2x^2 + 4x + 5))) + 3))) - 3 and g(x) = -1(2sin(2\u03c0((2(-5x + 5) - 2)/(2(-5x + 5) - 1)) - 2) + 1)^2 + 5(2sin(2\u03c0((2(-5x + 5) - 2)/(2(-5x + 5) - 1)) - 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": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1cos(3\u03c0(-4(2(2(-1x^2 - 2x + 3) + 3)^2 - 4(2(-1x^2 - 2x + 3) + 3) + 2) - 2) + 1) - 2, g(x) = (-2(1((1(3|x - 3| - 1) + 3)/(3(3|x - 3| - 1) - 2))^2 - 3((1(3|x - 3| - 1) + 3)/(3(3|x - 3| - 1) - 2)) + 2) + 1)/(1(1((1(3|x - 3| - 1) + 3)/(3(3|x - 3| - 1) - 2))^2 - 3((1(3|x - 3| - 1) + 3)/(3(3|x - 3| - 1) - 2)) + 2) - 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": "Determine the area of the region enclosed by the graphs of f(x) = (-3(3sin(2\u03c0(-2|((1(-2|x - 1|) - 1)/(1(-2|x - 1|) + 3)) + 1| + 1) - 3) - 3) - 3)/(1(3sin(2\u03c0(-2|((1(-2|x - 1|) - 1)/(1(-2|x - 1|) + 3)) + 1| + 1) - 3) - 3) + 2) and g(x) = (2(2sin(3\u03c0((1(2|x + 2| + 1) - 3)/(1(2|x + 2| + 1) - 2)) + 1) + 2) - 2)/(-2(2sin(3\u03c0((1(2|x + 2| + 1) - 3)/(1(2|x + 2| + 1) - 2)) + 1) + 2) + 1) 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": "1.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2e^(-2(1(-4(-1(-4x + 1)^2 - 4(-4x + 1) + 3) + 2) + 1)) - 3, g(x) = (-1(4(1(2e^(-1x) - 2)^2 - 3(2e^(-1x) - 2) - 1) - 4) - 2)/(2(4(1(2e^(-1x) - 2)^2 - 3(2e^(-1x) - 2) - 1) - 4) + 1), x = -1.0, and x = 0.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.8", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2|(-2(2(-3cos(3\u03c0((2x - 2)/(-3x - 2)) + 3) + 3)^2 - 1(-3cos(3\u03c0((2x - 2)/(-3x - 2)) + 3) + 3) + 4) - 4) + 1| - 2 and g(x) = -2|(-3|(5(-1x^2 + 2x + 1)^2 - 4) - 3| + 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": "9.9", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1(-3|(3((3((1x - 2)/(-3x + 1)) + 3)/(-1((1x - 2)/(-3x + 1)) + 2))^2 + 5((3((1x - 2)/(-3x + 1)) + 3)/(-1((1x - 2)/(-3x + 1)) + 2)) - 3) - 3| - 2)^2 + 3(-3|(3((3((1x - 2)/(-3x + 1)) + 3)/(-1((1x - 2)/(-3x + 1)) + 2))^2 + 5((3((1x - 2)/(-3x + 1)) + 3)/(-1((1x - 2)/(-3x + 1)) + 2)) - 3) - 3| - 2) + 3, g(x) = 3|(-3|(-4(-1x - 2)) + 2| - 1) - 2|, 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": "196.9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (2((-2(3|((3(-3x^2 - 5x + 1))/(2(-3x^2 - 5x + 1) - 3)) + 2| + 1) - 2)/(2(3|((3(-3x^2 - 5x + 1))/(2(-3x^2 - 5x + 1) - 3)) + 2| + 1) + 3)))/(1((-2(3|((3(-3x^2 - 5x + 1))/(2(-3x^2 - 5x + 1) - 3)) + 2| + 1) - 2)/(2(3|((3(-3x^2 - 5x + 1))/(2(-3x^2 - 5x + 1) - 3)) + 2| + 1) + 3))) and g(x) = -3|(-3sin(1\u03c0(-2|(-4x^2 - 4x + 3) - 2| - 3) + 2) - 1) - 1| + 2 from x = -2.8 to x = -2.6999999999999997. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (1(-4((3(4(-4x + 3) + 2) + 3)/(-1(4(-4x + 3) + 2) + 3))^2 + 2((3(4(-4x + 3) + 2) + 3)/(-1(4(-4x + 3) + 2) + 3)) + 2) + 3)/(2(-4((3(4(-4x + 3) + 2) + 3)/(-1(4(-4x + 3) + 2) + 3))^2 + 2((3(4(-4x + 3) + 2) + 3)/(-1(4(-4x + 3) + 2) + 3)) + 2) + 3) and g(x) = -3(-1(2((-3x - 3)/(3x - 2))^2 - 3((-3x - 3)/(3x - 2)) + 2) + 3)^2 - 4(-1(2((-3x - 3)/(3x - 2))^2 - 3((-3x - 3)/(3x - 2)) + 2) + 3) from x = -3.0 to x = -1.8. 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(5(1|(-2|(-2cos(3\u03c0x) - 3) + 3| + 1) - 1| - 2)^2 + 4(1|(-2|(-2cos(3\u03c0x) - 3) + 3| + 1) - 1| - 2) - 4) + 2)/(2(5(1|(-2|(-2cos(3\u03c0x) - 3) + 3| + 1) - 1| - 2)^2 + 4(1|(-2|(-2cos(3\u03c0x) - 3) + 3| + 1) - 1| - 2) - 4)) and g(x) = (2(1(2e^(1(-5x^2 - 3x - 3)) + 1) - 3) - 1)/(-1(1(2e^(1(-5x^2 - 3x - 3)) + 1) - 3) - 1) 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": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1|(-2(2|(3sin(2\u03c0(-1x^2 + 4x - 1) - 1) + 2) - 2|) - 4) - 3| + 1 and g(x) = -3(-2|(-1e^(1(-2|x - 3| + 2))) + 2| + 1)^2 + 5(-2|(-1e^(1(-2|x - 3| + 2))) + 2| + 1) + 3 from x = 1.7 to x = 2.6. 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((1(2((-2((1x + 1)/(3x + 1)) - 1)/(1((1x + 1)/(3x + 1)) - 3)) - 2) + 3)/(2(2((-2((1x + 1)/(3x + 1)) - 1)/(1((1x + 1)/(3x + 1)) - 3)) - 2)))^2 - 4((1(2((-2((1x + 1)/(3x + 1)) - 1)/(1((1x + 1)/(3x + 1)) - 3)) - 2) + 3)/(2(2((-2((1x + 1)/(3x + 1)) - 1)/(1((1x + 1)/(3x + 1)) - 3)) - 2))) + 1, g(x) = 4(3|(5((-2x - 1)/(-3x)) + 4) - 2| + 2)^2 - 2(3|(5((-2x - 1)/(-3x)) + 4) - 2| + 2) + 2, 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": "-468.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (3((-1(-2(-5(1|x - 1|) + 5) - 2) - 2)/(1(-2(-5(1|x - 1|) + 5) - 2) + 3)) + 1)/(2((-1(-2(-5(1|x - 1|) + 5) - 2) - 2)/(1(-2(-5(1|x - 1|) + 5) - 2) + 3)) - 1) and g(x) = 2(3(2e^(1(-3x^2 + 1x + 5)) - 2)^2 - 4(2e^(1(-3x^2 + 1x + 5)) - 2) - 5) + 1 from x = 1.5 to x = 2.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11.6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (3(3((3(-3sin(3\u03c0(1x) + 1) - 1) + 1)/(-3(-3sin(3\u03c0(1x) + 1) - 1) + 1)) + 1))/(-3(3((3(-3sin(3\u03c0(1x) + 1) - 1) + 1)/(-3(-3sin(3\u03c0(1x) + 1) - 1) + 1)) + 1) - 2) and g(x) = 1(-1e^(2(-2|(-2x^2 + 2) + 1|)) + 1) - 3 from x = 3.5 to x = 4.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2(1(-1(-1(-2x - 1) + 1)^2 + 4(-1(-2x - 1) + 1) + 4)^2 - 4(-1(-1(-2x - 1) + 1)^2 + 4(-1(-2x - 1) + 1) + 4) - 5) + 2, g(x) = (-2(-4(-1((-2x - 2)/(2x))^2 + 1((-2x - 2)/(2x)) + 5)^2 - 2) - 3)/(-3(-4(-1((-2x - 2)/(2x))^2 + 1((-2x - 2)/(2x)) + 5)^2 - 2) - 2), 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": "60.6", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-1(-3((3(4(3x) - 2) + 1)/(2(4(3x) - 2) - 1))^2 - 1((3(4(3x) - 2) + 1)/(2(4(3x) - 2) - 1)) - 1) - 1)/(1(-3((3(4(3x) - 2) + 1)/(2(4(3x) - 2) - 1))^2 - 1((3(4(3x) - 2) + 1)/(2(4(3x) - 2) - 1)) - 1) - 2), g(x) = 1|(-2sin(3\u03c0(-1((2x + 1)/(1x)) - 4) + 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1(2(4(1(-2|x - 1| - 3)^2 + 4(-2|x - 1| - 3)) - 5) - 5)^2 + 4(2(4(1(-2|x - 1| - 3)^2 + 4(-2|x - 1| - 3)) - 5) - 5), g(x) = (2(3sin(2\u03c0(-3(-4x^2 + 5x - 4) + 3) - 1) - 3) + 3)/(1(3sin(2\u03c0(-3(-4x^2 + 5x - 4) + 3) - 1) - 3) + 2), 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": "1.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-1(-1(1((1(3x^2 - 2x - 4) - 3)/(-2(3x^2 - 2x - 4) + 3)) - 5) + 3) + 2)/(1(-1(1((1(3x^2 - 2x - 4) - 3)/(-2(3x^2 - 2x - 4) + 3)) - 5) + 3) + 1) and g(x) = -1(3((-3(1|x + 1| - 1) + 1)/(3(1|x + 1| - 1) - 2))^2 + 1((-3(1|x + 1| - 1) + 1)/(3(1|x + 1| - 1) - 2))) + 2 between the vertical lines x = -2.5 and x = -1.1. 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": "Calculate the area enclosed between the functions f(x) = 3cos(3\u03c0(-2|(1(2(-1x + 3)^2 - 5(-1x + 3))^2 + 1(2(-1x + 3)^2 - 5(-1x + 3)) - 3) + 3| + 3) - 3) + 3 and g(x) = (3(-1(1(-1x + 5) - 4)^2 - 4(1(-1x + 5) - 4) - 3) + 3)/(2(-1(1(-1x + 5) - 4)^2 - 4(1(-1x + 5) - 4) - 3) + 3) from x = -2.3 to x = -2.1999999999999997. 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((-1(-1e^(1(3x - 4)) + 3) + 3)/(-3(-1e^(1(3x - 4)) + 3) - 3)) - 1)/(-1((-1(-1e^(1(3x - 4)) + 3) + 3)/(-3(-1e^(1(3x - 4)) + 3) - 3)) - 2)) + 1)/(2((3((-1(-1e^(1(3x - 4)) + 3) + 3)/(-3(-1e^(1(3x - 4)) + 3) - 3)) - 1)/(-1((-1(-1e^(1(3x - 4)) + 3) + 3)/(-3(-1e^(1(3x - 4)) + 3) - 3)) - 2)) + 2) and g(x) = (1(3|((1((1x + 2)/(-3x)) + 1)/(2((1x + 2)/(-3x)) - 3)) + 1| + 1) + 3)/(3(3|((1((1x + 2)/(-3x)) + 1)/(2((1x + 2)/(-3x)) - 3)) + 1| + 1) - 2) between the vertical lines x = 0.5 and x = 1.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3(1((-2(3|(-1x - 1) - 3| - 2) + 3)/(1(3|(-1x - 1) - 3| - 2) - 3)) - 3)^2 + 1(1((-2(3|(-1x - 1) - 3| - 2) + 3)/(1(3|(-1x - 1) - 3| - 2) - 3)) - 3) + 1 and g(x) = -2|(-3(-4(1|x - 2|)^2 - 1(1|x - 2|) + 1)^2 + 3(-4(1|x - 2|)^2 - 1(1|x - 2|) + 1) + 3)| - 2 from x = 1.1 to x = 2.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "125.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1(-2((-1((-1(3x + 3) + 2)/(1(3x + 3) + 3)) + 2)/(-2((-1(3x + 3) + 2)/(1(3x + 3) + 3)) - 3)) + 5)^2 - 1(-2((-1((-1(3x + 3) + 2)/(1(3x + 3) + 3)) + 2)/(-2((-1(3x + 3) + 2)/(1(3x + 3) + 3)) - 3)) + 5) - 5 and g(x) = 2(2|((1(-5x^2 + 2x - 2))/(-2(-5x^2 + 2x - 2) + 1))| - 3) from x = -3.3 to x = -2.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 4(3(-1(-1((1x - 2)/(2x - 1)) - 3) - 4) - 5), g(x) = -1(1|((-1(4x^2 + 5x - 3) - 3)/(-1(4x^2 + 5x - 3) - 2))| - 2)^2 + 3(1|((-1(4x^2 + 5x - 3) - 3)/(-1(4x^2 + 5x - 3) - 2))| - 2) - 1, x = -1.4, and x = -1.2999999999999998. 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) = (3(-1(-2|(-1|(-1x^2 + 4x - 4) + 1| - 1) + 2|)^2 - 5(-2|(-1|(-1x^2 + 4x - 4) + 1| - 1) + 2|) - 4) - 1)/(-2(-1(-2|(-1|(-1x^2 + 4x - 4) + 1| - 1) + 2|)^2 - 5(-2|(-1|(-1x^2 + 4x - 4) + 1| - 1) + 2|) - 4) - 1), g(x) = (-1(4((2((-3x - 1)/(-1x - 2)) + 1)/(-1((-3x - 1)/(-1x - 2)) - 3))^2 - 4((2((-3x - 1)/(-1x - 2)) + 1)/(-1((-3x - 1)/(-1x - 2)) - 3)) - 2) - 3)/(2(4((2((-3x - 1)/(-1x - 2)) + 1)/(-1((-3x - 1)/(-1x - 2)) - 3))^2 - 4((2((-3x - 1)/(-1x - 2)) + 1)/(-1((-3x - 1)/(-1x - 2)) - 3)) - 2)), x = 2.9, 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": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1|((1((1(3|((1x - 1)/(-2x - 1))| + 1) - 2)/(1(3|((1x - 1)/(-2x - 1))| + 1) + 2)) - 1)/(1((1(3|((1x - 1)/(-2x - 1))| + 1) - 2)/(1(3|((1x - 1)/(-2x - 1))| + 1) + 2)))) - 1| + 1, g(x) = -1|(-1sin(3\u03c0(-1(-1|x - 3|) + 4)))| - 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -5((-3(-1|(2e^(1(3x - 2))) - 3|) - 2)/(-3(-1|(2e^(1(3x - 2))) - 3|) + 2)) - 4, g(x) = 3sin(3\u03c0(-2((1(2|x - 3| + 2))/(-1(2|x - 3| + 2) + 3)) + 5) + 3) - 1, x = 0.8, and x = 0.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1|(5((-1(3|((2x + 3)/(3x - 1)) - 3|) + 1)/(1(3|((2x + 3)/(3x - 1)) - 3|) + 1))^2 - 2((-1(3|((2x + 3)/(3x - 1)) - 3|) + 1)/(1(3|((2x + 3)/(3x - 1)) - 3|) + 1)) + 4) - 1| + 2 and g(x) = (-1(-1(-2(-2cos(1\u03c0x + 1) + 3)^2 - 2) - 4) - 3)/(-1(-1(-2(-2cos(1\u03c0x + 1) + 3)^2 - 2) - 4) + 2) from x = -0.5 to x = -0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9.5", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2(1((2((-1(-1|x + 1| - 1) - 2)/(2(-1|x + 1| - 1))) + 3)/(-2((-1(-1|x + 1| - 1) - 2)/(2(-1|x + 1| - 1))) + 3))^2 - 5((2((-1(-1|x + 1| - 1) - 2)/(2(-1|x + 1| - 1))) + 3)/(-2((-1(-1|x + 1| - 1) - 2)/(2(-1|x + 1| - 1))) + 3)) - 3)^2 + 1, g(x) = -3|(1(4(-3|x - 1| + 1) + 3)^2 + 3(4(-3|x - 1| + 1) + 3) + 4) - 1| + 2, x = 0.7, and x = 1.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1|((-2(-1(4((-2x - 2)/(-3x - 1)) - 1) - 4) - 1)/(2(-1(4((-2x - 2)/(-3x - 1)) - 1) - 4) + 3))| - 3 and g(x) = 2|((-3(-4(4x + 3) + 3) + 2)/(-1(-4(4x + 3) + 3) - 3)) - 1| + 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": "3.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1|(-4(-4(-2(-1x - 4) - 2)^2 - 4(-2(-1x - 4) - 2)) + 4) - 1| - 1 and g(x) = -5(1|((-1((2x)/(-2x - 3)) - 1)/(-2((2x)/(-2x - 3)) - 3)) - 3| + 1)^2 - 2(1|((-1((2x)/(-2x - 3)) - 1)/(-2((2x)/(-2x - 3)) - 3)) - 3| + 1) + 5 between the vertical lines x = -3.8 and x = -2.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2|((-1((-1(-1((2x + 1)/(2x + 2)) + 1))/(1(-1((2x + 1)/(2x + 2)) + 1) + 1)) - 3)/(3((-1(-1((2x + 1)/(2x + 2)) + 1))/(1(-1((2x + 1)/(2x + 2)) + 1) + 1)) - 2)) + 2| - 2, g(x) = -3|(5(-2sin(1\u03c0(3|x + 3| + 3) + 2)) + 2) - 1| + 1, x = -1.9, and x = -1.7999999999999998. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2(1|(-4(1e^(2((1x - 3)/(-1x - 3))) - 3)^2 + 5(1e^(2((1x - 3)/(-1x - 3))) - 3) + 2)| - 2)^2 - 5(1|(-4(1e^(2((1x - 3)/(-1x - 3))) - 3)^2 + 5(1e^(2((1x - 3)/(-1x - 3))) - 3) + 2)| - 2) + 5 and g(x) = -3(-1(-3|(4x) - 3| - 1) - 2) + 2 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": "2.8", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1|(3(2cos(2\u03c0(-1((3x + 2)/(-1x + 2)) - 4) - 2) - 1) - 2) + 1| - 3, g(x) = (3(-1((-3(1|x + 3| + 3))/(-1(1|x + 3| + 3) + 3))^2 + 1((-3(1|x + 3| + 3))/(-1(1|x + 3| + 3) + 3)) + 1) + 1)/(-1(-1((-3(1|x + 3| + 3))/(-1(1|x + 3| + 3) + 3))^2 + 1((-3(1|x + 3| + 3))/(-1(1|x + 3| + 3) + 3)) + 1) + 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": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (2(3sin(3\u03c0(1|(-4((-2x + 3)/(1x + 2))) - 3| + 3) + 3) - 1) - 3)/(3(3sin(3\u03c0(1|(-4((-2x + 3)/(1x + 2))) - 3| + 3) + 3) - 1) - 2) and g(x) = 4(-1|(-2((-3x - 1)/(-2x - 2))^2 - 2) - 2| + 3)^2 + 1(-1|(-2((-3x - 1)/(-2x - 2))^2 - 2) - 2| + 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": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -4(2sin(1\u03c0((3(1(-3x - 2) - 2) - 3)/(2(1(-3x - 2) - 2) + 3)) - 2)) + 1, g(x) = 2|(1|(1|(-3cos(3\u03c0x - 3) + 3) + 2| + 3) + 2| - 1) - 2| - 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": "1.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2|(1((-3(3|((-2x - 1)/(1x + 3)) + 3| + 3) - 3)/(1(3|((-2x - 1)/(1x + 3)) + 3| + 3))) + 3) - 2| + 1 and g(x) = -2((-3(1sin(2\u03c0(-3|x + 1| - 3) - 3) + 2) - 2)/(2(1sin(2\u03c0(-3|x + 1| - 3) - 3) + 2) - 3)) - 5 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": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3(-1|(-1|((2(-4x^2 + 1x + 5))/(1(-4x^2 + 1x + 5) + 2)) - 3|) - 3| + 2) + 5, g(x) = 1e^(1((1((3(-3x^2 + 3x - 1) + 1)/(3(-3x^2 + 3x - 1) - 2)) - 3)/(1((3(-3x^2 + 3x - 1) + 1)/(3(-3x^2 + 3x - 1) - 2))))) + 1, x = -1.7, and x = -1.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (3(-2(2(3|(1x - 3) + 1|)^2 - 3(3|(1x - 3) + 1|) - 4)^2 + 4(2(3|(1x - 3) + 1|)^2 - 3(3|(1x - 3) + 1|) - 4) + 1) - 2)/(2(-2(2(3|(1x - 3) + 1|)^2 - 3(3|(1x - 3) + 1|) - 4)^2 + 4(2(3|(1x - 3) + 1|)^2 - 3(3|(1x - 3) + 1|) - 4) + 1)) and g(x) = 1sin(1\u03c0(-3((2(2|x + 1| + 1) - 1)/(-3(2|x + 1| + 1)))^2 - 2((2(2|x + 1| + 1) - 1)/(-3(2|x + 1| + 1))) - 4) - 3) 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((-3((-3(1(2x - 4) - 4) + 3)/(-3(1(2x - 4) - 4) - 2)))/(-3((-3(1(2x - 4) - 4) + 3)/(-3(1(2x - 4) - 4) - 2)) - 3))^2 + 5((-3((-3(1(2x - 4) - 4) + 3)/(-3(1(2x - 4) - 4) - 2)))/(-3((-3(1(2x - 4) - 4) + 3)/(-3(1(2x - 4) - 4) - 2)) - 3)) - 5 and g(x) = -2((2(-1((-1x + 3)/(-1x - 1))) - 3)/(-1(-1((-1x + 3)/(-1x - 1))) - 3))^2 - 2((2(-1((-1x + 3)/(-1x - 1))) - 3)/(-1(-1((-1x + 3)/(-1x - 1))) - 3)) between the vertical lines x = 4.2 and x = 4.4. 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) = -3((3((3(-3cos(3\u03c0(4x + 4) + 3) - 2) + 1)/(1(-3cos(3\u03c0(4x + 4) + 3) - 2) + 1)) + 1)/(-2((3(-3cos(3\u03c0(4x + 4) + 3) - 2) + 1)/(1(-3cos(3\u03c0(4x + 4) + 3) - 2) + 1))))^2 + 1((3((3(-3cos(3\u03c0(4x + 4) + 3) - 2) + 1)/(1(-3cos(3\u03c0(4x + 4) + 3) - 2) + 1)) + 1)/(-2((3(-3cos(3\u03c0(4x + 4) + 3) - 2) + 1)/(1(-3cos(3\u03c0(4x + 4) + 3) - 2) + 1)))) + 4 and g(x) = 5(-3(2((2x + 2)/(-2x)))^2 + 4(2((2x + 2)/(-2x))) + 1)^2 + 4(-3(2((2x + 2)/(-2x)))^2 + 4(2((2x + 2)/(-2x))) + 1) - 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": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (3(-1((-1(-2|(3x^2 + 5x + 4) - 2| + 2) - 3)/(2(-2|(3x^2 + 5x + 4) - 2| + 2) - 1))) - 2)/(3(-1((-1(-2|(3x^2 + 5x + 4) - 2| + 2) - 3)/(2(-2|(3x^2 + 5x + 4) - 2| + 2) - 1)))) and g(x) = 3((-1((-1(3x + 2) - 1)/(-3(3x + 2) - 1)) - 1)/(-1((-1(3x + 2) - 1)/(-3(3x + 2) - 1)) + 3)) - 4 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": "16.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 3|(-2|(2|(-2|(2x - 2) + 3| + 1) - 1| - 3) + 1| - 1) + 1| - 1 and g(x) = 1(1|((3((3x - 3)/(2x - 3)) + 1)/(-1((3x - 3)/(2x - 3)) - 1))| + 1) - 4 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": "54.5", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1(1sin(2\u03c0(3|(5(4x^2 + 4x + 5) + 5) - 3| + 3)))^2 - 4(1sin(2\u03c0(3|(5(4x^2 + 4x + 5) + 5) - 3| + 3))) + 2, g(x) = (-3(2e^(-1(1(-5x - 2)^2 - 3(-5x - 2))) - 3) + 2)/(2(2e^(-1(1(-5x - 2)^2 - 3(-5x - 2))) - 3) + 1), x = -1.0, and x = -0.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 3cos(3\u03c0(2(3(3(-3x^2 + 1x + 5)^2 + 4(-3x^2 + 1x + 5) + 3)^2 - 5(3(-3x^2 + 1x + 5)^2 + 4(-3x^2 + 1x + 5) + 3) + 2)^2 + 2) - 1) and g(x) = (-2(3|(-1(3x^2 + 1)^2 - 4) - 2| + 1) - 1)/(-2(3|(-1(3x^2 + 1)^2 - 4) - 2| + 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1sin(3\u03c0((-2(3(-2|(2|x + 3| - 3) - 2| - 3)^2 - 5(-2|(2|x + 3| - 3) - 2| - 3) - 5) - 3)/(2(3(-2|(2|x + 3| - 3) - 2| - 3)^2 - 5(-2|(2|x + 3| - 3) - 2| - 3) - 5) - 1)) - 3) - 3 and g(x) = -2|((-1(5(1x + 2)^2 + 2(1x + 2) - 2) + 2)/(2(5(1x + 2)^2 + 2(1x + 2) - 2) - 1)) - 1| - 2 between the vertical lines x = -3.0 and x = -2.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -5(-1sin(3\u03c0(3(2|(2|x - 1| + 3) + 1| + 1) - 2) + 1) + 2)^2 + 3(-1sin(3\u03c0(3(2|(2|x - 1| + 3) + 1| + 1) - 2) + 1) + 2) - 1, g(x) = 5(-2|(-1((1x + 3)/(1x + 1))^2 + 1)| - 3) - 2, x = 1.9, and x = 2.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (2(3(3|(-2|(2x^2 - 1x + 4) - 2| + 1) + 3| + 1) - 4) - 3)/(-2(3(3|(-2|(2x^2 - 1x + 4) - 2| + 1) + 3| + 1) - 4) - 2) and g(x) = -1sin(1\u03c0(-2|((2(-3x + 5) + 1)/(-1(-3x + 5) - 3))| + 1) - 1) - 1 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2cos(2\u03c0((-1(-4((1(-1|x + 1| + 3) + 1)/(1(-1|x + 1| + 3) + 2)) - 4) + 1)/(-3(-4((1(-1|x + 1| + 3) + 1)/(1(-1|x + 1| + 3) + 2)) - 4) + 4)) - 3) + 2 and g(x) = (-2(1(2(-5x - 3)^2 - 2(-5x - 3) - 4) - 5) + 3)/(-1(1(2(-5x - 3)^2 - 2(-5x - 3) - 4) - 5) - 3) 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1(2(1(-1sin(1\u03c0(-4x))))^2 + 3(1(-1sin(1\u03c0(-4x)))) + 1)^2 - 4(2(1(-1sin(1\u03c0(-4x))))^2 + 3(1(-1sin(1\u03c0(-4x)))) + 1) - 5, g(x) = 3sin(1\u03c0(2((-2(-4x^2 + 3x + 1) + 2)/(2(-4x^2 + 3x + 1) - 1)) + 4) + 1) - 2, x = 0.9, and x = 1.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3|((2(1((2(-3x^2 + 1x + 4) + 2)/(-1(-3x^2 + 1x + 4) - 3))^2 + 5((2(-3x^2 + 1x + 4) + 2)/(-1(-3x^2 + 1x + 4) - 3))) + 1)/(-3(1((2(-3x^2 + 1x + 4) + 2)/(-1(-3x^2 + 1x + 4) - 3))^2 + 5((2(-3x^2 + 1x + 4) + 2)/(-1(-3x^2 + 1x + 4) - 3))) + 2)) - 1| and g(x) = -2((2(3(-1x^2 - 2x - 4) - 2) + 2)/(1(3(-1x^2 - 2x - 4) - 2) - 2)) + 2 between the vertical lines x = -1.5 and x = -1.1. 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": "Determine the area of the region enclosed by the graphs of f(x) = 2|(1(3((1(3x + 5))/(1(3x + 5) - 3)) + 5) - 4)| - 1 and g(x) = (-2((-1(4((-1x + 2)/(-1x + 3)) + 1) + 2)/(2(4((-1x + 2)/(-1x + 3)) + 1) - 1)) - 3)/(-1((-1(4((-1x + 2)/(-1x + 3)) + 1) + 2)/(2(4((-1x + 2)/(-1x + 3)) + 1) - 1)) - 1) between the vertical lines x = -1.2 and x = 2.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "145.8", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3sin(2\u03c0((-1(-2|(-5(-2x - 2)^2 + 5(-2x - 2) + 5) - 2| - 3) + 3)/(1(-2|(-5(-2x - 2)^2 + 5(-2x - 2) + 5) - 2| - 3) + 1)) - 3) - 3 and g(x) = (2(-4(2e^(2(-4x)) + 3)^2 + 4(2e^(2(-4x)) + 3) - 3) - 2)/(-1(-4(2e^(2(-4x)) + 3)^2 + 4(2e^(2(-4x)) + 3) - 3) - 1) 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2|(2|((1(-1(-3|x - 1| + 2) + 1) + 1)/(-3(-1(-3|x - 1| + 2) + 1) - 1)) - 2| + 1) - 3| - 2, g(x) = -3((-1(4(-1cos(2\u03c0x - 3) + 2) - 4) + 1)/(-2(4(-1cos(2\u03c0x - 3) + 2) - 4) + 1)) + 5, x = 1.2, and x = 1.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13.9", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2((-1(4(2(-2e^(-2x) + 2)^2 - 3(-2e^(-2x) + 2) - 1)^2 + 3(2(-2e^(-2x) + 2)^2 - 3(-2e^(-2x) + 2) - 1) + 5) + 3)/(1(4(2(-2e^(-2x) + 2)^2 - 3(-2e^(-2x) + 2) - 1)^2 + 3(2(-2e^(-2x) + 2)^2 - 3(-2e^(-2x) + 2) - 1) + 5)))^2 - 1((-1(4(2(-2e^(-2x) + 2)^2 - 3(-2e^(-2x) + 2) - 1)^2 + 3(2(-2e^(-2x) + 2)^2 - 3(-2e^(-2x) + 2) - 1) + 5) + 3)/(1(4(2(-2e^(-2x) + 2)^2 - 3(-2e^(-2x) + 2) - 1)^2 + 3(2(-2e^(-2x) + 2)^2 - 3(-2e^(-2x) + 2) - 1) + 5))) - 2 and g(x) = -1(1(-1|(4x^2 - 1x - 4) - 2| + 2)^2 + 2(-1|(4x^2 - 1x - 4) - 2| + 2) - 3) - 5 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1|(2(-2(5((-1x)/(-3x + 4))^2 - 4((-1x)/(-3x + 4)) + 2)^2 - 1(5((-1x)/(-3x + 4))^2 - 4((-1x)/(-3x + 4)) + 2) - 4)^2 - 1(-2(5((-1x)/(-3x + 4))^2 - 4((-1x)/(-3x + 4)) + 2)^2 - 1(5((-1x)/(-3x + 4))^2 - 4((-1x)/(-3x + 4)) + 2) - 4) - 4)| + 3 and g(x) = -1(-1((-2(-4x - 3) + 3)/(-2(-4x - 3) - 1)) + 1)^2 + 4(-1((-2(-4x - 3) + 3)/(-2(-4x - 3) - 1)) + 1) - 4 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": "15.9", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -5(2sin(2\u03c0(-1((3(-3x - 1) - 1)/(1(-3x - 1)))^2 + 4((3(-3x - 1) - 1)/(1(-3x - 1))) - 4) - 2) - 1)^2 + 4(2sin(2\u03c0(-1((3(-3x - 1) - 1)/(1(-3x - 1)))^2 + 4((3(-3x - 1) - 1)/(1(-3x - 1))) - 4) - 2) - 1) - 5, g(x) = -1(-1((-1(3x^2 - 1x - 5) + 1)/(-2(3x^2 - 1x - 5) + 1))^2 + 5((-1(3x^2 - 1x - 5) + 1)/(-2(3x^2 - 1x - 5) + 1)) + 1)^2 - 2(-1((-1(3x^2 - 1x - 5) + 1)/(-2(3x^2 - 1x - 5) + 1))^2 + 5((-1(3x^2 - 1x - 5) + 1)/(-2(3x^2 - 1x - 5) + 1)) + 1) - 3, x = -0.2, and x = -0.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.9", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2|(1sin(1\u03c0(-2|(1|(-1x - 2) + 1| + 3) - 2| + 1) + 1) + 3) - 2| - 3 and g(x) = (-1((2(4(1x^2 - 2x - 2)^2 + 5(1x^2 - 2x - 2) - 3) - 2)/(3(4(1x^2 - 2x - 2)^2 + 5(1x^2 - 2x - 2) - 3) + 3)) - 1)/(1((2(4(1x^2 - 2x - 2)^2 + 5(1x^2 - 2x - 2) - 3) - 2)/(3(4(1x^2 - 2x - 2)^2 + 5(1x^2 - 2x - 2) - 3) + 3)) - 2) between the vertical lines x = -0.8 and x = -0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7.9", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (2(-4(-2((1(-3|x| - 2) + 3)/(-2(-3|x| - 2) - 2))^2 + 4) - 2) - 2)/(-1(-4(-2((1(-3|x| - 2) + 3)/(-2(-3|x| - 2) - 2))^2 + 4) - 2) - 2) and g(x) = -5(-1((3(-2cos(3\u03c0x + 3) + 1))/(2(-2cos(3\u03c0x + 3) + 1) - 1))^2 + 5) - 1 between the vertical lines x = 2.6 and x = 2.8. 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(-4(-3(3|x + 1|) + 3)^2 + 5) - 5) + 1 and g(x) = -2cos(2\u03c0(5(-1(-3x^2 - 3x - 5) - 2) + 2) + 1) + 3 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) = -1sin(2\u03c0(5(-1((2(2|x + 3| - 3) + 2)/(3(2|x + 3| - 3) + 1))^2 - 3((2(2|x + 3| - 3) + 2)/(3(2|x + 3| - 3) + 1)) - 2)^2 + 5) + 1) - 3 and g(x) = (-2(-5(-2sin(2\u03c0((1x + 3)/(1x - 3)) - 3) - 3)^2 + 5(-2sin(2\u03c0((1x + 3)/(1x - 3)) - 3) - 3) - 3))/(1(-5(-2sin(2\u03c0((1x + 3)/(1x - 3)) - 3) - 3)^2 + 5(-2sin(2\u03c0((1x + 3)/(1x - 3)) - 3) - 3) - 3) + 1) from x = -3.8 to x = -3.6999999999999997. 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(-3(5(4x + 5)^2 - 5(4x + 5) - 4)) + 1)/(1(-3(5(4x + 5)^2 - 5(4x + 5) - 4)) + 1))^2 - 1((1(-3(5(4x + 5)^2 - 5(4x + 5) - 4)) + 1)/(1(-3(5(4x + 5)^2 - 5(4x + 5) - 4)) + 1)) - 2 and g(x) = 1(-3(-1|(2e^(1x) - 3) + 1| + 2) + 4)^2 + 2(-3(-1|(2e^(1x) - 3) + 1| + 2) + 4) - 4 from x = -0.2 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": "Find the area of the region bounded by the curves f(x) = -2(-3cos(1\u03c0(3(2|(-1x^2 - 5x - 5) + 3| + 1) - 5) - 3)) + 3, g(x) = 3(-1(3sin(2\u03c0(-3x^2 + 1x) + 1) + 3) + 5) + 4, x = 4.9, and x = 5.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 5(1|(-2(-4(2x + 4)^2 - 1)^2 + 1(-4(2x + 4)^2 - 1) + 4) - 3| - 3)^2 - 2(1|(-2(-4(2x + 4)^2 - 1)^2 + 1(-4(2x + 4)^2 - 1) + 4) - 3| - 3) - 1 and g(x) = -3|(1|((-1(-3|x + 1| + 1) - 3)/(1(-3|x + 1| + 1) - 3)) + 3| - 3)| + 1 from x = -2.1 to x = -1.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 4(-3(-5(2((-1x - 2)/(-1x))^2 + 1((-1x - 2)/(-1x)) - 5)^2 - 1(2((-1x - 2)/(-1x))^2 + 1((-1x - 2)/(-1x)) - 5) + 5))^2 + 2(-3(-5(2((-1x - 2)/(-1x))^2 + 1((-1x - 2)/(-1x)) - 5)^2 - 1(2((-1x - 2)/(-1x))^2 + 1((-1x - 2)/(-1x)) - 5) + 5)) + 1 and g(x) = -1((3((3(1x - 1) - 1)/(1(1x - 1))))/(1((3(1x - 1) - 1)/(1(1x - 1))) + 2))^2 + 4((3((3(1x - 1) - 1)/(1(1x - 1))))/(1((3(1x - 1) - 1)/(1(1x - 1))) + 2)) + 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": "119.6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-2(-2sin(3\u03c0(4(-1|(1x + 5) + 1| + 3) + 1) + 2) - 1) + 3)/(-3(-2sin(3\u03c0(4(-1|(1x + 5) + 1| + 3) + 1) + 2) - 1)) and g(x) = 2|(5((-2((3x + 3)/(3x + 2)) + 3)/(1((3x + 3)/(3x + 2)) + 3)) - 5)| + 2 from x = -0.1 to x = -0.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.4", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -4((1((3((3(-3x - 5) - 2)/(-3(-3x - 5) + 4)) - 1)/(2((3(-3x - 5) - 2)/(-3(-3x - 5) + 4)) - 3)) + 3)/(1((3((3(-3x - 5) - 2)/(-3(-3x - 5) + 4)) - 1)/(2((3(-3x - 5) - 2)/(-3(-3x - 5) + 4)) - 3)) - 3))^2 - 3((1((3((3(-3x - 5) - 2)/(-3(-3x - 5) + 4)) - 1)/(2((3(-3x - 5) - 2)/(-3(-3x - 5) + 4)) - 3)) + 3)/(1((3((3(-3x - 5) - 2)/(-3(-3x - 5) + 4)) - 1)/(2((3(-3x - 5) - 2)/(-3(-3x - 5) + 4)) - 3)) - 3)) - 1 and g(x) = (3(-1(1(3x - 2) - 2) + 5) + 1)/(-2(-1(1(3x - 2) - 2) + 5) + 3) between the vertical lines x = -2.0 and x = -1.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2(-3sin(1\u03c0((-2(4(-2|x + 2| + 3) + 5) - 1)/(-2(4(-2|x + 2| + 3) + 5)))) + 2)^2 - 3(-3sin(1\u03c0((-2(4(-2|x + 2| + 3) + 5) - 1)/(-2(4(-2|x + 2| + 3) + 5)))) + 2) + 1, g(x) = 3|(1((3(3|x + 2| - 2))/(-3(3|x + 2| - 2) - 2))^2 - 3((3(3|x + 2| - 2))/(-3(3|x + 2| - 2) - 2)) + 2) + 3| - 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": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2(-1(4((-1((-1x + 1)/(-2x - 3)) - 2)/(3((-1x + 1)/(-2x - 3)) + 2)) + 1)^2 + 3) - 4, g(x) = -2|(3(-2|((2x - 3)/(-2x - 2)) + 3|)^2 + 3(-2|((2x - 3)/(-2x - 2)) + 3|) - 5) + 3| + 1, x = -2.8, 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": "3.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2(2cos(2\u03c0(-1|(-5(-4x - 3)^2 - 2(-4x - 3) - 1) - 2|) - 3) + 2) and g(x) = (-2((-1(-5(-2x - 5)^2 - 3(-2x - 5) - 3) - 2)/(-2(-5(-2x - 5)^2 - 3(-2x - 5) - 3) - 2)))/(1((-1(-5(-2x - 5)^2 - 3(-2x - 5) - 3) - 2)/(-2(-5(-2x - 5)^2 - 3(-2x - 5) - 3) - 2)) - 2) 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": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-1(3|(-1sin(2\u03c0(-5(-1x + 5)^2 - 1(-1x + 5) + 4)) + 1)| + 2) - 3)/(-3(3|(-1sin(2\u03c0(-5(-1x + 5)^2 - 1(-1x + 5) + 4)) + 1)| + 2) - 2), g(x) = 4((3(3(-3x + 2) - 2) + 1)/(-2(3(-3x + 2) - 2) + 3))^2 - 5((3(3(-3x + 2) - 2) + 1)/(-2(3(-3x + 2) - 2) + 3)) - 3, x = 0.6, and x = 0.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -5((3(-3|((1(-3cos(1\u03c0x) + 3) - 1)/(3(-3cos(1\u03c0x) + 3) - 1)) + 1| + 1) - 2)/(2(-3|((1(-3cos(1\u03c0x) + 3) - 1)/(3(-3cos(1\u03c0x) + 3) - 1)) + 1| + 1))) + 2, g(x) = 1((2(3sin(3\u03c0(4x - 3) + 3) + 1) + 1)/(2(3sin(3\u03c0(4x - 3) + 3) + 1) + 2))^2 + 1((2(3sin(3\u03c0(4x - 3) + 3) + 1) + 1)/(2(3sin(3\u03c0(4x - 3) + 3) + 1) + 2)) + 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": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2cos(1\u03c0((-2(1|(-1|(3|x - 3| - 3) - 2|) - 1| + 3) - 2)/(1(1|(-1|(3|x - 3| - 3) - 2|) - 1| + 3) - 3))) + 2 and g(x) = 3e^(2((2(2(2|x + 3| - 1) + 1) - 2)/(-2(2(2|x + 3| - 1) + 1) - 3))) + 2 from x = 4.5 to x = 4.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1(3|((-2((-3(-5x + 3) + 2)/(-2(-5x + 3) + 1)))/(1((-3(-5x + 3) + 2)/(-2(-5x + 3) + 1)) + 2)) + 1|) - 2 and g(x) = -3(2|(5(-1x - 3) - 1)| - 3) + 1 between the vertical lines x = -3.6 and x = -2.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -5(3(-2|((2(-2x - 3) - 3)/(3(-2x - 3) - 2)) - 3| + 2) - 2) + 5, g(x) = 1((1(1|(5x + 1) - 1| - 1) + 1)/(2(1|(5x + 1) - 1| - 1) - 3)) - 2, x = -1.7, and x = -1.5999999999999999. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -4(3|((-3(4(-2|x + 2| + 1)^2 - 1(-2|x + 2| + 1) + 5) - 1)/(1(4(-2|x + 2| + 1)^2 - 1(-2|x + 2| + 1) + 5) + 2))|)^2 + 4(3|((-3(4(-2|x + 2| + 1)^2 - 1(-2|x + 2| + 1) + 5) - 1)/(1(4(-2|x + 2| + 1)^2 - 1(-2|x + 2| + 1) + 5) + 2))|) - 3 and g(x) = -2|(4(3(2|x + 2| - 1)^2 - 5(2|x + 2| - 1) + 4)^2 - 3) + 1| + 2 from x = -3.5 to x = -2.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "137.4", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3(3e^(2(-3((-2(2x + 5) - 2)/(-3(2x + 5) + 4)) - 1)) + 3) - 2 and g(x) = (1(2sin(1\u03c0((-1((-3x + 1)/(-2x + 3)) + 2)/(-1((-3x + 1)/(-2x + 3)) + 3)) + 3) - 2) + 2)/(-2(2sin(1\u03c0((-1((-3x + 1)/(-2x + 3)) + 2)/(-1((-3x + 1)/(-2x + 3)) + 3)) + 3) - 2) - 3) between the vertical lines x = 2.2 and x = 2.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (3(3|(-2sin(3\u03c0(-2(3|x + 2|) - 4) + 1) - 1) - 2| - 3) + 3)/(-1(3|(-2sin(3\u03c0(-2(3|x + 2|) - 4) + 1) - 1) - 2| - 3) + 2) and g(x) = 4(-3(-2(1e^(2x)) - 3) + 5) - 3 between the vertical lines x = -0.3 and x = -0.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1(2(-4((-1(2|x + 1| + 3) + 1)/(-2(2|x + 1| + 3) + 1)) + 2) - 2) - 5 and g(x) = (3(-5(3|(1|x + 3| - 3) + 3| - 3) + 2) + 2)/(-1(-5(3|(1|x + 3| - 3) + 3| - 3) + 2) - 3) between the vertical lines x = -4.5 and x = -1.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1(-3(4((2(-5x + 1))/(1(-5x + 1) + 3)) - 1)^2 - 5(4((2(-5x + 1))/(1(-5x + 1) + 3)) - 1) + 5)^2 - 4(-3(4((2(-5x + 1))/(1(-5x + 1) + 3)) - 1)^2 - 5(4((2(-5x + 1))/(1(-5x + 1) + 3)) - 1) + 5) - 2 and g(x) = 3|((-1((-2(-2x + 2) + 3)/(1(-2x + 2) - 2)) + 2)/(1((-2(-2x + 2) + 3)/(1(-2x + 2) - 2)) + 3)) + 2| - 3 between the vertical lines x = 0.2 and x = 0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1(2(1|((3(2|x| + 1) - 1)/(-1(2|x| + 1) - 1))| + 2) - 5) - 5 and g(x) = (-1(-3(1(-1x + 3)^2 - 1(-1x + 3) - 2)^2 + 2(1(-1x + 3)^2 - 1(-1x + 3) - 2)) - 3)/(-3(-3(1(-1x + 3)^2 - 1(-1x + 3) - 2)^2 + 2(1(-1x + 3)^2 - 1(-1x + 3) - 2)) + 2) from x = 1.0 to x = 3.9. 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) = -2(-3|((3(1|(2sin(3\u03c0x - 2) + 1) + 2| + 2) - 2)/(-2(1|(2sin(3\u03c0x - 2) + 1) + 2| + 2) + 3)) + 1| + 1) + 5 and g(x) = 2|(-5(5(1cos(3\u03c0x - 2) + 1) - 3) + 1) + 1| - 2 from x = -2.3 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|(1sin(2\u03c0(-3|((-1(-3x^2 - 2) + 1)/(-1(-3x^2 - 2) - 2)) + 3| + 3) - 1) - 1) - 2|, g(x) = (-3(-3(-4(2cos(3\u03c0x + 1) + 1)^2 - 1(2cos(3\u03c0x + 1) + 1)) - 4) - 2)/(-3(-3(-4(2cos(3\u03c0x + 1) + 1)^2 - 1(2cos(3\u03c0x + 1) + 1)) - 4) + 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": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-1((-3(-4(3|(5x^2 + 1x - 5) + 1| - 2) - 3) + 3)/(-3(-4(3|(5x^2 + 1x - 5) + 1| - 2) - 3) - 3)))/(1((-3(-4(3|(5x^2 + 1x - 5) + 1| - 2) - 3) + 3)/(-3(-4(3|(5x^2 + 1x - 5) + 1| - 2) - 3) - 3))), g(x) = (2(1((1(-5x - 5) - 1)/(1(-5x - 5)))^2 - 3((1(-5x - 5) - 1)/(1(-5x - 5)))) - 1)/(2(1((1(-5x - 5) - 1)/(1(-5x - 5)))^2 - 3((1(-5x - 5) - 1)/(1(-5x - 5))))), 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": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -3|((-1(-3|(-2cos(1\u03c0(2|x - 2| + 2) + 3) - 3) + 1|))/(1(-3|(-2cos(1\u03c0(2|x - 2| + 2) + 3) - 3) + 1|) + 3)) + 2| + 1, g(x) = 2(-2(-3(-3e^(2x) - 1) - 5) + 4) - 4, 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": "1.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-3(-2(3cos(3\u03c0(4(-1|x - 3| - 3)^2 + 3(-1|x - 3| - 3) - 5) + 1) + 3) - 1) + 2)/(1(-2(3cos(3\u03c0(4(-1|x - 3| - 3)^2 + 3(-1|x - 3| - 3) - 5) + 1) + 3) - 1) + 3) and g(x) = (-1(1(1(1|x - 2| + 1))^2 - 3(1(1|x - 2| + 1)) - 3) - 2)/(3(1(1(1|x - 2| + 1))^2 - 3(1(1|x - 2| + 1)) - 3)) from x = 4.8 to x = 4.8999999999999995. 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|(-1sin(2\u03c0(2|(2|(-4x^2 - 1x - 3) + 3| + 2) + 2| + 2))) + 2| - 3, g(x) = -3cos(2\u03c0(-2|(2|(3x + 1) + 2|) - 3| - 2) - 1) + 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": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2|(-1|((2(-3|(2e^(1x) - 2) - 3| + 3))/(-1(-3|(2e^(1x) - 2) - 3| + 3) + 2)) - 1| - 2) + 1| - 1 and g(x) = (1(2|(-5(-2x + 5)^2 + 5(-2x + 5) - 2)| + 3) - 1)/(1(2|(-5(-2x + 5)^2 + 5(-2x + 5) - 2)| + 3) - 3) between the vertical lines x = 0.8 and x = 1.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "23.6", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1(1(-1(4(1x - 4)^2 - 5(1x - 4) + 2))^2 - 4(-1(4(1x - 4)^2 - 5(1x - 4) + 2)) - 4)^2 - 4, g(x) = (1((-3(3cos(3\u03c0(3x^2 + 3x + 1) + 3)) - 3)/(-1(3cos(3\u03c0(3x^2 + 3x + 1) + 3)) + 2)) + 1)/(-3((-3(3cos(3\u03c0(3x^2 + 3x + 1) + 3)) - 3)/(-1(3cos(3\u03c0(3x^2 + 3x + 1) + 3)) + 2)) - 3), x = 4.5, 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -5((-1(-1|(-3|((2x - 2)/(-1x + 2)) + 1| + 3) - 2| + 3) - 2)/(-3(-1|(-3|((2x - 2)/(-1x + 2)) + 1| + 3) - 2| + 3))) and g(x) = -1(-3(-1(-2sin(2\u03c0x - 1) - 2)^2 + 1(-2sin(2\u03c0x - 1) - 2) + 3)^2 - 4(-1(-2sin(2\u03c0x - 1) - 2)^2 + 1(-2sin(2\u03c0x - 1) - 2) + 3) + 4) + 2 between the vertical lines x = -2.3 and x = -2.1999999999999997. 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(2cos(1\u03c0(5((-3(-1x + 2) + 2)/(1(-1x + 2) + 3)) + 1) + 2) + 1) - 2)/(-2(2cos(1\u03c0(5((-3(-1x + 2) + 2)/(1(-1x + 2) + 3)) + 1) + 2) + 1) - 2) and g(x) = (3(3cos(2\u03c0(2((1x + 2)/(-3x + 4))^2 - 3((1x + 2)/(-3x + 4)) - 5) + 3) + 1) - 1)/(2(3cos(2\u03c0(2((1x + 2)/(-3x + 4))^2 - 3((1x + 2)/(-3x + 4)) - 5) + 3) + 1) - 1) 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1(-5(-4(2|((-2x - 2)/(2x)) + 3| - 2) + 3) + 1) + 2 and g(x) = 2(1|(-1cos(1\u03c0(-1x^2 - 1x - 1) + 2) + 3) + 3|) + 2 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": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1sin(1\u03c0(5(2(-2|(-2x^2 - 1x - 1) - 3| + 2)^2 - 4(-2|(-2x^2 - 1x - 1) - 3| + 2) - 5)^2 + 5(2(-2|(-2x^2 - 1x - 1) - 3| + 2)^2 - 4(-2|(-2x^2 - 1x - 1) - 3| + 2) - 5) + 3) - 1), g(x) = 3(-3(-1((-1x - 1)/(-2x + 3))^2 + 4((-1x - 1)/(-2x + 3)) + 2) - 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2(-2(2cos(3\u03c0(1|(-3x + 2) - 2|) - 3) - 2)^2 + 3(2cos(3\u03c0(1|(-3x + 2) - 2|) - 3) - 2) - 1)^2 - 4(-2(2cos(3\u03c0(1|(-3x + 2) - 2|) - 3) - 2)^2 + 3(2cos(3\u03c0(1|(-3x + 2) - 2|) - 3) - 2) - 1) - 2, g(x) = 2|(-4(-2|((2x + 2)/(1x - 2)) + 2| + 3)^2 + 5(-2|((2x + 2)/(1x - 2)) + 2| + 3) + 5) + 2| + 2, x = -4.4, 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": "21.5", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (1(-4(5((2(-3sin(2\u03c0x + 1)) + 2)/(3(-3sin(2\u03c0x + 1)) - 1)) + 1)^2 - 3(5((2(-3sin(2\u03c0x + 1)) + 2)/(3(-3sin(2\u03c0x + 1)) - 1)) + 1) - 1) + 1)/(2(-4(5((2(-3sin(2\u03c0x + 1)) + 2)/(3(-3sin(2\u03c0x + 1)) - 1)) + 1)^2 - 3(5((2(-3sin(2\u03c0x + 1)) + 2)/(3(-3sin(2\u03c0x + 1)) - 1)) + 1) - 1) - 1), g(x) = (1(2cos(3\u03c0(1((2x + 3)/(1x + 3)) + 4) + 3) - 2) + 1)/(-2(2cos(3\u03c0(1((2x + 3)/(1x + 3)) + 4) + 3) - 2) - 1), 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 5((1(-2(-3(2e^(-1x) + 1)^2 + 1(2e^(-1x) + 1) + 3)^2 - 4(-3(2e^(-1x) + 1)^2 + 1(2e^(-1x) + 1) + 3) - 2) - 3)/(2(-2(-3(2e^(-1x) + 1)^2 + 1(2e^(-1x) + 1) + 3)^2 - 4(-3(2e^(-1x) + 1)^2 + 1(2e^(-1x) + 1) + 3) - 2) - 3))^2 - 2((1(-2(-3(2e^(-1x) + 1)^2 + 1(2e^(-1x) + 1) + 3)^2 - 4(-3(2e^(-1x) + 1)^2 + 1(2e^(-1x) + 1) + 3) - 2) - 3)/(2(-2(-3(2e^(-1x) + 1)^2 + 1(2e^(-1x) + 1) + 3)^2 - 4(-3(2e^(-1x) + 1)^2 + 1(2e^(-1x) + 1) + 3) - 2) - 3)) - 2 and g(x) = 5(-5(-3|(2sin(1\u03c0x + 2)) + 1| + 2)^2 - 1(-3|(2sin(1\u03c0x + 2)) + 1| + 2) + 2) + 1 between the vertical lines x = -3.6 and x = -3.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 4((-1(4((2((1x - 3)/(1x - 3)) - 3)/(-3((1x - 3)/(1x - 3)))) + 4) + 2)/(-2(4((2((1x - 3)/(1x - 3)) - 3)/(-3((1x - 3)/(1x - 3)))) + 4) + 3)) - 3 and g(x) = 3sin(1\u03c0(-2|(-1(3x + 4)^2 + 5(3x + 4) + 5) + 3| - 3) + 2) + 1 between the vertical lines x = 4.6 and x = 4.699999999999999. 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(1|(3cos(1\u03c0((-2(4x^2 + 5x + 1) - 3)/(-3(4x^2 + 5x + 1)))) + 3) + 1| - 1)^2 + 3(1|(3cos(1\u03c0((-2(4x^2 + 5x + 1) - 3)/(-3(4x^2 + 5x + 1)))) + 3) + 1| - 1) + 2 and g(x) = (2(1((2(-3|x - 2|) + 2)/(-2(-3|x - 2|) + 1)) - 3) + 3)/(-3(1((2(-3|x - 2|) + 2)/(-2(-3|x - 2|) + 1)) - 3) - 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": "4.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -4(-1|((1(3cos(3\u03c0(1x^2 - 5x + 3) - 2) - 2))/(3(3cos(3\u03c0(1x^2 - 5x + 3) - 2) - 2) - 2)) + 3|) - 1 and g(x) = (3(2cos(3\u03c0(2|(4x - 4) - 3| + 2) + 1) - 2) - 1)/(3(2cos(3\u03c0(2|(4x - 4) - 3| + 2) + 1) - 2) - 1) from x = 2.2 to x = 2.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -4((-2(1|(-3(-3|x + 2| + 3) - 1) + 3| + 1) + 2)/(-1(1|(-3(-3|x + 2| + 3) - 1) + 3| + 1) + 2)) - 1 and g(x) = -1(4(-1(-3|x + 3| + 2)^2 - 5(-3|x + 3| + 2) + 2)^2 + 3(-1(-3|x + 3| + 2)^2 - 5(-3|x + 3| + 2) + 2) - 2) - 5 from x = -3.6 to x = -3.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (1((-3(-3|(2|(-3|x - 3| - 2) + 2| - 1) - 2| + 2) - 3)/(-2(-3|(2|(-3|x - 3| - 2) + 2| - 1) - 2| + 2) - 1)) - 2)/(1((-3(-3|(2|(-3|x - 3| - 2) + 2| - 1) - 2| + 2) - 3)/(-2(-3|(2|(-3|x - 3| - 2) + 2| - 1) - 2| + 2) - 1)) + 3) and g(x) = 4((1(-2e^(-1(5x - 5)) + 1) - 3)/(2(-2e^(-1(5x - 5)) + 1) + 1))^2 + 2((1(-2e^(-1(5x - 5)) + 1) - 3)/(2(-2e^(-1(5x - 5)) + 1) + 1)) from x = 3.4 to x = 3.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2(-1(2(-1(-5x)^2 + 5) - 5)) - 2 and g(x) = 3(-3(1|(1cos(1\u03c0x - 1) + 1) - 1| + 3) + 1) + 2 from x = -0.6 to x = 0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28.8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -5((1(-3sin(1\u03c0(-3(5x - 5) + 4) - 3) - 3) - 3)/(3(-3sin(1\u03c0(-3(5x - 5) + 4) - 3) - 3) + 2))^2 - 2((1(-3sin(1\u03c0(-3(5x - 5) + 4) - 3) - 3) - 3)/(3(-3sin(1\u03c0(-3(5x - 5) + 4) - 3) - 3) + 2)) + 4 and g(x) = -3sin(2\u03c0(1(1(-3|x| - 1) + 3) - 3) - 2) - 1 from x = 0.4 to x = 0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "74.4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1(-1(4(3|(1x) - 1| + 2) - 3) + 2) - 2 and g(x) = -1(-3(-2(3cos(1\u03c0x - 1) + 3)^2 + 2(3cos(1\u03c0x - 1) + 3) - 4) - 4)^2 + 1(-3(-2(3cos(1\u03c0x - 1) + 3)^2 + 2(3cos(1\u03c0x - 1) + 3) - 4) - 4) - 2 from x = -5.0 to x = -4.4. 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": "Determine the area of the region enclosed by the graphs of f(x) = (3(-1(-1(3e^(2(4x - 2)) - 2)^2 + 4(3e^(2(4x - 2)) - 2) + 1) + 2) + 3)/(1(-1(-1(3e^(2(4x - 2)) - 2)^2 + 4(3e^(2(4x - 2)) - 2) + 1) + 2) - 2) and g(x) = 1(-3(-4(3|x| - 2)^2 - 1)^2 + 1(-4(3|x| - 2)^2 - 1) - 3) + 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": "7.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3|(2cos(3\u03c0((3(2|((-2x + 1)/(-3x)) + 2| - 2) - 2)/(-3(2|((-2x + 1)/(-3x)) + 2| - 2) + 2))) + 2)| - 1, g(x) = 2((-2(-1((2x + 2)/(-2x - 3))) - 2)/(2(-1((2x + 2)/(-2x - 3))) + 1))^2 + 4((-2(-1((2x + 2)/(-2x - 3))) - 2)/(2(-1((2x + 2)/(-2x - 3))) + 1)) - 4, 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": "-1.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2|(-1|(-2|((2(4x + 1) - 3)/(3(4x + 1))) + 3| - 3) + 2| + 2) - 2| + 3 and g(x) = -3|(1cos(2\u03c0(-2|(1x^2 - 2x + 4) + 3| - 3) + 1) + 3) - 2| from x = -0.2 to x = -0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-1((-2((1(1(-3x^2 - 5x - 3)^2 + 5(-3x^2 - 5x - 3) - 5) - 1)/(-3(1(-3x^2 - 5x - 3)^2 + 5(-3x^2 - 5x - 3) - 5) - 3)) + 1)/(3((1(1(-3x^2 - 5x - 3)^2 + 5(-3x^2 - 5x - 3) - 5) - 1)/(-3(1(-3x^2 - 5x - 3)^2 + 5(-3x^2 - 5x - 3) - 5) - 3)))) - 1)/(-1((-2((1(1(-3x^2 - 5x - 3)^2 + 5(-3x^2 - 5x - 3) - 5) - 1)/(-3(1(-3x^2 - 5x - 3)^2 + 5(-3x^2 - 5x - 3) - 5) - 3)) + 1)/(3((1(1(-3x^2 - 5x - 3)^2 + 5(-3x^2 - 5x - 3) - 5) - 1)/(-3(1(-3x^2 - 5x - 3)^2 + 5(-3x^2 - 5x - 3) - 5) - 3)))) - 2) and g(x) = 4(1|((-1(1x))/(-1(1x) + 3)) + 1| - 3) + 5 from x = 0.7 to x = 2.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-1(-3sin(1\u03c0(-4(-5(-1x + 4) + 2) + 5) + 2)))/(1(-3sin(1\u03c0(-4(-5(-1x + 4) + 2) + 5) + 2)) + 1), g(x) = 1|(2(-4(1cos(1\u03c0x - 2) + 1)^2 - 3(1cos(1\u03c0x - 2) + 1) + 5) + 2) - 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": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (3((2(-2|(-1(-2|x - 2| + 3)^2 - 3(-2|x - 2| + 3) + 4) + 2| + 1))/(2(-2|(-1(-2|x - 2| + 3)^2 - 3(-2|x - 2| + 3) + 4) + 2| + 1) + 3)))/(-2((2(-2|(-1(-2|x - 2| + 3)^2 - 3(-2|x - 2| + 3) + 4) + 2| + 1))/(2(-2|(-1(-2|x - 2| + 3)^2 - 3(-2|x - 2| + 3) + 4) + 2| + 1) + 3)) - 2) and g(x) = 5(3sin(3\u03c0(-3(2|x - 3| - 2) + 5)) + 2)^2 + 5(3sin(3\u03c0(-3(2|x - 3| - 2) + 5)) + 2) + 4 between the vertical lines x = 1.2 and x = 2.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "98.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2((1(3((-3((-2x + 3)/(-2x - 3)) + 2)/(3((-2x + 3)/(-2x - 3)) + 2))^2 + 1((-3((-2x + 3)/(-2x - 3)) + 2)/(3((-2x + 3)/(-2x - 3)) + 2))))/(-2(3((-3((-2x + 3)/(-2x - 3)) + 2)/(3((-2x + 3)/(-2x - 3)) + 2))^2 + 1((-3((-2x + 3)/(-2x - 3)) + 2)/(3((-2x + 3)/(-2x - 3)) + 2))) + 3))^2 - 2((1(3((-3((-2x + 3)/(-2x - 3)) + 2)/(3((-2x + 3)/(-2x - 3)) + 2))^2 + 1((-3((-2x + 3)/(-2x - 3)) + 2)/(3((-2x + 3)/(-2x - 3)) + 2))))/(-2(3((-3((-2x + 3)/(-2x - 3)) + 2)/(3((-2x + 3)/(-2x - 3)) + 2))^2 + 1((-3((-2x + 3)/(-2x - 3)) + 2)/(3((-2x + 3)/(-2x - 3)) + 2))) + 3)) - 1, g(x) = (2((1((-3(-1x^2 - 3x - 4) - 1)/(1(-1x^2 - 3x - 4))) + 3)/(-1((-3(-1x^2 - 3x - 4) - 1)/(1(-1x^2 - 3x - 4))) - 2)) - 1)/(-3((1((-3(-1x^2 - 3x - 4) - 1)/(1(-1x^2 - 3x - 4))) + 3)/(-1((-3(-1x^2 - 3x - 4) - 1)/(1(-1x^2 - 3x - 4))) - 2)) + 2), x = -2.3, and x = -1.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "185.7", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 5(1(-2(1|((-3x)/(1x + 3)) + 1| - 3) - 3)^2 - 2(-2(1|((-3x)/(1x + 3)) + 1| - 3) - 3) - 5)^2 - 4(1(-2(1|((-3x)/(1x + 3)) + 1| - 3) - 3)^2 - 2(-2(1|((-3x)/(1x + 3)) + 1| - 3) - 3) - 5) and g(x) = -1(-2e^(1(-3(-3|x - 1| - 2)^2 - 4(-3|x - 1| - 2) - 2)) - 3) + 5 between the vertical lines x = -1.0 and x = -0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-3(-2|(2cos(2\u03c0(1(1|x| + 3)) + 2) - 3) - 1| + 3))/(1(-2|(2cos(2\u03c0(1(1|x| + 3)) + 2) - 3) - 1| + 3) + 3) and g(x) = -4(-2(1|((-3x - 3)/(2x + 3)) - 3| - 1)^2 - 4(1|((-3x - 3)/(2x + 3)) - 3| - 1) + 1) from x = 0.8 to x = 1.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "96.7", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2(-2sin(1\u03c0(3(-1|(2x + 2) + 3| + 1)^2 - 4(-1|(2x + 2) + 3| + 1)) - 2) + 1)^2 - 2(-2sin(1\u03c0(3(-1|(2x + 2) + 3| + 1)^2 - 4(-1|(2x + 2) + 3| + 1)) - 2) + 1) - 2 and g(x) = (2(-1((-1(-1|x + 2| + 1) - 1)/(-2(-1|x + 2| + 1) + 1)) - 4) + 3)/(-2(-1((-1(-1|x + 2| + 1) - 1)/(-2(-1|x + 2| + 1) + 1)) - 4) + 3) 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": "7.5", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1((-3(-1sin(3\u03c0((3((-2x + 2)/(-1x + 2)) + 1)/(1((-2x + 2)/(-1x + 2)) + 3)) + 3) + 2) - 1)/(3(-1sin(3\u03c0((3((-2x + 2)/(-1x + 2)) + 1)/(1((-2x + 2)/(-1x + 2)) + 3)) + 3) + 2) - 2)) - 3, g(x) = -1|(1(-3|((-3x - 2)/(2x + 3)) + 3| + 2) + 5) + 1| + 2, x = -1.7, and x = -1.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "167.7", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2|((2(-4(-2e^(-2((-3x + 2)/(2x - 3))))^2 - 2(-2e^(-2((-3x + 2)/(2x - 3)))) + 2) - 2)/(-3(-4(-2e^(-2((-3x + 2)/(2x - 3))))^2 - 2(-2e^(-2((-3x + 2)/(2x - 3)))) + 2) + 1)) - 2| - 1, g(x) = 5((-3(2(-3e^(1x) - 2) - 3) - 1)/(-3(2(-3e^(1x) - 2) - 3) - 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": "0.9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-2(-1(3|((-1(-4x^2 + 2x + 3))/(2(-4x^2 + 2x + 3) + 2)) + 2| + 2) - 2) - 1)/(-1(-1(3|((-1(-4x^2 + 2x + 3))/(2(-4x^2 + 2x + 3) + 2)) + 2| + 2) - 2) - 1) and g(x) = 1(1|(-3sin(1\u03c0(-1x - 2) + 1)) - 3|)^2 + 2(1|(-3sin(1\u03c0(-1x - 2) + 1)) - 3|) + 2 from x = 0.9 to x = 2.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38.7", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-2(-3(-1(3cos(2\u03c0(-3|x + 1| + 2) - 1) - 2)^2 + 3(3cos(2\u03c0(-3|x + 1| + 2) - 1) - 2) + 3) - 2) + 3)/(-1(-3(-1(3cos(2\u03c0(-3|x + 1| + 2) - 1) - 2)^2 + 3(3cos(2\u03c0(-3|x + 1| + 2) - 1) - 2) + 3) - 2) + 2) and g(x) = 4((-2((3(3e^(1x) + 2))/(-2(3e^(1x) + 2) - 2)))/(-2((3(3e^(1x) + 2))/(-2(3e^(1x) + 2) - 2)) - 1))^2 - 3((-2((3(3e^(1x) + 2))/(-2(3e^(1x) + 2) - 2)))/(-2((3(3e^(1x) + 2))/(-2(3e^(1x) + 2) - 2)) - 1)) + 4 between the vertical lines x = -0.6 and x = 3.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "26.4", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (2((-1(-3(-3sin(2\u03c0((-2x + 1)/(1x))) + 1)^2 + 2(-3sin(2\u03c0((-2x + 1)/(1x))) + 1) - 1) - 3)/(-1(-3(-3sin(2\u03c0((-2x + 1)/(1x))) + 1)^2 + 2(-3sin(2\u03c0((-2x + 1)/(1x))) + 1) - 1) + 2)))/(1((-1(-3(-3sin(2\u03c0((-2x + 1)/(1x))) + 1)^2 + 2(-3sin(2\u03c0((-2x + 1)/(1x))) + 1) - 1) - 3)/(-1(-3(-3sin(2\u03c0((-2x + 1)/(1x))) + 1)^2 + 2(-3sin(2\u03c0((-2x + 1)/(1x))) + 1) - 1) + 2))) and g(x) = 3cos(1\u03c0(3(-2|(-2x - 1) - 2| + 3) + 5) - 2) + 3 between the vertical lines x = -1.3 and x = -1.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2|((-1(-1sin(1\u03c0(-2|((1x)/(-1x)) + 1| + 2) - 1) - 2) - 3)/(-1(-1sin(1\u03c0(-2|((1x)/(-1x)) + 1| + 2) - 1) - 2) - 2)) - 2| and g(x) = (-3(-1(-3|(-3|x - 3|) + 1|) - 2) + 2)/(-3(-1(-3|(-3|x - 3|) + 1|) - 2)) from x = 2.3 to x = 3.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-1((-1(-4(-1(3x^2 + 1x + 3) + 3) - 5) - 1)/(-2(-4(-1(3x^2 + 1x + 3) + 3) - 5))))/(1((-1(-4(-1(3x^2 + 1x + 3) + 3) - 5) - 1)/(-2(-4(-1(3x^2 + 1x + 3) + 3) - 5))) - 2) and g(x) = 3((1((-3(-3|x + 1| - 1) - 1)/(3(-3|x + 1| - 1) - 2)) - 3)/(2((-3(-3|x + 1| - 1) - 1)/(3(-3|x + 1| - 1) - 2)))) + 1 from x = -0.9 to x = 0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1(-2|(-2|(-3(-3x - 5) + 5) + 2|)| - 3) and g(x) = -2e^(-1(-1|(1(1|x - 1| - 1)^2 - 3(1|x - 1| - 1) - 2) + 1| + 3)) - 2 from x = -4.6 to x = -2.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "75.6", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2|(-3e^(1(-3(3|(-3x^2 - 3x)| - 3) - 4)) + 1)| and g(x) = 3((-2(1sin(3\u03c0(-1x + 4)) - 1) + 3)/(2(1sin(3\u03c0(-1x + 4)) - 1)))^2 - 4((-2(1sin(3\u03c0(-1x + 4)) - 1) + 3)/(2(1sin(3\u03c0(-1x + 4)) - 1))) between the vertical lines x = -0.9 and x = -0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-20.8", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (3(1(1|((2(4x^2 + 1x - 1) - 3)/(-1(4x^2 + 1x - 1)))| + 3)^2 + 1(1|((2(4x^2 + 1x - 1) - 3)/(-1(4x^2 + 1x - 1)))| + 3) - 5) + 3)/(2(1(1|((2(4x^2 + 1x - 1) - 3)/(-1(4x^2 + 1x - 1)))| + 3)^2 + 1(1|((2(4x^2 + 1x - 1) - 3)/(-1(4x^2 + 1x - 1)))| + 3) - 5) - 3) and g(x) = -3((1(2(-4x^2 - 1x + 5)^2 - 2(-4x^2 - 1x + 5) - 5) + 1)/(2(2(-4x^2 - 1x + 5)^2 - 2(-4x^2 - 1x + 5) - 5) - 3))^2 + 2((1(2(-4x^2 - 1x + 5)^2 - 2(-4x^2 - 1x + 5) - 5) + 1)/(2(2(-4x^2 - 1x + 5)^2 - 2(-4x^2 - 1x + 5) - 5) - 3)) + 4 between the vertical lines x = -0.9 and x = 0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-1(-3cos(2\u03c0((3((-1(4x + 4))/(3(4x + 4) - 1)) + 3)/(3((-1(4x + 4))/(3(4x + 4) - 1)) - 2)) - 1) + 3) + 2)/(1(-3cos(2\u03c0((3((-1(4x + 4))/(3(4x + 4) - 1)) + 3)/(3((-1(4x + 4))/(3(4x + 4) - 1)) - 2)) - 1) + 3) + 1) and g(x) = 3(-3|((3((1x - 1)/(3x - 1)) - 2)/(2((1x - 1)/(3x - 1)) + 1)) - 2|)^2 - 1(-3|((3((1x - 1)/(3x - 1)) - 2)/(2((1x - 1)/(3x - 1)) + 1)) - 2|) - 4 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": "6.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -5(1|((3(-4(1x^2 - 1x + 2) + 3) + 3)/(-3(-4(1x^2 - 1x + 2) + 3) + 2)) + 2| - 1) + 4, g(x) = 3|(1((-3((3x + 2)/(3x - 1)) - 3)/(3((3x + 2)/(3x - 1)))) - 2) - 3| - 1, 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) = -2((-2((2(-3|(1x + 4) - 2| - 1) + 2)/(-2(-3|(1x + 4) - 2| - 1) - 3)) + 1)/(3((2(-3|(1x + 4) - 2| - 1) + 2)/(-2(-3|(1x + 4) - 2| - 1) - 3)) + 1))^2 + 5((-2((2(-3|(1x + 4) - 2| - 1) + 2)/(-2(-3|(1x + 4) - 2| - 1) - 3)) + 1)/(3((2(-3|(1x + 4) - 2| - 1) + 2)/(-2(-3|(1x + 4) - 2| - 1) - 3)) + 1)) + 4 and g(x) = -3|((2(1(1x - 1)^2 - 5(1x - 1) + 2) - 3)/(-1(1(1x - 1)^2 - 5(1x - 1) + 2) - 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": "17.4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2e^(-2(-5(-3(2|(-1x - 2) - 2| - 2) - 3) + 3)) - 2 and g(x) = -1sin(3\u03c0((-1((3((-3x + 3)/(1x)) - 2)/(1((-3x + 3)/(1x)) + 1)))/(1((3((-3x + 3)/(1x)) - 2)/(1((-3x + 3)/(1x)) + 1)) - 2)) + 1) - 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3|(-1|(-1(2|(-1x - 5)| + 1) - 2) + 1| - 1) + 3| + 2, g(x) = 4((-3(4((3x)/(-3x + 4))^2 + 1((3x)/(-3x + 4)) - 3) - 2)/(-2(4((3x)/(-3x + 4))^2 + 1((3x)/(-3x + 4)) - 3) - 2)) - 3, x = -4.1, and x = 0.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "75.5", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2|(-2|(-3(-2cos(1\u03c0(2|x + 1| + 2) + 2))^2 - 4(-2cos(1\u03c0(2|x + 1| + 2) + 2)) + 5)| - 3) - 2|, g(x) = -4(-2cos(1\u03c0(2((2x)/(-2x + 3)) - 5) + 2) - 1)^2 - 5(-2cos(1\u03c0(2((2x)/(-2x + 3)) - 5) + 2) - 1) - 3, x = 1.6, and x = 1.7000000000000002. 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(-3|(2e^(1(-2((2x - 3)/(-1x - 2))^2 + 3((2x - 3)/(-1x - 2)) + 2)) + 1) - 2| + 1) - 3)/(2(-3|(2e^(1(-2((2x - 3)/(-1x - 2))^2 + 3((2x - 3)/(-1x - 2)) + 2)) + 1) - 2| + 1)) and g(x) = (-1((1(-5(2|x|)^2 + 4(2|x|) + 2) + 3)/(-1(-5(2|x|)^2 + 4(2|x|) + 2) - 2)) - 2)/(3((1(-5(2|x|)^2 + 4(2|x|) + 2) + 3)/(-1(-5(2|x|)^2 + 4(2|x|) + 2) - 2)) + 3) between the vertical lines x = 2.9 and x = 3.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33.7", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 4((3(5(1sin(2\u03c0((-2x - 3)/(3x + 2)) + 1) + 2)) + 2)/(-3(5(1sin(2\u03c0((-2x - 3)/(3x + 2)) + 1) + 2)) + 4))^2 - 1 and g(x) = (3(2|(-3((-2x - 1)/(-1x - 3))^2 + 3) - 1| - 1) - 1)/(-3(2|(-3((-2x - 1)/(-1x - 3))^2 + 3) - 1| - 1) - 3) between the vertical lines x = 1.1 and x = 1.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (1(-1|((3((3((-2x - 1)/(-2x + 3)) + 2)/(-3((-2x - 1)/(-2x + 3)) - 3)) + 2)/(-3((3((-2x - 1)/(-2x + 3)) + 2)/(-3((-2x - 1)/(-2x + 3)) - 3)) + 4)) + 3| + 1) + 1)/(3(-1|((3((3((-2x - 1)/(-2x + 3)) + 2)/(-3((-2x - 1)/(-2x + 3)) - 3)) + 2)/(-3((3((-2x - 1)/(-2x + 3)) + 2)/(-3((-2x - 1)/(-2x + 3)) - 3)) + 4)) + 3| + 1) + 3) and g(x) = 2|(-4(1(4x^2 - 2x - 4) + 3)^2 + 5) + 3| between the vertical lines x = -0.6 and x = 1.1. 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) = -2|(1|(1|((3(5x - 1))/(-2(5x - 1) + 3)) + 3| + 3)| - 1) + 1| + 1, g(x) = 4(-2sin(1\u03c0(-1((2x + 1)/(2x + 3))^2 - 2((2x + 1)/(2x + 3)) - 2) + 2)), x = 2.3, 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": "Determine the area of the region enclosed by the graphs of f(x) = 3|((2(-2(2sin(3\u03c0(1x - 4) + 1) + 3) + 5))/(3(-2(2sin(3\u03c0(1x - 4) + 1) + 3) + 5) - 2)) + 3| - 1 and g(x) = -1|(-1e^(1(1((-2x)/(3x - 2))^2 + 4((-2x)/(3x - 2)) + 1)) - 1) + 1| + 2 between the vertical lines x = -0.8 and x = -0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2sin(1\u03c0(5(-2(1(5x + 5)^2 - 3(5x + 5) + 5)^2 + 3(1(5x + 5)^2 - 3(5x + 5) + 5) + 1)^2 - 4(-2(1(5x + 5)^2 - 3(5x + 5) + 5)^2 + 3(1(5x + 5)^2 - 3(5x + 5) + 5) + 1) + 1) - 3) + 1 and g(x) = 1|((-1(1((3x - 2)/(3x + 3)) + 5) - 3)/(2(1((3x - 2)/(3x + 3)) + 5))) + 1| + 1 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (2(1|(-1sin(1\u03c0(3(-3x^2 - 3x - 5) - 3) + 2) + 1) - 2| - 1) + 2)/(1(1|(-1sin(1\u03c0(3(-3x^2 - 3x - 5) - 3) + 2) + 1) - 2| - 1)) and g(x) = -2cos(2\u03c0((-2(-2(2x - 3)^2 - 5(2x - 3) + 2) - 1)/(-2(-2(2x - 3)^2 - 5(2x - 3) + 2) + 3)) + 2) - 3 from x = 2.4 to x = 2.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1(-2((-2(5(-2|x - 2| + 3)) - 1)/(1(5(-2|x - 2| + 3))))) - 4 and g(x) = -2|(3(-1(-2|x| - 3) - 2) + 2) + 1| - 2 between the vertical lines x = 0.5 and x = 3.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "123.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -5(-1(4(5(-1x^2 + 5x)^2 + 5(-1x^2 + 5x) - 3) + 1) + 2) - 1 and g(x) = -4((-2(1(4x + 3) + 3) - 1)/(-3(1(4x + 3) + 3) - 1)) + 3 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": "22.8", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2|(-5(-3|(2cos(1\u03c0(-5x^2 + 4x + 1) - 1) + 1)|)) + 1|, g(x) = -2(-3(1(-1x)^2 - 2(-1x) + 1) - 2)^2 - 4(-3(1(-1x)^2 - 2(-1x) + 1) - 2) + 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": "2.6", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -5(-3cos(1\u03c0(-1|((2(-2x^2 + 3x - 4) - 2)/(-1(-2x^2 + 3x - 4) + 3)) - 1| + 2) + 3) - 1) and g(x) = 3(2((1(-1|x| + 1) + 1)/(1(-1|x| + 1)))^2 + 5((1(-1|x| + 1) + 1)/(1(-1|x| + 1))) - 2) - 1 between the vertical lines x = -1.2 and x = 1.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35.9", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-3((-1((-2(3|(3x^2 - 5x - 4) + 1| + 3) + 2)/(-1(3|(3x^2 - 5x - 4) + 1| + 3) + 2)) + 1)/(-1((-2(3|(3x^2 - 5x - 4) + 1| + 3) + 2)/(-1(3|(3x^2 - 5x - 4) + 1| + 3) + 2)) + 3)) - 3)/(-2((-1((-2(3|(3x^2 - 5x - 4) + 1| + 3) + 2)/(-1(3|(3x^2 - 5x - 4) + 1| + 3) + 2)) + 1)/(-1((-2(3|(3x^2 - 5x - 4) + 1| + 3) + 2)/(-1(3|(3x^2 - 5x - 4) + 1| + 3) + 2)) + 3)) - 2) and g(x) = -4(3sin(2\u03c0(1(2|x - 1| - 2)^2 + 5(2|x - 1| - 2) + 3) - 3) + 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": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2(3cos(1\u03c0(-1|((3((-3x + 3)/(3x + 3)) - 3)/(-3((-3x + 3)/(3x + 3)) - 2)) + 2| - 3) + 3) - 2)^2 + 2(3cos(1\u03c0(-1|((3((-3x + 3)/(3x + 3)) - 3)/(-3((-3x + 3)/(3x + 3)) - 2)) + 2| - 3) + 3) - 2) + 1 and g(x) = -3(1cos(2\u03c0(1(5x + 4) + 3) - 3) - 3) + 3 between the vertical lines x = 4.3 and x = 4.3999999999999995. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2((2(3|(-4((3x - 1)/(2x + 1))^2 + 1((3x - 1)/(2x + 1)) + 1) + 1| - 1) + 2)/(-3(3|(-4((3x - 1)/(2x + 1))^2 + 1((3x - 1)/(2x + 1)) + 1) + 1| - 1) + 4)) - 3 and g(x) = -2|(2((-3(-2x + 1) - 3)/(-2(-2x + 1) - 1)) - 3) - 3| + 2 between the vertical lines x = 0.1 and x = 0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.9", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1((2((-1((-3(2|x - 3| - 1))/(-1(2|x - 3| - 1) + 3)) + 3)/(-3((-3(2|x - 3| - 1))/(-1(2|x - 3| - 1) + 3)) + 1)) - 3)/(3((-1((-3(2|x - 3| - 1))/(-1(2|x - 3| - 1) + 3)) + 3)/(-3((-3(2|x - 3| - 1))/(-1(2|x - 3| - 1) + 3)) + 1)) - 1))^2 - 5((2((-1((-3(2|x - 3| - 1))/(-1(2|x - 3| - 1) + 3)) + 3)/(-3((-3(2|x - 3| - 1))/(-1(2|x - 3| - 1) + 3)) + 1)) - 3)/(3((-1((-3(2|x - 3| - 1))/(-1(2|x - 3| - 1) + 3)) + 3)/(-3((-3(2|x - 3| - 1))/(-1(2|x - 3| - 1) + 3)) + 1)) - 1)) - 5, g(x) = 1((3(-3((2x + 2)/(1x)) - 5))/(3(-3((2x + 2)/(1x)) - 5) + 1))^2 - 4((3(-3((2x + 2)/(1x)) - 5))/(3(-3((2x + 2)/(1x)) - 5) + 1)) + 4, 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": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1|(3((3(1|(-2x^2 - 4x - 4)| - 3) + 2)/(1(1|(-2x^2 - 4x - 4)| - 3))) - 4)| - 1 and g(x) = (-3(2cos(3\u03c0(4((-1x)/(-2x + 3))^2 + 3((-1x)/(-2x + 3)) + 1) + 1) - 1) + 2)/(-1(2cos(3\u03c0(4((-1x)/(-2x + 3))^2 + 3((-1x)/(-2x + 3)) + 1) + 1) - 1) - 3) between the vertical lines x = 1.6 and x = 1.7000000000000002. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36.9", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 3(-1|(-4(3|((3x - 3)/(-3x + 4)) + 1| - 1) + 5) + 3|) + 4 and g(x) = -1(2(2(-4x^2 + 1x + 5) + 3) - 2) + 3 between the vertical lines x = 0.2 and x = 1.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1|(-3(3|(4((-1x - 3)/(3x - 2)) + 3) + 1| - 2)^2 + 2(3|(4((-1x - 3)/(3x - 2)) + 3) + 1| - 2) - 3) - 3| - 3 and g(x) = (-2(2(-5(-1|x - 1| + 2)^2 + 4)^2 - 2(-5(-1|x - 1| + 2)^2 + 4) - 5))/(-1(2(-5(-1|x - 1| + 2)^2 + 4)^2 - 2(-5(-1|x - 1| + 2)^2 + 4) - 5) + 2) from x = 2.0 to x = 2.4. 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": "Find the area of the region bounded by the curves f(x) = -1(3|((1(1|(-3|x - 2|) - 3| - 2) - 1)/(1(1|(-3|x - 2|) - 3| - 2) - 3))| - 3)^2 + 4(3|((1(1|(-3|x - 2|) - 3| - 2) - 1)/(1(1|(-3|x - 2|) - 3| - 2) - 3))| - 3) + 1, g(x) = 2(-4(3|((-2x)/(2x + 1)) + 3| + 1)^2 + 1(3|((-2x)/(2x + 1)) + 3| + 1) - 2) + 4, x = 2.6, and x = 2.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-380.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -3(2sin(1\u03c0(4(4((-2x + 2)/(-3x - 3)) + 1) + 5)) + 2)^2 - 4(2sin(1\u03c0(4(4((-2x + 2)/(-3x - 3)) + 1) + 5)) + 2) + 1, g(x) = (1(-1(-2|(-3x^2 - 5x + 1) + 3| + 3)^2 - 4(-2|(-3x^2 - 5x + 1) + 3| + 3) - 5) - 2)/(-1(-1(-2|(-3x^2 - 5x + 1) + 3| + 3)^2 - 4(-2|(-3x^2 - 5x + 1) + 3| + 3) - 5) - 1), 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": "2.4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3(5((-2(-1e^(-1((3x + 2)/(-2x + 3))) - 1))/(2(-1e^(-1((3x + 2)/(-2x + 3))) - 1) - 1))^2 + 5((-2(-1e^(-1((3x + 2)/(-2x + 3))) - 1))/(2(-1e^(-1((3x + 2)/(-2x + 3))) - 1) - 1)) + 4) - 3 and g(x) = -3(2cos(3\u03c0(-5(2|x + 1| - 3)^2 - 1(2|x + 1| - 3) + 3) - 1) + 3) - 1 from x = -3.8 to x = -3.6999999999999997. 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(3(2(2e^(-1x) + 1) - 4)^2 - 5(2(2e^(-1x) + 1) - 4) - 4) + 2)/(-3(3(2(2e^(-1x) + 1) - 4)^2 - 5(2(2e^(-1x) + 1) - 4) - 4))) - 2 and g(x) = (-1(1(1|(4x - 1)| - 1) + 2))/(-1(1(1|(4x - 1)| - 1) + 2)) from x = -0.1 to x = 1.1. 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": "Calculate the area enclosed between the functions f(x) = 3|(-3(1|(2|(-2x - 1) - 1| - 3) + 3| - 2) - 1) + 2| - 2 and g(x) = (-1((2((2(-2cos(3\u03c0x - 2) + 3) - 1)/(2(-2cos(3\u03c0x - 2) + 3) - 1)) + 2)/(-2((2(-2cos(3\u03c0x - 2) + 3) - 1)/(2(-2cos(3\u03c0x - 2) + 3) - 1)) - 3)))/(-3((2((2(-2cos(3\u03c0x - 2) + 3) - 1)/(2(-2cos(3\u03c0x - 2) + 3) - 1)) + 2)/(-2((2(-2cos(3\u03c0x - 2) + 3) - 1)/(2(-2cos(3\u03c0x - 2) + 3) - 1)) - 3)) - 3) from x = -1.6 to x = -1.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1(2|(-2(-4(-4x^2 - 2x + 5)^2 - 3(-4x^2 - 2x + 5) - 4) - 4) - 3| - 2)^2 - 2(2|(-2(-4(-4x^2 - 2x + 5)^2 - 3(-4x^2 - 2x + 5) - 4) - 4) - 3| - 2) - 1 and g(x) = -3|(1(-2|((-2x + 3)/(1x - 3)) - 2| + 3) - 3) + 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": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2|(3(3|(-1cos(1\u03c0(-1|x - 3| + 2) - 2) - 1) + 3|)^2 + 3(3|(-1cos(1\u03c0(-1|x - 3| + 2) - 2) - 1) + 3|) - 1) - 3| + 1 and g(x) = -3(-2|(-2|(-3e^(1x) + 2) - 3|) - 1| + 2)^2 - 2(-2|(-2|(-3e^(1x) + 2) - 3|) - 1| + 2) + 4 between the vertical lines x = -2.4 and x = -2.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-1(1cos(2\u03c0(-1(-4(1|x + 3| + 2)^2 + 4(1|x + 3| + 2) + 4)^2 - 4(-4(1|x + 3| + 2)^2 + 4(1|x + 3| + 2) + 4) - 2) + 2)) + 1)/(-3(1cos(2\u03c0(-1(-4(1|x + 3| + 2)^2 + 4(1|x + 3| + 2) + 4)^2 - 4(-4(1|x + 3| + 2)^2 + 4(1|x + 3| + 2) + 4) - 2) + 2)) - 3), g(x) = (3((-2(-5(3|x + 1|)^2 + 3(3|x + 1|) - 3) - 3)/(2(-5(3|x + 1|)^2 + 3(3|x + 1|) - 3) + 1)))/(-3((-2(-5(3|x + 1|)^2 + 3(3|x + 1|) - 3) - 3)/(2(-5(3|x + 1|)^2 + 3(3|x + 1|) - 3) + 1))), 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": "4.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -5(-2cos(1\u03c0(-1(2|(-2x^2 + 2x - 4) - 2| - 2)^2 + 1(2|(-2x^2 + 2x - 4) - 2| - 2) + 3) + 2) - 2) - 2 and g(x) = 1(3|(-1|(4x + 5) + 3| + 1) - 3| + 2) + 5 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": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 3sin(2\u03c0(5(4(-2(1x + 1) - 3))^2 - 4(4(-2(1x + 1) - 3)) + 1) - 2) - 3 and g(x) = 5(2((-1((-1x + 3)/(1x + 2)))/(-1((-1x + 3)/(1x + 2)) + 3))^2 - 5((-1((-1x + 3)/(1x + 2)))/(-1((-1x + 3)/(1x + 2)) + 3)) - 2) - 5 from x = 0.6 to x = 0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2(1(5((1(-2|x| + 2))/(3(-2|x| + 2) - 2)) + 2)^2 - 5(5((1(-2|x| + 2))/(3(-2|x| + 2) - 2)) + 2)) - 4, g(x) = -2|((2(3(-3x^2 - 3x + 3) + 5) + 2)/(-3(3(-3x^2 - 3x + 3) + 5)))| - 1, x = -0.2, and x = 0.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -4(5(4(-1((3x + 3)/(-2x - 1)) + 3)^2 + 1(-1((3x + 3)/(-2x - 1)) + 3) - 5) + 2) - 2 and g(x) = -5(3|((3(-5x + 5) + 1)/(-3(-5x + 5))) + 3|) 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": "12.6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1(-4(-3|(1|((-3x + 1)/(-2x - 2)) - 2| - 1) - 3| + 2) + 5)^2 - 1(-4(-3|(1|((-3x + 1)/(-2x - 2)) - 2| - 1) - 3| + 2) + 5) - 5 and g(x) = -2(-2(-2((1x + 1)/(3x + 3)))^2 - 4(-2((1x + 1)/(3x + 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": "Calculate the area enclosed between the functions f(x) = (3((-3(-3cos(2\u03c0(-2((2x + 2)/(-3x - 3)) - 1) + 1) + 3) - 2)/(-1(-3cos(2\u03c0(-2((2x + 2)/(-3x - 3)) - 1) + 1) + 3) + 3)))/(-1((-3(-3cos(2\u03c0(-2((2x + 2)/(-3x - 3)) - 1) + 1) + 3) - 2)/(-1(-3cos(2\u03c0(-2((2x + 2)/(-3x - 3)) - 1) + 1) + 3) + 3)) + 2) and g(x) = -2|(3(1cos(2\u03c0(3x^2 - 2x + 5) + 3) + 1)) - 2| from x = -2.0 to x = -1.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 5(5(5(2(-2x^2 - 5x + 2)^2 - 4(-2x^2 - 5x + 2) - 1)^2 + 1(2(-2x^2 - 5x + 2)^2 - 4(-2x^2 - 5x + 2) - 1)) - 5) + 5 and g(x) = -3|(-3e^(-2(2|(-4x^2 + 3x - 2) - 3| + 1)) + 1) - 3| + 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": "228.9", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (2(-1(3(-1e^(1(-3|x + 3| - 3)) - 3)^2 + 5(-1e^(1(-3|x + 3| - 3)) - 3) + 5) - 1) + 3)/(-1(-1(3(-1e^(1(-3|x + 3| - 3)) - 3)^2 + 5(-1e^(1(-3|x + 3| - 3)) - 3) + 5) - 1) - 1) and g(x) = (3(-4(-3(1x + 2) - 4)^2 + 4(-3(1x + 2) - 4) + 5) - 1)/(-3(-4(-3(1x + 2) - 4)^2 + 4(-3(1x + 2) - 4) + 5) - 3) between the vertical lines x = -4.0 and x = -3.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.6", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (2(4(2((-3(1sin(3\u03c0x - 3) + 2) + 2)/(-1(1sin(3\u03c0x - 3) + 2) - 2))^2 + 1((-3(1sin(3\u03c0x - 3) + 2) + 2)/(-1(1sin(3\u03c0x - 3) + 2) - 2)) - 4)^2 + 5(2((-3(1sin(3\u03c0x - 3) + 2) + 2)/(-1(1sin(3\u03c0x - 3) + 2) - 2))^2 + 1((-3(1sin(3\u03c0x - 3) + 2) + 2)/(-1(1sin(3\u03c0x - 3) + 2) - 2)) - 4) + 4) - 3)/(-2(4(2((-3(1sin(3\u03c0x - 3) + 2) + 2)/(-1(1sin(3\u03c0x - 3) + 2) - 2))^2 + 1((-3(1sin(3\u03c0x - 3) + 2) + 2)/(-1(1sin(3\u03c0x - 3) + 2) - 2)) - 4)^2 + 5(2((-3(1sin(3\u03c0x - 3) + 2) + 2)/(-1(1sin(3\u03c0x - 3) + 2) - 2))^2 + 1((-3(1sin(3\u03c0x - 3) + 2) + 2)/(-1(1sin(3\u03c0x - 3) + 2) - 2)) - 4) + 4)), g(x) = 2((2((-2(-3|x + 3| + 3) + 3)/(3(-3|x + 3| + 3) - 1)) + 3)/(-2((-2(-3|x + 3| + 3) + 3)/(3(-3|x + 3| + 3) - 1)) + 3))^2 + 5((2((-2(-3|x + 3| + 3) + 3)/(3(-3|x + 3| + 3) - 1)) + 3)/(-2((-2(-3|x + 3| + 3) + 3)/(3(-3|x + 3| + 3) - 1)) + 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1(2(-1cos(1\u03c0(-1(2|x + 3| + 2) + 4) + 2) - 3) - 1) + 2 and g(x) = (2((2(-3sin(3\u03c0((-3x + 1)/(1x - 2)) + 3) - 3) + 3)/(3(-3sin(3\u03c0((-3x + 1)/(1x - 2)) + 3) - 3) + 3)) - 3)/(-1((2(-3sin(3\u03c0((-3x + 1)/(1x - 2)) + 3) - 3) + 3)/(3(-3sin(3\u03c0((-3x + 1)/(1x - 2)) + 3) - 3) + 3)) + 2) 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": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-1((-2((1(2(-2x + 2) + 1) + 2)/(2(2(-2x + 2) + 1) + 2)) - 2)/(3((1(2(-2x + 2) + 1) + 2)/(2(2(-2x + 2) + 1) + 2)) - 1)) + 1)/(2((-2((1(2(-2x + 2) + 1) + 2)/(2(2(-2x + 2) + 1) + 2)) - 2)/(3((1(2(-2x + 2) + 1) + 2)/(2(2(-2x + 2) + 1) + 2)) - 1)) - 3), g(x) = -4((-3(-3((-2x + 3)/(3x))^2 - 2((-2x + 3)/(3x)) + 3) - 1)/(-2(-3((-2x + 3)/(3x))^2 - 2((-2x + 3)/(3x)) + 3) - 2)) + 1, x = 0.7, 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": "3.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1(3(-1(-3e^(1(-1|x + 1| - 2)) + 1) - 1))^2 - 1(3(-1(-3e^(1(-1|x + 1| - 2)) + 1) - 1)), g(x) = (-1((3(3cos(2\u03c0(-1|x + 3| + 3) + 2) + 3) + 2)/(-1(3cos(2\u03c0(-1|x + 3| + 3) + 2) + 3) - 3)) - 3)/(2((3(3cos(2\u03c0(-1|x + 3| + 3) + 2) + 3) + 2)/(-1(3cos(2\u03c0(-1|x + 3| + 3) + 2) + 3) - 3)) + 3), x = -0.0, and x = 0.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21.8", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2((2(3(5(-3cos(1\u03c0x - 2) - 2)) - 4) + 1)/(2(3(5(-3cos(1\u03c0x - 2) - 2)) - 4))) - 1 and g(x) = -1sin(1\u03c0(4(5((2x - 2)/(-1x - 1)) + 1)^2 - 4(5((2x - 2)/(-1x - 1)) + 1) + 5) + 2) + 2 between the vertical lines x = 1.9 and x = 3.4. 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) = 5(-3sin(1\u03c0(1(-1(2|x| - 2)^2 - 5(2|x| - 2) - 1)^2 + 1(-1(2|x| - 2)^2 - 5(2|x| - 2) - 1) - 4) - 3)) - 4, g(x) = -1(2|(-3(1|x - 1| - 2) + 4) - 1|) + 1, x = 0.6, and x = 0.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (3(2|(2|(2|(2|x + 3| - 2) - 3| - 1) - 2| - 2) + 2| - 3) - 3)/(-3(2|(2|(2|(2|x + 3| - 2) - 3| - 1) - 2| - 2) + 2| - 3) - 3), g(x) = -3|((-3(-2e^(-1((1x)/(1x + 1))) - 2) + 1)/(2(-2e^(-1((1x)/(1x + 1))) - 2) + 3)) + 2| + 1, x = -0.9, and x = -0.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -4((-1((-1(3(3x + 4)^2 - 5(3x + 4) - 4))/(-1(3(3x + 4)^2 - 5(3x + 4) - 4) + 3)) + 2)/(2((-1(3(3x + 4)^2 - 5(3x + 4) - 4))/(-1(3(3x + 4)^2 - 5(3x + 4) - 4) + 3)) + 1))^2 + 4 and g(x) = (-1(3|(-4(1x^2 + 5x + 3)^2 - 1(1x^2 + 5x + 3) - 5) + 2| + 3) + 1)/(3(3|(-4(1x^2 + 5x + 3)^2 - 1(1x^2 + 5x + 3) - 5) + 2| + 3) - 1) from x = -1.5 to x = -0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-1(-5((1(-1(3cos(2\u03c0x - 2) - 2) - 5) + 2)/(2(-1(3cos(2\u03c0x - 2) - 2) - 5)))^2) + 3)/(-3(-5((1(-1(3cos(2\u03c0x - 2) - 2) - 5) + 2)/(2(-1(3cos(2\u03c0x - 2) - 2) - 5)))^2) - 3) and g(x) = -2(-1(2sin(1\u03c0((2x - 3)/(3x)) + 2))^2 + 4(2sin(1\u03c0((2x - 3)/(3x)) + 2)) + 1) - 4 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": "1.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-2(3|((2(-3|(-2|x - 3| + 2) + 3| - 1) + 1)/(3(-3|(-2|x - 3| + 2) + 3| - 1) - 1)) + 2|) - 2)/(-2(3|((2(-3|(-2|x - 3| + 2) + 3| - 1) + 1)/(3(-3|(-2|x - 3| + 2) + 3| - 1) - 1)) + 2|) - 3) and g(x) = -1(-3|(1(1cos(3\u03c0x + 1) - 1) - 3) + 1| + 3) - 3 between the vertical lines x = -4.9 and 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(-2(-5(-1|((1x - 2)/(-2x - 2)) - 1| + 3) + 1) - 3)^2 + 2(-2(-5(-1|((1x - 2)/(-2x - 2)) - 1| + 3) + 1) - 3) + 2 and g(x) = 5(-3|(-1(-3|x - 3| - 3) - 3) - 3| - 3)^2 + 4(-3|(-1(-3|x - 3| - 3) - 3) - 3| - 3) + 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": "6.7", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1|(-3|(-2((2(2sin(1\u03c0x - 2) - 2) + 2)/(-3(2sin(1\u03c0x - 2) - 2) - 2))^2 + 2((2(2sin(1\u03c0x - 2) - 2) + 2)/(-3(2sin(1\u03c0x - 2) - 2) - 2)) + 3) + 3|) + 1| - 3 and g(x) = (3((-1(1(1|x - 3| - 1) - 5) - 2)/(3(1(1|x - 3| - 1) - 5) + 3)) - 3)/(-3((-1(1(1|x - 3| - 1) - 5) - 2)/(3(1(1|x - 3| - 1) - 5) + 3)) + 2) between the vertical lines x = 3.3 and x = 3.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3cos(1\u03c0((2(-2|(-4(4x^2 - 5)^2 - 5(4x^2 - 5) - 3) + 2| - 2) - 2)/(2(-2|(-4(4x^2 - 5)^2 - 5(4x^2 - 5) - 3) + 2| - 2) + 3)) - 2) + 1, g(x) = -1(-3(-2e^(-1(-1x^2 - 3x + 2)) - 2) - 4)^2 + 4(-3(-2e^(-1(-1x^2 - 3x + 2)) - 2) - 4) - 4, x = -1.0, and x = -0.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (3(-1(2sin(2\u03c0(-5(1x + 2) - 4) - 3) - 3) + 5) + 1)/(1(-1(2sin(2\u03c0(-5(1x + 2) - 4) - 3) - 3) + 5) - 2), g(x) = 2((1(2|(-1cos(3\u03c0x + 2) - 3) + 3| + 1) - 2)/(2(2|(-1cos(3\u03c0x + 2) - 3) + 3| + 1) - 1))^2 - 2((1(2|(-1cos(3\u03c0x + 2) - 3) + 3| + 1) - 2)/(2(2|(-1cos(3\u03c0x + 2) - 3) + 3| + 1) - 1)) + 1, x = 1.0, and x = 1.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-2((2(1(-1e^(1(-3|x - 2| + 2)) - 1)^2 + 2(-1e^(1(-3|x - 2| + 2)) - 1) + 4) - 3)/(3(1(-1e^(1(-3|x - 2| + 2)) - 1)^2 + 2(-1e^(1(-3|x - 2| + 2)) - 1) + 4))) - 2)/(1((2(1(-1e^(1(-3|x - 2| + 2)) - 1)^2 + 2(-1e^(1(-3|x - 2| + 2)) - 1) + 4) - 3)/(3(1(-1e^(1(-3|x - 2| + 2)) - 1)^2 + 2(-1e^(1(-3|x - 2| + 2)) - 1) + 4))) + 3) and g(x) = (-2(-2|((-1(-5x^2 + 4) - 1)/(3(-5x^2 + 4) - 2)) - 2| + 2) - 1)/(3(-2|((-1(-5x^2 + 4) - 1)/(3(-5x^2 + 4) - 2)) - 2| + 2) + 2) 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-3(-3cos(3\u03c0(3|(2(3x + 3) + 3)| + 3) - 2) + 3) + 2)/(2(-3cos(3\u03c0(3|(2(3x + 3) + 3)| + 3) - 2) + 3) - 1) and g(x) = 3(3|(3e^(-2((-1x - 3)/(-2x))))| + 3) + 5 from x = 2.1 to x = 2.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.8", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1(1(1|(1sin(2\u03c0(-2|x + 1| + 3) + 1) - 3) - 3| - 3) - 5)^2 + 5 and g(x) = (2(1|(-3e^(1(-1x + 2)) - 1) - 3|) - 3)/(3(1|(-3e^(1(-1x + 2)) - 1) - 3|)) between the vertical lines x = -2.6 and x = -2.3. 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": "Determine the area of the region enclosed by the graphs of f(x) = (2(-3sin(3\u03c0(-1|(-1(-2x - 1)^2 - 2(-2x - 1) + 3) - 3| - 2) + 2) - 2) + 1)/(1(-3sin(3\u03c0(-1|(-1(-2x - 1)^2 - 2(-2x - 1) + 3) - 3| - 2) + 2) - 2) + 2) and g(x) = -1sin(2\u03c0(-5(-1|(3|x + 3| + 1) - 2| - 2) + 5) - 1) - 1 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": "0.7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (2(-4(-1|(-5(-1x^2 - 1x) - 2) - 1| + 3) + 1) + 2)/(3(-4(-1|(-5(-1x^2 - 1x) - 2) - 1| + 3) + 1) + 2) and g(x) = 2(1|((-2(5x + 5) + 1)/(3(5x + 5) - 1)) - 1| + 3)^2 + 1(1|((-2(5x + 5) + 1)/(3(5x + 5) - 1)) - 1| + 3) - 5 from x = -1.1 to x = 0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "77.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1e^(1(-1(1(-3|(3x^2 + 5x + 1)| + 1) - 3)^2 + 4(1(-3|(3x^2 + 5x + 1)| + 1) - 3) + 3)) + 2 and g(x) = -3sin(2\u03c0(2|((1(3x + 4) + 1)/(-1(3x + 4) + 2)) - 2| + 3) - 3) + 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1(3|((-1(4(-4x^2 - 2x + 3)^2 + 4(-4x^2 - 2x + 3) - 3) - 1)/(2(4(-4x^2 - 2x + 3)^2 + 4(-4x^2 - 2x + 3) - 3) - 1)) - 3| + 3) + 5 and g(x) = 1(4((2(1x - 2) - 3)/(-3(1x - 2) + 1))^2 - 3) - 4 between the vertical lines x = -1.1 and x = 0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10.4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2sin(2\u03c0(2|(5((-2(1|x - 1|) - 2)/(3(1|x - 1|) + 2)) - 1)|) + 1) - 2 and g(x) = 3sin(2\u03c0(2(-2(-2|x| - 3)^2 + 3(-2|x| - 3) + 2)^2 - 1(-2(-2|x| - 3)^2 + 3(-2|x| - 3) + 2) + 1) - 2) + 1 from x = 0.3 to x = 0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1|((1((-1(2|((2x + 2)/(3x - 2)) - 1| - 2) + 2)/(1(2|((2x + 2)/(3x - 2)) - 1| - 2) + 2)) + 2)/(1((-1(2|((2x + 2)/(3x - 2)) - 1| - 2) + 2)/(1(2|((2x + 2)/(3x - 2)) - 1| - 2) + 2)))) - 2| + 2 and g(x) = 4(1cos(2\u03c0(3|((3x + 1)/(-1x - 2)) + 3| - 1) + 2) - 1) - 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": "28.6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-1(2cos(2\u03c0((1(-2(-2|x + 2| + 1) + 2) - 1)/(-3(-2(-2|x + 2| + 1) + 2) + 1)) - 3) + 1))/(-3(2cos(2\u03c0((1(-2(-2|x + 2| + 1) + 2) - 1)/(-3(-2(-2|x + 2| + 1) + 2) + 1)) - 3) + 1) - 1) and g(x) = 2|(-1(-2|((-3x + 3)/(-3x - 1)) - 3| + 1)^2 - 5(-2|((-3x + 3)/(-3x - 1)) - 3| + 1) + 1) + 1| 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (3(-3(3sin(2\u03c0(-4((-3x - 1)/(-1x + 2))^2 - 5((-3x - 1)/(-1x + 2)) - 3) + 2) - 1)^2 - 2(3sin(2\u03c0(-4((-3x - 1)/(-1x + 2))^2 - 5((-3x - 1)/(-1x + 2)) - 3) + 2) - 1) + 2) + 1)/(-2(-3(3sin(2\u03c0(-4((-3x - 1)/(-1x + 2))^2 - 5((-3x - 1)/(-1x + 2)) - 3) + 2) - 1)^2 - 2(3sin(2\u03c0(-4((-3x - 1)/(-1x + 2))^2 - 5((-3x - 1)/(-1x + 2)) - 3) + 2) - 1) + 2)) and g(x) = (2((-2(-5(-1x + 2)^2 - 4(-1x + 2) - 3) + 2)/(-1(-5(-1x + 2)^2 - 4(-1x + 2) - 3))) + 2)/(-2((-2(-5(-1x + 2)^2 - 4(-1x + 2) - 3) + 2)/(-1(-5(-1x + 2)^2 - 4(-1x + 2) - 3))) + 1) 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -4(3(1|((-1(-2sin(2\u03c0x + 2) - 1) - 1)/(-1(-2sin(2\u03c0x + 2) - 1) + 2)) + 3| + 1)^2 + 2(1|((-1(-2sin(2\u03c0x + 2) - 1) - 1)/(-1(-2sin(2\u03c0x + 2) - 1) + 2)) + 3| + 1) + 3) - 2, g(x) = -2e^(1(-2((1(-2|x - 3| - 2) + 1)/(-2(-2|x - 3| - 2) + 3)) + 4)) - 1, 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": "19.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3|(-2e^(-1((-1(3|(-1x^2 - 1x - 5) + 1| + 2))/(-1(3|(-1x^2 - 1x - 5) + 1| + 2) - 1))) - 1) + 2| and g(x) = 2cos(3\u03c0(-5((-3(4x + 4) - 1)/(2(4x + 4) - 3))^2 + 2((-3(4x + 4) - 1)/(2(4x + 4) - 3)) - 4) + 1) from x = 0.0 to x = 0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1|(-2e^(1(-3(2(1x)^2 + 4(1x) - 1)^2 + 2(2(1x)^2 + 4(1x) - 1))) - 2) + 2| and g(x) = -3(2|(4(-1x^2 - 1x - 1) + 2) + 3| - 2) + 1 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": "2.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2|((3(-3(1e^(2(4x + 5))) + 5) + 2)/(-2(-3(1e^(2(4x + 5))) + 5) - 3))| - 1, g(x) = 3|(2|(1(5x^2 - 4x + 1) - 4) - 3| - 2) + 3| - 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2cos(2\u03c0(1|((2(-3(-1x^2 + 2x + 2)^2 + 4(-1x^2 + 2x + 2) + 5) - 2)/(-1(-3(-1x^2 + 2x + 2)^2 + 4(-1x^2 + 2x + 2) + 5))) + 2|) + 1) - 3, g(x) = 1sin(3\u03c0(-4((-2(-2|x - 3| - 1))/(-3(-2|x - 3| - 1) - 3))^2 + 5((-2(-2|x - 3| - 1))/(-3(-2|x - 3| - 1) - 3)) - 4) - 3) - 2, 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": "1.4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3|((-3(-4(-2(-1x + 4) + 2) + 4) - 3)/(-1(-4(-2(-1x + 4) + 2) + 4) - 1)) + 1| - 3 and g(x) = (3((1(1(3|x| - 1)^2 - 4(3|x| - 1) - 5) - 1)/(1(1(3|x| - 1)^2 - 4(3|x| - 1) - 5) - 2)) - 1)/(1((1(1(3|x| - 1)^2 - 4(3|x| - 1) - 5) - 1)/(1(1(3|x| - 1)^2 - 4(3|x| - 1) - 5) - 2)) + 2) from x = -2.1 to x = 2.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "65.5", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 5((3(2sin(1\u03c0(2((2x - 2)/(-1x + 3))^2 + 4((2x - 2)/(-1x + 3)) + 4) - 1) - 2) - 2)/(2(2sin(1\u03c0(2((2x - 2)/(-1x + 3))^2 + 4((2x - 2)/(-1x + 3)) + 4) - 1) - 2) - 1)) - 1, g(x) = 2|(1(-2|(2x + 3) + 1| + 2) - 2)| + 3, x = -2.5, and x = -1.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.8", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3|((3(2sin(3\u03c0(5((2x + 1)/(3x)) + 3) - 2) + 1) - 2)/(-3(2sin(3\u03c0(5((2x + 1)/(3x)) + 3) - 2) + 1) + 1)) - 3| and g(x) = -1(1(4(-5x - 5)^2 + 5(-5x - 5) - 5)^2 - 3(4(-5x - 5)^2 + 5(-5x - 5) - 5) + 5)^2 + 4(1(4(-5x - 5)^2 + 5(-5x - 5) - 5)^2 - 3(4(-5x - 5)^2 + 5(-5x - 5) - 5) + 5) - 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": "22.8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-2(3(-1(-5(1x^2 + 3x + 4)^2 - 3(1x^2 + 3x + 4)) + 3)^2 + 4(-1(-5(1x^2 + 3x + 4)^2 - 3(1x^2 + 3x + 4)) + 3) + 2))/(2(3(-1(-5(1x^2 + 3x + 4)^2 - 3(1x^2 + 3x + 4)) + 3)^2 + 4(-1(-5(1x^2 + 3x + 4)^2 - 3(1x^2 + 3x + 4)) + 3) + 2) + 1) and g(x) = 2|(3|(-5(-1x^2 - 4x + 4)^2 - 3(-1x^2 - 4x + 4) - 1) + 3|) - 3| - 3 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -4(1|(3sin(1\u03c0(-1(4x - 5) - 2) - 3) + 2) + 2| - 1) + 3 and g(x) = (3(-2(-1(-1x^2 + 3x) - 3)^2 - 4(-1(-1x^2 + 3x) - 3) - 2))/(3(-2(-1(-1x^2 + 3x) - 3)^2 - 4(-1(-1x^2 + 3x) - 3) - 2) + 3) 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": "4.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2|((2((-2((-3((3x)/(1x - 2)) - 2)/(-1((3x)/(1x - 2)) + 3)) + 1)/(-3((-3((3x)/(1x - 2)) - 2)/(-1((3x)/(1x - 2)) + 3)) + 1)) - 2)/(2((-2((-3((3x)/(1x - 2)) - 2)/(-1((3x)/(1x - 2)) + 3)) + 1)/(-3((-3((3x)/(1x - 2)) - 2)/(-1((3x)/(1x - 2)) + 3)) + 1)) + 3)) - 2| - 3, g(x) = (-3(2|((3(3x + 3) + 3)/(-2(3x + 3) + 3)) + 3|) + 2)/(2(2|((3(3x + 3) + 3)/(-2(3x + 3) + 3)) + 3|)), 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": "4.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3|(-1(-3((3((-3x + 1)/(3x + 2)) + 2)/(-1((-3x + 1)/(3x + 2)) + 2))^2 - 1((3((-3x + 1)/(3x + 2)) + 2)/(-1((-3x + 1)/(3x + 2)) + 2)) + 1) + 5) + 3| - 3, g(x) = (3(1|(-3|(-3sin(3\u03c0x - 3)) - 3|) + 2| + 1) - 1)/(-1(1|(-3|(-3sin(3\u03c0x - 3)) - 3|) + 2| + 1) + 2), x = -3.9, 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": "6.6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1(-2((-2((-1(-3x^2 - 4x + 3) - 3)/(1(-3x^2 - 4x + 3) - 2)))/(-3((-1(-3x^2 - 4x + 3) - 3)/(1(-3x^2 - 4x + 3) - 2))))^2 - 1((-2((-1(-3x^2 - 4x + 3) - 3)/(1(-3x^2 - 4x + 3) - 2)))/(-3((-1(-3x^2 - 4x + 3) - 3)/(1(-3x^2 - 4x + 3) - 2)))) - 5) + 1 and g(x) = -4(-5(-1(3|x + 3|) - 1) - 5) + 2 from x = -3.1 to x = -2.9. 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(-4(2|(1|x + 2|) - 1| - 1)^2 - 1(2|(1|x + 2|) - 1| - 1)) - 1)/(3(-4(2|(1|x + 2|) - 1| - 1)^2 - 1(2|(1|x + 2|) - 1| - 1)) + 2)) - 1)/(-1((-1(-4(2|(1|x + 2|) - 1| - 1)^2 - 1(2|(1|x + 2|) - 1| - 1)) - 1)/(3(-4(2|(1|x + 2|) - 1| - 1)^2 - 1(2|(1|x + 2|) - 1| - 1)) + 2)) - 1), g(x) = 3|((-2((-2(-2x + 2))/(1(-2x + 2) - 2)) + 3)/(-2((-2(-2x + 2))/(1(-2x + 2) - 2)) - 2)) + 1| + 1, 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": "8.4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-3((-3((-2(3|(5x + 5) - 3| + 3))/(1(3|(5x + 5) - 3| + 3))) - 2)/(1((-2(3|(5x + 5) - 3| + 3))/(1(3|(5x + 5) - 3| + 3))) - 2)) - 3)/(3((-3((-2(3|(5x + 5) - 3| + 3))/(1(3|(5x + 5) - 3| + 3))) - 2)/(1((-2(3|(5x + 5) - 3| + 3))/(1(3|(5x + 5) - 3| + 3))) - 2))) and g(x) = (-2(2(2|(1x^2 - 1x)| - 1)^2 - 5(2|(1x^2 - 1x)| - 1)) + 3)/(3(2(2|(1x^2 - 1x)| - 1)^2 - 5(2|(1x^2 - 1x)| - 1))) from x = -1.0 to x = -0.3. 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(3|(3(3sin(1\u03c0((3x - 2)/(2x)) + 3))^2 + 1(3sin(1\u03c0((3x - 2)/(2x)) + 3)) + 5) - 1| + 2) + 2)/(2(3|(3(3sin(1\u03c0((3x - 2)/(2x)) + 3))^2 + 1(3sin(1\u03c0((3x - 2)/(2x)) + 3)) + 5) - 1| + 2) - 1), g(x) = 3cos(2\u03c0(4(1(-1x^2 + 3x + 3)^2 - 2(-1x^2 + 3x + 3) + 4) + 3) - 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1(3(4(1e^(2(-4x^2 - 5x - 3)) - 1)^2 + 5(1e^(2(-4x^2 - 5x - 3)) - 1) - 2) - 2) + 4, g(x) = (-2((3(2sin(2\u03c0(-3x + 4) + 1) - 1) + 1)/(2(2sin(2\u03c0(-3x + 4) + 1) - 1))) + 3)/(2((3(2sin(2\u03c0(-3x + 4) + 1) - 1) + 1)/(2(2sin(2\u03c0(-3x + 4) + 1) - 1))) + 2), x = -4.1, 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": "25.6", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -4(-3(-1(5(-1x - 3)^2 - 3(-1x - 3) - 2) - 3)^2 + 1(-1(5(-1x - 3)^2 - 3(-1x - 3) - 2) - 3) - 1) - 5 and g(x) = (-3(-1cos(2\u03c0(3|(-5x^2 + 1)| + 3))) + 2)/(3(-1cos(2\u03c0(3|(-5x^2 + 1)| + 3)))) between the vertical lines x = -3.5 and 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": "Find the area of the region bounded by the curves f(x) = 3(-3cos(1\u03c0(2(-3(5x^2 + 3x - 4))^2 - 5(-3(5x^2 + 3x - 4)) + 1) + 2) + 1) - 3, g(x) = -3|(1cos(1\u03c0(2|(2x - 5) + 1| + 1) + 3) + 3) - 3| + 2, x = 2.8, and x = 2.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2sin(3\u03c0(-5(2(-1(-4x^2 - 4x)^2 + 2(-4x^2 - 4x) + 4) + 5)^2 - 1(2(-1(-4x^2 - 4x)^2 + 2(-4x^2 - 4x) + 4) + 5) + 4) + 2) + 1 and g(x) = -3(3sin(2\u03c0(-2(2|x + 3| - 1)^2 + 4(2|x + 3| - 1)) - 2) + 3)^2 + 3(3sin(2\u03c0(-2(2|x + 3| - 1)^2 + 4(2|x + 3| - 1)) - 2) + 3) - 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": "3.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-3(-1|(-3|(-2|(-3x + 4) - 3| - 1) + 3| - 3) - 3| + 1) - 3)/(3(-1|(-3|(-2|(-3x + 4) - 3| - 1) + 3| - 3) - 3| + 1)) and g(x) = -3(2cos(1\u03c0((-1(3|x - 1|) + 2)/(2(3|x - 1|) + 2)))) - 4 from x = 0.9 to x = 1.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1|(-4((2(-3|(4x + 3) + 1| + 3) - 2)/(2(-3|(4x + 3) + 1| + 3) + 3))^2 + 3((2(-3|(4x + 3) + 1| + 3) - 2)/(2(-3|(4x + 3) + 1| + 3) + 3))) + 2| + 1, g(x) = -2sin(2\u03c0(3(4(4x^2 - 3x - 3)^2 - 1(4x^2 - 3x - 3) + 1)^2 + 4(4(4x^2 - 3x - 3)^2 - 1(4x^2 - 3x - 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1((-1(-3|(3|(-3|x - 3| - 3) - 1| - 2) - 3| + 3))/(1(-3|(3|(-3|x - 3| - 3) - 1| - 2) - 3| + 3) + 2)) + 1 and g(x) = (-1((-2(-1|(-4x + 4) + 1|) + 1)/(-3(-1|(-4x + 4) + 1|) - 2)) - 3)/(2((-2(-1|(-4x + 4) + 1|) + 1)/(-3(-1|(-4x + 4) + 1|) - 2)) - 1) from x = 1.1 to x = 1.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2(-5((3(3cos(2\u03c0(5x^2 + 2x - 3) - 2) - 1) + 1)/(3(3cos(2\u03c0(5x^2 + 2x - 3) - 2) - 1) + 2)) + 1) and g(x) = 3(-2sin(3\u03c0((1((-3x + 2)/(-3x - 3)) + 1)/(1((-3x + 2)/(-3x - 3)) - 3)) + 3) + 1) - 3 between the vertical lines x = 4.9 and x = 5.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3|((1((3(-1|((-1x + 2)/(3x + 2))| - 1) + 3)/(-1(-1|((-1x + 2)/(3x + 2))| - 1) - 1)) - 2)/(-3((3(-1|((-1x + 2)/(3x + 2))| - 1) + 3)/(-1(-1|((-1x + 2)/(3x + 2))| - 1) - 1)) - 3)) + 2| and g(x) = -1|((1(-2|(2x) + 1| + 1) - 3)/(-2(-2|(2x) + 1| + 1) - 1)) + 2| + 1 between the vertical lines x = -1.0 and x = -0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (1(2|((2(-1|((1x - 1)/(-1x)) + 3| - 3) + 2)/(-1(-1|((1x - 1)/(-1x)) + 3| - 3) + 2))| + 3) + 1)/(3(2|((2(-1|((1x - 1)/(-1x)) + 3| - 3) + 2)/(-1(-1|((1x - 1)/(-1x)) + 3| - 3) + 2))| + 3) - 2), g(x) = (2(-2|(-3(-1|x - 3| + 3) + 3) - 3| + 3) + 3)/(3(-2|(-3(-1|x - 3| + 3) + 3) - 3| + 3) - 2), x = 1.5, 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2sin(1\u03c0((-3(-4(-2|(4x - 1) - 1|)^2 - 5) - 3)/(-2(-4(-2|(4x - 1) - 1|)^2 - 5) + 3)) + 1) - 1, g(x) = -1((3(-1cos(1\u03c0(-5x + 4) - 3)))/(3(-1cos(1\u03c0(-5x + 4) - 3)) + 2)) + 4, x = 3.0, and x = 3.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3(-3|(1(-5(3e^(-2x) - 3) + 4) + 2) - 2| + 3) - 1 and g(x) = -1|(-3(1sin(2\u03c0(-1x^2 + 2x + 5)))^2 + 4(1sin(2\u03c0(-1x^2 + 2x + 5))) + 2) - 2| between the vertical lines x = -0.1 and x = 0.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2sin(3\u03c0(-1(-5(-2(1x^2 + 3x + 2) + 2) - 4)^2 - 1(-5(-2(1x^2 + 3x + 2) + 2) - 4) + 4)), g(x) = -2((-1(2e^(-1(2x^2 + 3x - 4)) + 2) + 1)/(1(2e^(-1(2x^2 + 3x - 4)) + 2) - 2))^2 + 4((-1(2e^(-1(2x^2 + 3x - 4)) + 2) + 1)/(1(2e^(-1(2x^2 + 3x - 4)) + 2) - 2)) + 5, x = -0.4, and x = -0.30000000000000004. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1|(-2|(4(2|(-5x^2 + 2x) + 1| - 1)^2 + 1(2|(-5x^2 + 2x) + 1| - 1) + 5) - 3| + 3) + 2| - 3 and g(x) = 1(-1(-1|(-1|x + 2| + 3) - 2| - 3)^2 - 2(-1|(-1|x + 2| + 3) - 2| - 3) + 1)^2 - 4 between the vertical lines x = -0.5 and x = 1.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "119.7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-1((1(1(1(-3x - 3) + 5) + 2) + 1)/(-2(1(1(-3x - 3) + 5) + 2))) - 1)/(-2((1(1(1(-3x - 3) + 5) + 2) + 1)/(-2(1(1(-3x - 3) + 5) + 2))) + 3) and g(x) = 1(1|(2|(-1x^2 + 3x + 5) + 3| + 1) - 2|) - 4 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": "27.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2e^(2((-1(3|(3(5x + 1) + 2) + 1|) - 3)/(-2(3|(3(5x + 1) + 2) + 1|) - 2))), g(x) = 2|(4(-4(-1|x + 1|)^2 + 3(-1|x + 1|) + 1) - 1) + 3| - 2, x = -0.9, and x = -0.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1e^(1((-2(3(-1(-2x - 4)^2 - 1(-2x - 4) + 3) + 1))/(-2(3(-1(-2x - 4)^2 - 1(-2x - 4) + 3) + 1) - 2))) - 1, g(x) = (1(-1|(2(1x)^2 - 5(1x) - 5)| - 2) + 2)/(-1(-1|(2(1x)^2 - 5(1x) - 5)| - 2) - 1), x = -2.7, 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": "4.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -3|(2(5((-3(2x^2 - 4x + 5) - 3)/(-2(2x^2 - 4x + 5) + 3))) + 5) + 1| + 1, g(x) = (-1(-1(-2(3e^(2x) - 1)^2 + 5(3e^(2x) - 1) + 2) + 2) - 3)/(-1(-1(-2(3e^(2x) - 1)^2 + 5(3e^(2x) - 1) + 2) + 2)), x = -0.6, and x = 0.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "63.7", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-2((2((2((2(-5x^2 - 1) - 2)/(2(-5x^2 - 1) - 3)) - 2)/(-2((2(-5x^2 - 1) - 2)/(2(-5x^2 - 1) - 3)) - 2)) + 3)/(1((2((2(-5x^2 - 1) - 2)/(2(-5x^2 - 1) - 3)) - 2)/(-2((2(-5x^2 - 1) - 2)/(2(-5x^2 - 1) - 3)) - 2)) + 1)) - 2)/(-2((2((2((2(-5x^2 - 1) - 2)/(2(-5x^2 - 1) - 3)) - 2)/(-2((2(-5x^2 - 1) - 2)/(2(-5x^2 - 1) - 3)) - 2)) + 3)/(1((2((2(-5x^2 - 1) - 2)/(2(-5x^2 - 1) - 3)) - 2)/(-2((2(-5x^2 - 1) - 2)/(2(-5x^2 - 1) - 3)) - 2)) + 1))), g(x) = (1(1((1(3cos(1\u03c0x - 2) + 1) - 2)/(-1(3cos(1\u03c0x - 2) + 1)))^2 + 5((1(3cos(1\u03c0x - 2) + 1) - 2)/(-1(3cos(1\u03c0x - 2) + 1))) - 1) + 1)/(-1(1((1(3cos(1\u03c0x - 2) + 1) - 2)/(-1(3cos(1\u03c0x - 2) + 1)))^2 + 5((1(3cos(1\u03c0x - 2) + 1) - 2)/(-1(3cos(1\u03c0x - 2) + 1))) - 1) - 2), x = -1.0, 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": "2.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-1((1(-4((2(-3x - 3))/(3(-3x - 3)))^2 + 1((2(-3x - 3))/(3(-3x - 3))) - 1) - 1)/(-2(-4((2(-3x - 3))/(3(-3x - 3)))^2 + 1((2(-3x - 3))/(3(-3x - 3))) - 1) + 3)) - 3)/(-1((1(-4((2(-3x - 3))/(3(-3x - 3)))^2 + 1((2(-3x - 3))/(3(-3x - 3))) - 1) - 1)/(-2(-4((2(-3x - 3))/(3(-3x - 3)))^2 + 1((2(-3x - 3))/(3(-3x - 3))) - 1) + 3)) - 1) and g(x) = 3(1(-2|(-5x^2) - 1| - 1) + 3)^2 + 4 between the vertical lines x = -0.2 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(3(-1|(-1sin(3\u03c0x + 1) + 1) - 3| + 3)^2 - 2)^2 - 4(3(-1|(-1sin(3\u03c0x + 1) + 1) - 3| + 3)^2 - 2) - 4) + 3)/(3(4(3(-1|(-1sin(3\u03c0x + 1) + 1) - 3| + 3)^2 - 2)^2 - 4(3(-1|(-1sin(3\u03c0x + 1) + 1) - 3| + 3)^2 - 2) - 4) + 3) and g(x) = -3sin(3\u03c0((3(-3(-3x - 4) - 4) + 3)/(3(-3(-3x - 4) - 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 4((-3(1|(1(-5x + 3) + 1) - 1| + 2) - 1)/(3(1|(1(-5x + 3) + 1) - 1| + 2) - 2)) - 2, g(x) = (-1((1((1(-2x^2 + 4x - 2) + 3)/(1(-2x^2 + 4x - 2))) + 2)/(-1((1(-2x^2 + 4x - 2) + 3)/(1(-2x^2 + 4x - 2))))) + 2)/(1((1((1(-2x^2 + 4x - 2) + 3)/(1(-2x^2 + 4x - 2))) + 2)/(-1((1(-2x^2 + 4x - 2) + 3)/(1(-2x^2 + 4x - 2))))) + 3), x = -1.2, 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": "24.7", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1|(-5(2|((-2(-2x^2 - 3x))/(-2(-2x^2 - 3x) + 3)) - 1| + 2) + 2)| + 1, g(x) = (3(-1cos(2\u03c0(1|(-5x + 4) - 2|) - 2) - 1) - 3)/(-2(-1cos(2\u03c0(1|(-5x + 4) - 2|) - 2) - 1) - 3), 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": "4.7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1|(1e^(-1(-2|(-3(3x^2 + 3x - 3)^2 - 3(3x^2 + 3x - 3) + 2) - 2| - 1)) - 3) - 1| and g(x) = -2(-5((2(-1x + 3) + 2)/(2(-1x + 3))) + 5)^2 + 2(-5((2(-1x + 3) + 2)/(2(-1x + 3))) + 5) + 5 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": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3|((2(4(-4(-2x^2 + 1x + 2)^2 + 4(-2x^2 + 1x + 2) + 4) - 1))/(2(4(-4(-2x^2 + 1x + 2)^2 + 4(-2x^2 + 1x + 2) + 4) - 1) - 1)) + 3| - 3, g(x) = (1(2(2sin(3\u03c0(-3x - 2) - 1) + 1) - 5) - 2)/(-1(2(2sin(3\u03c0(-3x - 2) - 1) + 1) - 5) - 3), 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": "1.5", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1(2|(4((-1((3x - 1)/(-2x + 3)) + 3)/(2((3x - 1)/(-2x + 3)) - 1)) - 4) + 2| + 3)^2 - 3(2|(4((-1((3x - 1)/(-2x + 3)) + 3)/(2((3x - 1)/(-2x + 3)) - 1)) - 4) + 2| + 3), g(x) = (-3(-2sin(2\u03c0(1(-2x + 2)^2 - 5(-2x + 2) + 5) + 1)) - 2)/(3(-2sin(2\u03c0(1(-2x + 2)^2 - 5(-2x + 2) + 5) + 1)) - 2), x = 1.0, 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": "18.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-1((-1(-2sin(2\u03c0(-2(-2x + 4)^2 - 1(-2x + 4) + 3) - 1)) + 1)/(-3(-2sin(2\u03c0(-2(-2x + 4)^2 - 1(-2x + 4) + 3) - 1)) + 1)))/(-1((-1(-2sin(2\u03c0(-2(-2x + 4)^2 - 1(-2x + 4) + 3) - 1)) + 1)/(-3(-2sin(2\u03c0(-2(-2x + 4)^2 - 1(-2x + 4) + 3) - 1)) + 1))), g(x) = -1(-1cos(1\u03c0(4(1x^2 - 1x + 3) + 1) - 2) - 2)^2 + 1(-1cos(1\u03c0(4(1x^2 - 1x + 3) + 1) - 2) - 2) + 4, x = -1.8, and x = -1.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1((3(-2|(-3|(-1x + 2) + 1| + 2) + 1| + 1) + 1)/(1(-2|(-3|(-1x + 2) + 1| + 2) + 1| + 1) + 1)) + 2 and g(x) = 3e^(2(-4((3((3x)/(1x)) - 2)/(3((3x)/(1x)) + 1)) + 3)) - 1 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1((-2(-1sin(1\u03c0(-1(-2x - 2) + 4) + 1)) - 2)/(3(-1sin(1\u03c0(-1(-2x - 2) + 4) + 1)) - 2))^2 - 1((-2(-1sin(1\u03c0(-1(-2x - 2) + 4) + 1)) - 2)/(3(-1sin(1\u03c0(-1(-2x - 2) + 4) + 1)) - 2)) - 5 and g(x) = -2(-1|(5((-2x - 2)/(-2x)) + 3) - 2| + 2)^2 + 3 from x = -4.2 to x = -3.6. 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) = -1(2(1(-3e^(1(-1|x - 1| + 1)) - 3) + 1)^2 - 1(1(-3e^(1(-1|x - 1| + 1)) - 3) + 1) + 1) - 3, g(x) = -1(3cos(3\u03c0(2(-1|x| - 1)^2 - 5(-1|x| - 1) - 1)) - 3)^2 - 3(3cos(3\u03c0(2(-1|x| - 1)^2 - 5(-1|x| - 1) - 1)) - 3) + 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": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -3(1|(-2(3|(2x + 4) - 2|)^2 - 4(3|(2x + 4) - 2|) - 5) + 3| + 2) + 2, g(x) = -3(-3sin(3\u03c0(3(-1|x + 1|) - 1) - 3) - 2)^2 - 3(-3sin(3\u03c0(3(-1|x + 1|) - 1) - 3) - 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": "1.9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 5((3(-2|(-1(-2x^2 - 1x + 2) + 4) - 3| + 2) + 3)/(-2(-2|(-1(-2x^2 - 1x + 2) + 4) - 3| + 2) - 3)) + 3 and g(x) = (3(1|(-1sin(1\u03c0(-1|x + 1|) + 3) - 2) - 2| - 3))/(2(1|(-1sin(1\u03c0(-1|x + 1|) + 3) - 2) - 2| - 3) - 1) 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": "11.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1sin(3\u03c0(1(-2((-1(3x^2 + 5x + 2) - 2)/(-3(3x^2 + 5x + 2) + 1)) - 3)^2 + 4(-2((-1(3x^2 + 5x + 2) - 2)/(-3(3x^2 + 5x + 2) + 1)) - 3) - 1)) - 1, g(x) = 1sin(1\u03c0(5(4(2|x + 2| - 3)^2 + 2(2|x + 2| - 3) + 1)) + 2) - 1, x = 1.8, and x = 1.9000000000000001. 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((-3((1(-5(-1|x - 3| - 1) + 3) + 1)/(1(-5(-1|x - 3| - 1) + 3))) - 2)/(3((1(-5(-1|x - 3| - 1) + 3) + 1)/(1(-5(-1|x - 3| - 1) + 3))))) - 4 and g(x) = -1|(-3sin(3\u03c0((-2((1x + 2)/(-1x + 2)) + 1)/(3((1x + 2)/(-1x + 2)))) + 2) - 1) + 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-2((2(2(1e^(2(3x + 3)) + 2) - 5) - 2)/(2(2(1e^(2(3x + 3)) + 2) - 5) + 2)) - 3)/(2((2(2(1e^(2(3x + 3)) + 2) - 5) - 2)/(2(2(1e^(2(3x + 3)) + 2) - 5) + 2)) - 1) and g(x) = 5(-3sin(2\u03c0(-1(3|x - 3| + 1) - 4) + 3) + 1) + 2 between the vertical lines x = -0.0 and x = 0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.9", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (1((-1((-3(-3e^(2(1|x + 3| + 1)) + 1))/(-1(-3e^(2(1|x + 3| + 1)) + 1) - 1)) + 2)/(-2((-3(-3e^(2(1|x + 3| + 1)) + 1))/(-1(-3e^(2(1|x + 3| + 1)) + 1) - 1)) + 3)) + 2)/(-2((-1((-3(-3e^(2(1|x + 3| + 1)) + 1))/(-1(-3e^(2(1|x + 3| + 1)) + 1) - 1)) + 2)/(-2((-3(-3e^(2(1|x + 3| + 1)) + 1))/(-1(-3e^(2(1|x + 3| + 1)) + 1) - 1)) + 3))) and g(x) = (-3(-2sin(3\u03c0(3|(-3x^2 - 2x - 2)| + 3)) - 1) - 3)/(-1(-2sin(3\u03c0(3|(-3x^2 - 2x - 2)| + 3)) - 1)) 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": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1|(-3|(-1(2sin(3\u03c0(5x - 2)) + 2) + 4) - 3| - 2)| - 3 and g(x) = -5((1(-5((-3x + 1)/(-3x - 3)) - 4) - 1)/(-1(-5((-3x + 1)/(-3x - 3)) - 4) - 1)) from x = 4.0 to x = 4.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2(2(1(3|((-2x)/(-1x - 1)) + 3| - 2) - 1)^2 - 3(1(3|((-2x)/(-1x - 1)) + 3| - 2) - 1) - 3)^2 - 4(2(1(3|((-2x)/(-1x - 1)) + 3| - 2) - 1)^2 - 3(1(3|((-2x)/(-1x - 1)) + 3| - 2) - 1) - 3) - 1 and g(x) = (-2((-1((2((-2x - 3)/(2x - 1)))/(3((-2x - 3)/(2x - 1)))) + 1)/(-3((2((-2x - 3)/(2x - 1)))/(3((-2x - 3)/(2x - 1)))) + 2)) - 1)/(-2((-1((2((-2x - 3)/(2x - 1)))/(3((-2x - 3)/(2x - 1)))) + 1)/(-3((2((-2x - 3)/(2x - 1)))/(3((-2x - 3)/(2x - 1)))) + 2)) + 3) between the vertical lines x = -0.7 and x = -0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "43.8", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2(-3((-1(-3|(4x^2 + 5x - 4) + 1| + 2))/(-1(-3|(4x^2 + 5x - 4) + 1| + 2) + 3))^2 + 4((-1(-3|(4x^2 + 5x - 4) + 1| + 2))/(-1(-3|(4x^2 + 5x - 4) + 1| + 2) + 3)) - 3)^2 + 5(-3((-1(-3|(4x^2 + 5x - 4) + 1| + 2))/(-1(-3|(4x^2 + 5x - 4) + 1| + 2) + 3))^2 + 4((-1(-3|(4x^2 + 5x - 4) + 1| + 2))/(-1(-3|(4x^2 + 5x - 4) + 1| + 2) + 3)) - 3) + 3 and g(x) = -2(2(-3e^(1(-1|x - 2| + 1)))^2 + 4(-3e^(1(-1|x - 2| + 1))) - 2) + 3 between the vertical lines x = -1.6 and x = 0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2(-4(-2(5((1x)/(2x - 1)) + 1) + 5)^2 - 1(-2(5((1x)/(2x - 1)) + 1) + 5) - 4) and g(x) = (3(-4(-3(-3sin(2\u03c0x + 3) - 3) - 5) - 4) + 1)/(-3(-4(-3(-3sin(2\u03c0x + 3) - 3) - 5) - 4)) from x = -0.9 to x = -0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.8", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-2(-2|((2(3(2cos(2\u03c0x + 3) + 1) - 5) + 1)/(-2(3(2cos(2\u03c0x + 3) + 1) - 5) - 1))| + 3) + 2)/(-1(-2|((2(3(2cos(2\u03c0x + 3) + 1) - 5) + 1)/(-2(3(2cos(2\u03c0x + 3) + 1) - 5) - 1))| + 3) + 2), g(x) = -1|(1cos(1\u03c0(-3(2x^2 - 5x + 1)^2 - 5) + 3) + 2) - 3|, x = -3.8, and x = -3.6999999999999997. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2((-3(-1sin(3\u03c0(-2(-4x + 1)^2 - 4(-4x + 1) + 2) + 2) + 2) + 1)/(1(-1sin(3\u03c0(-2(-4x + 1)^2 - 4(-4x + 1) + 2) + 2) + 2) + 3))^2 + 3((-3(-1sin(3\u03c0(-2(-4x + 1)^2 - 4(-4x + 1) + 2) + 2) + 2) + 1)/(1(-1sin(3\u03c0(-2(-4x + 1)^2 - 4(-4x + 1) + 2) + 2) + 2) + 3)) + 4, g(x) = -1|(1e^(1(4(-1|x - 3| - 3))) - 2) + 1|, x = 2.0, and x = 2.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3(2(-1sin(3\u03c0(4(-3x + 4) + 1) - 3) + 3) - 1) + 5 and g(x) = -5(3((1(3x + 5) - 3)/(-2(3x + 5) - 2)) - 5) - 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": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (2((1(-3|(-3|(5x^2 + 1x) - 3| + 1) + 3| - 2) - 3)/(1(-3|(-3|(5x^2 + 1x) - 3| + 1) + 3| - 2))) + 3)/(1((1(-3|(-3|(5x^2 + 1x) - 3| + 1) + 3| - 2) - 3)/(1(-3|(-3|(5x^2 + 1x) - 3| + 1) + 3| - 2))) + 1) and g(x) = 2(-5(5(1e^(-2x) - 2) - 5) + 1)^2 + 4(-5(5(1e^(-2x) - 2) - 5) + 1) + 4 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": "4.4", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2|(4(-2(3cos(3\u03c0((-3x + 1)/(-3x + 2)) + 1) + 2)^2 - 4(3cos(3\u03c0((-3x + 1)/(-3x + 2)) + 1) + 2) + 1) + 3) - 3| + 3, g(x) = 3(1(5(-2e^(-1x) + 2) - 5) + 1) - 5, 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": "17.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1(-1|(-1(-3|(-3x + 2)|) - 5) - 1| - 2)^2 - 4(-1|(-1(-3|(-3x + 2)|) - 5) - 1| - 2) and g(x) = (1((-2(3|(-1x^2 - 3x - 1)| - 1) + 2)/(-1(3|(-1x^2 - 3x - 1)| - 1) + 2)) - 3)/(1((-2(3|(-1x^2 - 3x - 1)| - 1) + 2)/(-1(3|(-1x^2 - 3x - 1)| - 1) + 2)) + 3) between the vertical lines x = -0.9 and x = -0.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-3(1|(3|(-1|(3x - 3) - 1| - 1) + 2| + 1) - 1| - 3) + 3)/(2(1|(3|(-1|(3x - 3) - 1| - 1) + 2| + 1) - 1| - 3) + 3) and g(x) = 4(3(1(3x^2 - 2x - 3)^2 + 2(3x^2 - 2x - 3) - 1))^2 - 4(3(1(3x^2 - 2x - 3)^2 + 2(3x^2 - 2x - 3) - 1)) - 2 from x = -0.8 to x = -0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "50.4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1(-3|(-4((3((-1x + 3)/(1x - 2)) - 2)/(1((-1x + 3)/(1x - 2)) + 1))^2 + 3((3((-1x + 3)/(1x - 2)) - 2)/(1((-1x + 3)/(1x - 2)) + 1)) + 2)| + 1)^2 + 1(-3|(-4((3((-1x + 3)/(1x - 2)) - 2)/(1((-1x + 3)/(1x - 2)) + 1))^2 + 3((3((-1x + 3)/(1x - 2)) - 2)/(1((-1x + 3)/(1x - 2)) + 1)) + 2)| + 1) + 2 and g(x) = 1(-2|((-1(4x^2 + 5x - 3) + 2)/(3(4x^2 + 5x - 3)))| - 2)^2 + 5(-2|((-1(4x^2 + 5x - 3) + 2)/(3(4x^2 + 5x - 3)))| - 2) + 4 from x = 2.4 to x = 2.7. 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) = 1sin(2\u03c0(-2|(-3|(5(-1|x|)^2 + 1(-1|x|) - 3) + 2| + 2)| - 2) + 3) + 2, g(x) = 4(1(1((3x)/(-2x - 1))^2 + 5((3x)/(-2x - 1)) + 2)^2 + 4(1((3x)/(-2x - 1))^2 + 5((3x)/(-2x - 1)) + 2) + 4)^2 + 3(1(1((3x)/(-2x - 1))^2 + 5((3x)/(-2x - 1)) + 2)^2 + 4(1((3x)/(-2x - 1))^2 + 5((3x)/(-2x - 1)) + 2) + 4) + 2, x = 1.1, and x = 1.2000000000000002. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2|((-1(1(1e^(2(-2x^2 + 1x - 2)) + 3)^2 - 5(1e^(2(-2x^2 + 1x - 2)) + 3) - 4) - 1)/(-2(1(1e^(2(-2x^2 + 1x - 2)) + 3)^2 - 5(1e^(2(-2x^2 + 1x - 2)) + 3) - 4) - 1)) - 2| + 1 and g(x) = -5(-4(1((1x - 1)/(2x - 1))^2 + 4((1x - 1)/(2x - 1)) + 1) - 1) + 4 from x = 0.6 to x = 0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3((-1(-2|((2(-1x^2 - 5x + 2) + 2)/(2(-1x^2 - 5x + 2) - 1)) - 1| + 2) - 1)/(-1(-2|((2(-1x^2 - 5x + 2) + 2)/(2(-1x^2 - 5x + 2) - 1)) - 1| + 2) - 2)) + 3 and g(x) = (-3(-3e^(2(-3(3x - 3) + 3)) - 1) - 2)/(-2(-3e^(2(-3(3x - 3) + 3)) - 1) - 1) 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": "4.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 5(1|((-1(1(2x^2 + 3x - 2)) + 1)/(-3(1(2x^2 + 3x - 2)) + 2))|) + 3 and g(x) = 3(-1sin(2\u03c0(2(-4x^2 + 4x + 1)^2 + 1(-4x^2 + 4x + 1) + 5) - 1) + 2) - 2 from x = -2.0 to x = -1.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2cos(1\u03c0(5(4((-1(1|x + 3| + 3) - 1)/(2(1|x + 3| + 3) - 3))^2 + 3((-1(1|x + 3| + 3) - 1)/(2(1|x + 3| + 3) - 3)))^2 - 3(4((-1(1|x + 3| + 3) - 1)/(2(1|x + 3| + 3) - 3))^2 + 3((-1(1|x + 3| + 3) - 1)/(2(1|x + 3| + 3) - 3))) - 4) + 2) + 3 and g(x) = 3(2(2|(-2x^2 + 5x - 1) - 3|) - 4) - 1 from x = 0.8 to x = 1.6. 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": "Calculate the area enclosed between the functions f(x) = -3|((2(2e^(1(5(-1|x + 2| - 3) + 2)) + 3) - 1)/(2(2e^(1(5(-1|x + 2| - 3) + 2)) + 3) - 3)) + 3| + 2 and g(x) = -3(2(4(1|x + 2| - 1)^2 + 1(1|x + 2| - 1) - 5) - 4)^2 - 1(2(4(1|x + 2| - 1)^2 + 1(1|x + 2| - 1) - 5) - 4) - 5 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": "0.9", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2|((-1(4(-1(-3|x - 2|) + 2) + 2) + 3)/(3(4(-1(-3|x - 2|) + 2) + 2) - 2)) - 3| - 3, g(x) = (-3(1|(3((2x + 3)/(-1x + 3)) - 4) - 1| - 2) + 2)/(2(1|(3((2x + 3)/(-1x + 3)) - 4) - 1| - 2) - 3), x = -0.7, and x = 1.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "23.8", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (3(-1|(-4((-2(-2x - 2) + 1)/(3(-2x - 2) + 1)) - 2) + 1| + 1) + 2)/(1(-1|(-4((-2(-2x - 2) + 1)/(3(-2x - 2) + 1)) - 2) + 1| + 1)) and g(x) = (3(5((2(3cos(3\u03c0x - 3) + 2) + 1)/(3(3cos(3\u03c0x - 3) + 2) - 1))^2 - 4((2(3cos(3\u03c0x - 3) + 2) + 1)/(3(3cos(3\u03c0x - 3) + 2) - 1)) - 1))/(-1(5((2(3cos(3\u03c0x - 3) + 2) + 1)/(3(3cos(3\u03c0x - 3) + 2) - 1))^2 - 4((2(3cos(3\u03c0x - 3) + 2) + 1)/(3(3cos(3\u03c0x - 3) + 2) - 1)) - 1) + 3) between the vertical lines x = 4.5 and x = 4.6. 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": "Find the area of the region bounded by the curves f(x) = -3e^(2(1((1(-1|((-3x + 3)/(3x + 1))| - 3))/(2(-1|((-3x + 3)/(3x + 1))| - 3) - 3)) - 1)) - 3, g(x) = -2|(4(4(2|x - 2| + 1)^2 - 4(2|x - 2| + 1) - 3) + 5)| - 2, x = 1.8, and x = 1.9000000000000001. 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(2sin(1\u03c0(-5(3((-1x - 1)/(1x - 3)) + 5)^2 + 5(3((-1x - 1)/(1x - 3)) + 5) + 5))) - 3)/(-1(2sin(1\u03c0(-5(3((-1x - 1)/(1x - 3)) + 5)^2 + 5(3((-1x - 1)/(1x - 3)) + 5) + 5)))) and g(x) = -2(3|(-2|(5x^2 - 4x - 2) + 3| + 1) + 1| + 2)^2 + 3(3|(-2|(5x^2 - 4x - 2) + 3| + 1) + 1| + 2) - 5 between the vertical lines x = -0.2 and x = -0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6.8", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (3(-2(5(-4((-3x + 3)/(-3x + 2)) + 3)^2 - 5(-4((-3x + 3)/(-3x + 2)) + 3) - 2) + 1) - 3)/(-2(-2(5(-4((-3x + 3)/(-3x + 2)) + 3)^2 - 5(-4((-3x + 3)/(-3x + 2)) + 3) - 2) + 1)) and g(x) = (3(-3cos(1\u03c0((-2(-3|x + 1| - 3) - 2)/(2(-3|x + 1| - 3) - 1))) - 2) + 2)/(2(-3cos(1\u03c0((-2(-3|x + 1| - 3) - 2)/(2(-3|x + 1| - 3) - 1))) - 2) + 3) between the vertical lines x = -0.9 and x = 1.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.6", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (3(-3(5(-3|((-1x - 1)/(3x - 2)) + 2| - 1) + 5) + 1) + 3)/(-3(-3(5(-3|((-1x - 1)/(3x - 2)) + 2| - 1) + 5) + 1) - 2) and g(x) = -1(-2|(1|((-1x)/(-2x + 3))| - 3) + 2| + 1) - 5 between the vertical lines x = 1.3 and x = 1.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "54.7", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-2((-3((2(2sin(1\u03c0(-3x - 2) - 1) + 2) - 3)/(-1(2sin(1\u03c0(-3x - 2) - 1) + 2) - 2)) + 3)/(-1((2(2sin(1\u03c0(-3x - 2) - 1) + 2) - 3)/(-1(2sin(1\u03c0(-3x - 2) - 1) + 2) - 2)) + 2)) - 1)/(3((-3((2(2sin(1\u03c0(-3x - 2) - 1) + 2) - 3)/(-1(2sin(1\u03c0(-3x - 2) - 1) + 2) - 2)) + 3)/(-1((2(2sin(1\u03c0(-3x - 2) - 1) + 2) - 3)/(-1(2sin(1\u03c0(-3x - 2) - 1) + 2) - 2)) + 2)) + 3) and g(x) = 1(-3|((-2(-1|x + 2| - 1) + 1)/(-2(-1|x + 2| - 1) - 1)) + 3| + 1) + 5 between the vertical lines x = 3.4 and x = 4.1. 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(3sin(1\u03c0(4(1|(-1x^2 - 4x) + 1| + 3) + 5) + 2) + 1)^2 - 1(3sin(1\u03c0(4(1|(-1x^2 - 4x) + 1| + 3) + 5) + 2) + 1) + 4 and g(x) = -4((2(-2|((-1x + 3)/(3x - 2))| - 3) + 2)/(2(-2|((-1x + 3)/(3x - 2))| - 3) + 2)) - 1 from x = 3.4 to x = 3.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (3(-2e^(-2(3|(1(2|x + 3| + 3)^2 - 1(2|x + 3| + 3) - 1) + 3| + 1)) + 2) - 1)/(2(-2e^(-2(3|(1(2|x + 3| + 3)^2 - 1(2|x + 3| + 3) - 1) + 3| + 1)) + 2)), g(x) = 3cos(3\u03c0((-1(-3((-2x - 3)/(-1x - 1)) + 3) - 1)/(1(-3((-2x - 3)/(-1x - 1)) + 3) - 3)) + 1) + 3, x = -1.5, and x = -1.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2((-1(-1((1(-3|x + 2| + 3) + 1)/(3(-3|x + 2| + 3) - 2))^2 - 2((1(-3|x + 2| + 3) + 1)/(3(-3|x + 2| + 3) - 2)) + 5) - 1)/(-2(-1((1(-3|x + 2| + 3) + 1)/(3(-3|x + 2| + 3) - 2))^2 - 2((1(-3|x + 2| + 3) + 1)/(3(-3|x + 2| + 3) - 2)) + 5))) + 2 and g(x) = 1sin(3\u03c0(3|((1(2|x - 1| + 1) + 1)/(-3(2|x - 1| + 1) - 1)) - 3| - 2) - 3) - 3 from x = -2.6 to x = -1.4. 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": "Find the area of the region bounded by the curves f(x) = -3sin(3\u03c0((1(-5(1(-3|x| + 3)^2 - 4(-3|x| + 3) - 1)^2 + 5(1(-3|x| + 3)^2 - 4(-3|x| + 3) - 1) - 1))/(1(-5(1(-3|x| + 3)^2 - 4(-3|x| + 3) - 1)^2 + 5(1(-3|x| + 3)^2 - 4(-3|x| + 3) - 1) - 1)))) + 1, g(x) = 4(1cos(1\u03c0(-3(-4x^2 - 5x + 4)^2 - 5(-4x^2 - 5x + 4) - 5) - 3) - 1) + 3, x = 2.5, 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": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (2((-2(-5((1(3x - 2))/(-2(3x - 2) - 3))^2 + 1((1(3x - 2))/(-2(3x - 2) - 3)) + 1) - 2)/(1(-5((1(3x - 2))/(-2(3x - 2) - 3))^2 + 1((1(3x - 2))/(-2(3x - 2) - 3)) + 1))) - 1)/(1((-2(-5((1(3x - 2))/(-2(3x - 2) - 3))^2 + 1((1(3x - 2))/(-2(3x - 2) - 3)) + 1) - 2)/(1(-5((1(3x - 2))/(-2(3x - 2) - 3))^2 + 1((1(3x - 2))/(-2(3x - 2) - 3)) + 1))) + 1) and g(x) = -3|((-3(3cos(3\u03c0(-2|x - 1| + 2)) - 1) - 3)/(-2(3cos(3\u03c0(-2|x - 1| + 2)) - 1) + 1)) - 3| + 2 between the vertical lines x = -2.2 and x = -2.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1|(1|(1cos(2\u03c0(-3((3x - 2)/(3x - 2))) + 1) + 1) + 1| + 3)| - 2 and g(x) = -3(-3(1e^(1(5x^2 + 1x - 5)) - 3)^2 + 5(1e^(1(5x^2 + 1x - 5)) - 3) + 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": "3.7", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 3((2(-3cos(2\u03c0(-2|(4x)| - 2) - 3) - 2) + 1)/(1(-3cos(2\u03c0(-2|(4x)| - 2) - 3) - 2) + 3)) + 4 and g(x) = -1(-2(2cos(1\u03c0((3x - 3)/(-3x - 1)))) + 2)^2 + 3(-2(2cos(1\u03c0((3x - 3)/(-3x - 1)))) + 2) - 4 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": "2.8", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2|(4(-1|(1(1|x - 2| + 3) - 5) + 1| - 3) - 2) - 2| + 2 and g(x) = (1(-1sin(1\u03c0(-3(3|x - 1| - 2) - 5) + 3) + 3) - 1)/(-1(-1sin(1\u03c0(-3(3|x - 1| - 2) - 5) + 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": "5.7", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1(3(-5(-1cos(3\u03c0((1x - 1)/(2x + 3)) - 2) - 1)^2 + 5(-1cos(3\u03c0((1x - 1)/(2x + 3)) - 2) - 1) + 4) + 3) + 1, g(x) = 1|((-1(3|(3x^2 + 2x - 5) + 3|) + 1)/(3(3|(3x^2 + 2x - 5) + 3|) + 3)) - 1| + 3, x = -3.0, 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": "22.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3((-2(-1(1((-2x - 3)/(-1x - 1))^2 + 2((-2x - 3)/(-1x - 1)) + 2)^2 - 4(1((-2x - 3)/(-1x - 1))^2 + 2((-2x - 3)/(-1x - 1)) + 2) + 1) - 1)/(1(-1(1((-2x - 3)/(-1x - 1))^2 + 2((-2x - 3)/(-1x - 1)) + 2)^2 - 4(1((-2x - 3)/(-1x - 1))^2 + 2((-2x - 3)/(-1x - 1)) + 2) + 1) + 3)) + 5 and g(x) = 4(3(-1|(-5x^2 + 2x + 1) + 1|) + 3)^2 - 4(3(-1|(-5x^2 + 2x + 1) + 1|) + 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": "0.9", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2cos(3\u03c0(3|((-3(2(-3x^2 - 5x + 5)^2 - 2(-3x^2 - 5x + 5) - 4) - 1)/(3(2(-3x^2 - 5x + 5)^2 - 2(-3x^2 - 5x + 5) - 4) + 2)) - 2|) - 2) - 2 and g(x) = -2((3(-3|(-1|x + 3| + 3) - 2|) - 3)/(1(-3|(-1|x + 3| + 3) - 2|) - 3))^2 - 5((3(-3|(-1|x + 3| + 3) - 2|) - 3)/(1(-3|(-1|x + 3| + 3) - 2|) - 3)) + 5 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1|(1(1(1((-2x + 2)/(-1x - 3)) + 2) - 4) + 4) + 2| - 2, g(x) = -3e^(1(-4(2|(-3x + 3) + 3| + 1) + 4)), x = -2.0, 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": "0.9", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1|(2cos(3\u03c0((-2((1((2x + 1)/(-1x + 2)))/(3((2x + 1)/(-1x + 2)))) - 2)/(-3((1((2x + 1)/(-1x + 2)))/(3((2x + 1)/(-1x + 2)))) + 2)) + 2) + 2) - 2| - 1, g(x) = 3((1((3(1x^2 - 1x - 2) + 3)/(1(1x^2 - 1x - 2) + 3)) + 1)/(-2((3(1x^2 - 1x - 2) + 3)/(1(1x^2 - 1x - 2) + 3)) - 1)) - 4, x = -0.4, and x = 1.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.8", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2e^(-1(-1|((-1(-1(1x + 5)) - 1)/(-2(-1(1x + 5)))) + 3| + 3)) - 2 and g(x) = (-1(1(2|(-2sin(2\u03c0x - 1) - 3) + 1| - 1) - 1) - 1)/(3(1(2|(-2sin(2\u03c0x - 1) - 3) + 1| - 1) - 1) - 2) between the vertical lines x = -3.9 and x = -3.3. 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": "Find the area of the region bounded by the curves f(x) = -3(2|((1(2|(3|x + 2| - 1) + 3| - 3) + 3)/(3(2|(3|x + 2| - 1) + 3| - 3))) + 1| - 2) - 2, g(x) = 2(2(-2e^(-1(-3|x - 2| + 3)) + 1))^2 - 5(2(-2e^(-1(-3|x - 2| + 3)) + 1)) - 2, x = 1.4, 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": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 3cos(3\u03c0(2|((1(3|(2|x - 1| + 3)| + 3) - 2)/(1(3|(2|x - 1| + 3)| + 3) - 2)) - 1| - 3) - 3) - 2 and g(x) = 2cos(2\u03c0(-1|(-3|((1x - 3)/(-3x - 3))| - 3) + 3| - 1) + 1) + 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": "Find the area of the region bounded by the curves f(x) = 3|((1(3|(3|(1|x - 1| - 1) - 1| + 2) - 2| + 3) + 1)/(2(3|(3|(1|x - 1| - 1) - 1| + 2) - 2| + 3) - 1)) - 2| + 3, g(x) = 1(2|(-5(-1x)^2 - 1(-1x) + 4) - 1| + 1) - 1, x = -1.0, and x = 1.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7.9", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1|(-2(1(-3(-3x^2 + 1x)^2 + 2(-3x^2 + 1x) + 1) + 2) - 4) + 1| - 2, g(x) = (-3(-2|(-2|(3x - 2) + 3| - 3)| + 1) + 1)/(1(-2|(-2|(3x - 2) + 3| - 3)| + 1) - 3), x = -0.4, 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": "7.7", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 3((1(5(-3cos(2\u03c0((-2x + 2)/(-2x - 3)) - 3) - 3) + 5) + 3)/(-2(5(-3cos(2\u03c0((-2x + 2)/(-2x - 3)) - 3) - 3) + 5))) + 4 and g(x) = -2|((-2(-3(-1x^2 + 3x - 5) - 2) + 2)/(3(-3(-1x^2 + 3x - 5) - 2) - 1)) + 2| - 1 between the vertical lines x = -1.1 and x = -1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1|((1((-3((-2((2x + 2)/(1x)))/(-1((2x + 2)/(1x)) + 2)))/(2((-2((2x + 2)/(1x)))/(-1((2x + 2)/(1x)) + 2)) + 1)) + 3)/(-3((-3((-2((2x + 2)/(1x)))/(-1((2x + 2)/(1x)) + 2)))/(2((-2((2x + 2)/(1x)))/(-1((2x + 2)/(1x)) + 2)) + 1)) - 1)) + 1|, g(x) = -1(3|(2sin(2\u03c0(5x^2 - 1x + 2) + 3) - 3) - 2| - 3) - 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": "1.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 3(-3|((3(-2((1x + 1)/(1x - 2)) - 2) + 3)/(-1(-2((1x + 1)/(1x - 2)) - 2)))|) and g(x) = (-2(2(3|(-3e^(2x) + 2) + 1| + 2) + 2))/(1(2(3|(-3e^(2x) + 2) + 1| + 2) + 2)) between the vertical lines x = -0.0 and x = 0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-1(3sin(3\u03c0(4(-2|((1x + 2)/(-2x)) - 1| + 3) + 3)) + 2) - 3)/(-1(3sin(3\u03c0(4(-2|((1x + 2)/(-2x)) - 1| + 3) + 3)) + 2) + 2) and g(x) = 4(-1(1cos(1\u03c0((1x)/(2x + 2)) - 1) - 1) - 4) - 5 between the vertical lines x = 2.0 and x = 2.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.9", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-2(-3|(1sin(2\u03c0(1(-2x^2 - 1x + 3)^2 + 2) + 2) + 1) + 3| - 2) - 3)/(-2(-3|(1sin(2\u03c0(1(-2x^2 - 1x + 3)^2 + 2) + 2) + 1) + 3| - 2) - 2), g(x) = -1(5(-3|((-2x + 2)/(-2x + 1)) + 1| + 1)) - 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2((1(-1sin(1\u03c0(2(-3|x + 2| + 1) + 5) - 3) + 1) - 3)/(-2(-1sin(1\u03c0(2(-3|x + 2| + 1) + 5) - 3) + 1) - 1))^2 + 3((1(-1sin(1\u03c0(2(-3|x + 2| + 1) + 5) - 3) + 1) - 3)/(-2(-1sin(1\u03c0(2(-3|x + 2| + 1) + 5) - 3) + 1) - 1)) + 4, g(x) = -1(1(3sin(1\u03c0(-3|x - 1| + 1) - 2) - 3)^2 - 3(3sin(1\u03c0(-3|x - 1| + 1) - 2) - 3) - 1)^2 - 4(1(3sin(1\u03c0(-3|x - 1| + 1) - 2) - 3)^2 - 3(3sin(1\u03c0(-3|x - 1| + 1) - 2) - 3) - 1) + 3, 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": "1.9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-3(-1(1(3|(-2sin(2\u03c0x + 2)) + 2| + 3) - 3) + 2) + 1)/(3(-1(1(3|(-2sin(2\u03c0x + 2)) + 2| + 3) - 3) + 2) + 2) and g(x) = 2e^(-1(2(-1|(-2|x| + 2) + 3| + 1) - 3)) - 2 from x = 2.1 to x = 2.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8.6", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2|(1|((2(3|(-3sin(2\u03c0x + 2) - 1) - 2| + 2))/(2(3|(-3sin(2\u03c0x + 2) - 1) - 2| + 2))) + 3|)| + 2, g(x) = (-1((-1(-2(1|x + 3| - 2)^2 + 5(1|x + 3| - 2) + 1) + 2)/(-1(-2(1|x + 3| - 2)^2 + 5(1|x + 3| - 2) + 1))) - 1)/(-3((-1(-2(1|x + 3| - 2)^2 + 5(1|x + 3| - 2) + 1) + 2)/(-1(-2(1|x + 3| - 2)^2 + 5(1|x + 3| - 2) + 1))) - 1), x = -0.9, and x = 1.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16.4", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-3(2|(-4(-3e^(-2((-2x + 2)/(1x))) - 3)^2 - 5(-3e^(-2((-2x + 2)/(1x))) - 3))| + 1) - 2)/(2(2|(-4(-3e^(-2((-2x + 2)/(1x))) - 3)^2 - 5(-3e^(-2((-2x + 2)/(1x))) - 3))| + 1)) and g(x) = (-1(1(-2|(-3x + 5) - 3| - 3) + 4) + 2)/(1(1(-2|(-3x + 5) - 3| - 3) + 4)) between the vertical lines x = -0.2 and x = 1.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1(5(-3((-2(4x + 1) + 3)/(-1(4x + 1))) - 3)^2 - 2(-3((-2(4x + 1) + 3)/(-1(4x + 1))) - 3) - 4) + 5 and g(x) = -5(-1|(-4(4x^2 - 1x + 3)^2 + 2) - 1| - 3)^2 - 5(-1|(-4(4x^2 - 1x + 3)^2 + 2) - 1| - 3) - 4 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": "-18707.8", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -5(3((1(-2|(-1|x + 1|)| + 2) + 2)/(1(-2|(-1|x + 1|)| + 2))) - 5)^2 - 3(3((1(-2|(-1|x + 1|)| + 2) + 2)/(1(-2|(-1|x + 1|)| + 2))) - 5) - 5 and g(x) = 5(-1|(3sin(2\u03c0(2x^2 + 3x + 4) + 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": "1.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1|(-3|((-3(-1|((-3x - 1)/(-3x)) - 1|) + 1)/(2(-1|((-3x - 1)/(-3x)) - 1|) + 1)) - 1| - 1) + 3| + 2 and g(x) = (-2(-1sin(1\u03c0(1|((-2x - 1)/(-1x - 1)) - 1| + 2) + 1)) - 3)/(3(-1sin(1\u03c0(1|((-2x - 1)/(-1x - 1)) - 1| + 2) + 1)) + 2) from x = -1.2 to x = -1.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.7", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (3(-3|(1sin(2\u03c0(1(4x^2 - 3x - 3) - 2)) + 3)| + 3) - 3)/(-3(-3|(1sin(2\u03c0(1(4x^2 - 3x - 3) - 2)) + 3)| + 3)) and g(x) = 2sin(2\u03c0((2(-2|((2x + 3)/(-3x - 2)) + 2| - 2) - 2)/(-2(-2|((2x + 3)/(-3x - 2)) + 2| - 2) - 1)) - 2) - 2 between the vertical lines x = -0.5 and x = -0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-2(-3|(-1(1(1x^2 - 5x - 3) + 2)^2 - 4(1(1x^2 - 5x - 3) + 2) - 3) - 3|) + 1)/(-2(-3|(-1(1(1x^2 - 5x - 3) + 2)^2 - 4(1(1x^2 - 5x - 3) + 2) - 3) - 3|) - 1) and g(x) = 4(3(-1|(-2|x - 1| + 2) + 1| + 2)^2 - 1(-1|(-2|x - 1| + 2) + 1| + 2) - 2) + 1 between the vertical lines x = 2.0 and x = 3.0. 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(5(-3((2(3x - 2) - 1)/(-2(3x - 2) - 1))^2 + 5((2(3x - 2) - 1)/(-2(3x - 2) - 1)) - 1) + 4)^2 - 4(5(-3((2(3x - 2) - 1)/(-2(3x - 2) - 1))^2 + 5((2(3x - 2) - 1)/(-2(3x - 2) - 1)) - 1) + 4) and g(x) = -2e^(-1((2(-3|(-1x^2 + 3x + 1) - 2| - 1) + 3)/(1(-3|(-1x^2 + 3x + 1) - 2| - 1) + 1))) - 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": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (3(-3(-1|(1(-3e^(-1x))^2 + 4(-3e^(-1x)) - 4) - 3|)^2 + 4(-1|(1(-3e^(-1x))^2 + 4(-3e^(-1x)) - 4) - 3|) + 2) - 2)/(-3(-3(-1|(1(-3e^(-1x))^2 + 4(-3e^(-1x)) - 4) - 3|)^2 + 4(-1|(1(-3e^(-1x))^2 + 4(-3e^(-1x)) - 4) - 3|) + 2) - 2) and g(x) = 1(-2((-2(1x - 5) - 2)/(1(1x - 5))) - 4)^2 - 5 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 3cos(3\u03c0((-2(5((-3(5x^2 - 2x - 1))/(-2(5x^2 - 2x - 1) + 3)) + 4) - 2)/(2(5((-3(5x^2 - 2x - 1))/(-2(5x^2 - 2x - 1) + 3)) + 4))) - 2) + 1 and g(x) = 3|((2((-1(2x - 5) + 3)/(-2(2x - 5) - 3)) + 1)/(3((-1(2x - 5) + 3)/(-2(2x - 5) - 3))))| + 2 from x = 2.0 to x = 3.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2(2|((1(-3(-2x^2 - 5x - 4) - 3) - 3)/(-1(-3(-2x^2 - 5x - 4) - 3) - 2)) + 1| - 1)^2 - 4(2|((1(-3(-2x^2 - 5x - 4) - 3) - 3)/(-1(-3(-2x^2 - 5x - 4) - 3) - 2)) + 1| - 1) + 3 and g(x) = 3|(-3(3(3|x + 3| + 1) - 3)^2 - 4(3(3|x + 3| + 1) - 3) + 1) + 2| + 2 between the vertical lines x = -3.0 and x = -2.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 4(-1(-2sin(3\u03c0(1((1x + 1)/(3x - 2)) - 1) + 1) - 1) - 3) + 4 and g(x) = (2(-2(-3|(-4x^2 + 3x + 5) + 1| + 1)^2 - 5(-3|(-4x^2 + 3x + 5) + 1| + 1) + 4) + 1)/(-3(-2(-3|(-4x^2 + 3x + 5) + 1| + 1)^2 - 5(-3|(-4x^2 + 3x + 5) + 1| + 1) + 4) + 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": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2|(-4((-2((2((3x - 1)/(-2x - 2)) + 1)/(1((3x - 1)/(-2x - 2)) - 3)) - 1)/(-1((2((3x - 1)/(-2x - 2)) + 1)/(1((3x - 1)/(-2x - 2)) - 3)))) + 5)| + 1 and g(x) = -3((2(2(1cos(2\u03c0x + 2)) + 3))/(1(2(1cos(2\u03c0x + 2)) + 3) + 1)) + 1 between the vertical lines x = -0.5 and x = 0.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2(-2|(-5(3(-4x - 4)^2 - 2(-4x - 4) + 1) + 1) - 3| + 3) - 5 and g(x) = 3(-2|(5((1x - 3)/(-1x - 1))^2 - 4((1x - 3)/(-1x - 1)) - 1) + 2| + 2) + 1 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": "-3877.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1cos(2\u03c0(-3((-2((1(1|x + 1| + 2))/(2(1|x + 1| + 2))) + 1)/(-2((1(1|x + 1| + 2))/(2(1|x + 1| + 2))) - 3))^2 + 4((-2((1(1|x + 1| + 2))/(2(1|x + 1| + 2))) + 1)/(-2((1(1|x + 1| + 2))/(2(1|x + 1| + 2))) - 3)) + 2)) - 1 and g(x) = -2|(5(-2(4x - 1) - 4)^2 + 5(-2(4x - 1) - 4) + 4) - 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (1((-1((2((3(2x^2 - 4x - 2) + 1)/(1(2x^2 - 4x - 2))) + 2)/(1((3(2x^2 - 4x - 2) + 1)/(1(2x^2 - 4x - 2))))) + 2)/(2((2((3(2x^2 - 4x - 2) + 1)/(1(2x^2 - 4x - 2))) + 2)/(1((3(2x^2 - 4x - 2) + 1)/(1(2x^2 - 4x - 2))))) - 3)) - 1)/(-2((-1((2((3(2x^2 - 4x - 2) + 1)/(1(2x^2 - 4x - 2))) + 2)/(1((3(2x^2 - 4x - 2) + 1)/(1(2x^2 - 4x - 2))))) + 2)/(2((2((3(2x^2 - 4x - 2) + 1)/(1(2x^2 - 4x - 2))) + 2)/(1((3(2x^2 - 4x - 2) + 1)/(1(2x^2 - 4x - 2))))) - 3)) + 1) and g(x) = 1cos(2\u03c0((2(-1(-2x + 1) + 1) - 2)/(2(-1(-2x + 1) + 1) + 3)) - 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1((-1(-5((-3(2x - 1) + 2)/(-1(2x - 1) - 1))^2 - 2((-3(2x - 1) + 2)/(-1(2x - 1) - 1)) + 2) - 3)/(-3(-5((-3(2x - 1) + 2)/(-1(2x - 1) - 1))^2 - 2((-3(2x - 1) + 2)/(-1(2x - 1) - 1)) + 2) + 2)) - 5 and g(x) = -2|(-4(2(-1x^2 + 2x + 3) + 5) - 3)| + 2 between the vertical lines x = -1.5 and x = 1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "175.6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3cos(3\u03c0(-2(3(2|((-1x + 3)/(2x - 1)) + 3| - 2) - 4) - 2) - 1) - 2 and g(x) = 2sin(2\u03c0(-1|(-2((3x + 2)/(-1x + 3)) + 2) + 3| - 2) - 3) - 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1((3(-1(5(-4x^2 + 3x + 4) + 5) - 3) - 3)/(-1(-1(5(-4x^2 + 3x + 4) + 5) - 3) + 3)) + 3, g(x) = 1((-2(-3(-3x + 3)) + 3)/(3(-3(-3x + 3)))) - 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": "20.8", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3(-1|(1(1(-3sin(2\u03c0x) - 2) + 2)^2 + 3) - 1| + 2), g(x) = (2(-1|(-2((-3x)/(1x + 3)) + 5) - 3| + 1) - 2)/(-2(-1|(-2((-3x)/(1x + 3)) + 5) - 3| + 1) + 3), x = -2.0, and x = -1.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (2(2(-3((3(2cos(1\u03c0x + 1) + 2) + 3)/(1(2cos(1\u03c0x + 1) + 2) - 2))^2 + 2) + 4) + 1)/(-2(2(-3((3(2cos(1\u03c0x + 1) + 2) + 3)/(1(2cos(1\u03c0x + 1) + 2) - 2))^2 + 2) + 4) - 3) and g(x) = (-3((-2(3|(-1x^2 + 3x - 3) + 2| - 2) - 3)/(-2(3|(-1x^2 + 3x - 3) + 2| - 2) + 3)) - 3)/(3((-2(3|(-1x^2 + 3x - 3) + 2| - 2) - 3)/(-2(3|(-1x^2 + 3x - 3) + 2| - 2) + 3)) + 1) between the vertical lines x = -0.1 and x = 1.2. 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) = 4((-3(2(1|(-3cos(2\u03c0x + 1) + 2) + 3| - 3)^2 + 2(1|(-3cos(2\u03c0x + 1) + 2) + 3| - 3) - 4) + 1)/(2(2(1|(-3cos(2\u03c0x + 1) + 2) + 3| - 3)^2 + 2(1|(-3cos(2\u03c0x + 1) + 2) + 3| - 3) - 4))) + 1 and g(x) = -1|(1|(-2(-1x^2 - 5x - 3)) - 3| - 3) - 3| - 3 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": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1(-3cos(1\u03c0((-1((-1(-3x^2 + 3x + 2) + 3)/(2(-3x^2 + 3x + 2))) + 2)/(-3((-1(-3x^2 + 3x + 2) + 3)/(2(-3x^2 + 3x + 2))) + 2)) - 3)) + 1 and g(x) = (-2(5(-1sin(1\u03c0((2x - 2)/(-2x - 1)) + 1) + 1)) - 3)/(-2(5(-1sin(1\u03c0((2x - 2)/(-2x - 1)) + 1) + 1)) + 1) from x = -0.3 to x = -0.19999999999999998. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1|(-2sin(2\u03c0((2(2|(-5x + 3) - 2| - 3) - 2)/(-2(2|(-5x + 3) - 2| - 3) + 3)) + 1) - 2) + 3| + 2 and g(x) = (3(1((-1(-3cos(2\u03c0x + 3) - 2) + 2)/(-2(-3cos(2\u03c0x + 3) - 2) - 1)) + 2) + 1)/(-1(1((-1(-3cos(2\u03c0x + 3) - 2) + 2)/(-2(-3cos(2\u03c0x + 3) - 2) - 1)) + 2) - 3) from x = 0.9 to x = 1.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2((3(3e^(1(1(-1|x + 1| - 1) - 2)) + 1) - 3)/(-3(3e^(1(1(-1|x + 1| - 1) - 2)) + 1) + 1))^2 - 4((3(3e^(1(1(-1|x + 1| - 1) - 2)) + 1) - 3)/(-3(3e^(1(1(-1|x + 1| - 1) - 2)) + 1) + 1)) and g(x) = 1sin(3\u03c0(-3(1((-2x - 1)/(-3x + 1)) - 4) + 5) - 2) between the vertical lines x = 0.1 and x = 0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -4(2sin(3\u03c0(-4(4(-4x^2 - 3x - 1)^2 - 2(-4x^2 - 3x - 1) - 1)^2 + 5(4(-4x^2 - 3x - 1)^2 - 2(-4x^2 - 3x - 1) - 1)) - 2) - 2) - 3 and g(x) = -3cos(2\u03c0(3(-3|(1|x - 1| + 3) - 2| + 1)^2 + 4(-3|(1|x - 1| + 3) - 2| + 1))) + 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": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 3((-1(3|(-3|(-3x + 5) - 1|) + 1|))/(-2(3|(-3|(-3x + 5) - 1|) + 1|) + 3))^2 - 3((-1(3|(-3|(-3x + 5) - 1|) + 1|))/(-2(3|(-3|(-3x + 5) - 1|) + 1|) + 3)) and g(x) = 3(2|((3(2|x| - 3) + 2)/(1(2|x| - 3)))| + 3) - 4 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": "-0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2(-2|(4(-1(1e^(1x) - 3)^2 + 1(1e^(1x) - 3))^2 + 4(-1(1e^(1x) - 3)^2 + 1(1e^(1x) - 3)) + 3) + 3| - 1) - 5 and g(x) = 2|(5(3|(1|x - 1| + 3) + 2| - 3)) + 2| - 3 between the vertical lines x = 0.5 and x = 1.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "107.9", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1((-3(-5(3(3|x + 2| + 2) + 3)^2 + 1(3(3|x + 2| + 2) + 3) + 2) + 1)/(-3(-5(3(3|x + 2| + 2) + 3)^2 + 1(3(3|x + 2| + 2) + 3) + 2)))^2 - 3((-3(-5(3(3|x + 2| + 2) + 3)^2 + 1(3(3|x + 2| + 2) + 3) + 2) + 1)/(-3(-5(3(3|x + 2| + 2) + 3)^2 + 1(3(3|x + 2| + 2) + 3) + 2))) and g(x) = -3((3(5(2e^(1x))^2 + 2(2e^(1x)) - 4) + 3)/(1(5(2e^(1x))^2 + 2(2e^(1x)) - 4) + 3))^2 - 1((3(5(2e^(1x))^2 + 2(2e^(1x)) - 4) + 3)/(1(5(2e^(1x))^2 + 2(2e^(1x)) - 4) + 3)) + 5 between the vertical lines x = -1.4 and x = -0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -5(4(1|(2|((1x)/(-3x - 1))| - 1) - 1|)^2 - 2(1|(2|((1x)/(-3x - 1))| - 1) - 1|) - 1) + 5, g(x) = -3|((-3(-3|(3x - 1) + 2|))/(1(-3|(3x - 1) + 2|))) + 2| + 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": "2.7", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-3(-3|(2|((-2(-1x - 1) + 1)/(2(-1x - 1))) + 3| + 3) - 2| - 3) + 3)/(-2(-3|(2|((-2(-1x - 1) + 1)/(2(-1x - 1))) + 3| + 3) - 2| - 3) - 3) and g(x) = -1((1(-3sin(2\u03c0(5x^2 + 2x) + 2) - 2))/(-2(-3sin(2\u03c0(5x^2 + 2x) + 2) - 2) - 2)) + 4 between the vertical lines x = -1.5 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": "Find the area of the region bounded by the curves f(x) = 5(1((-2((-1(-3x - 4) + 1)/(-1(-3x - 4) + 2)) + 1)/(2((-1(-3x - 4) + 1)/(-1(-3x - 4) + 2)) + 3)) - 4)^2 - 4, g(x) = 2|(-1(3(2e^(-1x) - 3)^2 + 3(2e^(-1x) - 3) - 5) + 3) + 3| + 1, x = -1.9, and x = -1.7999999999999998. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16.5", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 5(1(-3|(-3|(1x - 5) + 3| + 3) + 3| - 1)^2 + 1(-3|(-3|(1x - 5) + 3| + 3) + 3| - 1) - 2)^2 - 4(1(-3|(-3|(1x - 5) + 3| + 3) + 3| - 1)^2 + 1(-3|(-3|(1x - 5) + 3| + 3) + 3| - 1) - 2) - 4, g(x) = 3|(3|(4(-1e^(1x) + 2)^2 + 5(-1e^(1x) + 2) - 2) - 1| + 2) + 2| + 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": "24.7", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2(1(-1|((2(-4x^2 + 5x - 5))/(2(-4x^2 + 5x - 5) - 3)) + 1| + 2)^2 - 4(-1|((2(-4x^2 + 5x - 5))/(2(-4x^2 + 5x - 5) - 3)) + 1| + 2) + 2) + 2, g(x) = (-1((-1(-3(-3sin(1\u03c0x + 3))^2 + 4) - 2)/(-1(-3(-3sin(1\u03c0x + 3))^2 + 4) - 1)))/(1((-1(-3(-3sin(1\u03c0x + 3))^2 + 4) - 2)/(-1(-3(-3sin(1\u03c0x + 3))^2 + 4) - 1)) + 3), x = 0.2, 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": "2.9", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2(1|(1(3e^(1(-1|x - 1| - 1)) - 3) + 3) - 3| + 1) + 2 and g(x) = -2|(2(-5((1x - 3)/(3x + 2)) - 3)^2 - 5(-5((1x - 3)/(3x + 2)) - 3) + 5)| + 3 between the vertical lines x = 0.2 and x = 0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2(-2(2(-1|(5x - 5) + 2| + 3) - 3) + 5) and g(x) = 3|(-1(-5(2|x - 1| + 2) - 4) + 1) - 2| - 3 from x = -4.4 to x = 3.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "163.6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (1(-1|(1(-3cos(2\u03c0((2x - 1)/(1x + 1)) + 3) + 1)) + 1| + 2) - 2)/(3(-1|(1(-3cos(2\u03c0((2x - 1)/(1x + 1)) + 3) + 1)) + 1| + 2)) and g(x) = (-3(2cos(2\u03c0(1|((-3x)/(1x + 3)) + 2| + 1) - 2) - 1) + 1)/(3(2cos(2\u03c0(1|((-3x)/(1x + 3)) + 2| + 1) - 2) - 1) - 1) from x = -2.7 to x = -2.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (2(1sin(1\u03c0(-3|((2(-5x + 3))/(-1(-5x + 3) - 1)) - 1| - 2) + 3) - 2) - 3)/(-3(1sin(1\u03c0(-3|((2(-5x + 3))/(-1(-5x + 3) - 1)) - 1| - 2) + 3) - 2) + 2) and g(x) = 5(-3cos(1\u03c0(-3(-3x^2 + 3x + 4)^2 + 2) + 2))^2 + 2(-3cos(1\u03c0(-3(-3x^2 + 3x + 4)^2 + 2) + 2)) - 3 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": "2.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1(-2cos(3\u03c0(-2(2(2x^2 - 2x - 4)) + 1)) + 1) + 5 and g(x) = 3(-2sin(1\u03c0(2|(-2x + 4)| + 1) + 3) + 1)^2 + 5(-2sin(1\u03c0(2|(-2x + 4)| + 1) + 3) + 1) - 2 from x = -2.8 to x = -2.6999999999999997. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3((1(1|(2sin(1\u03c0(4x^2 + 4x + 1) + 1) - 3) + 3| - 2) - 3)/(3(1|(2sin(1\u03c0(4x^2 + 4x + 1) + 1) - 3) + 3| - 2) - 2)) - 2, g(x) = 2(-5(3(-1e^(-1x) + 2)^2 - 3(-1e^(-1x) + 2) - 3) - 1)^2 + 5(-5(3(-1e^(-1x) + 2)^2 - 3(-1e^(-1x) + 2) - 3) - 1) + 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-2(-2|(-3|(1e^(-1(2x^2 - 1x + 3)) - 1) - 3| + 1) - 2| + 3) - 1)/(2(-2|(-3|(1e^(-1(2x^2 - 1x + 3)) - 1) - 3| + 1) - 2| + 3) - 1) and g(x) = -2cos(1\u03c0(-3((-2(-4x^2 - 1x + 2) + 2)/(-1(-4x^2 - 1x + 2) + 2))^2 + 2((-2(-4x^2 - 1x + 2) + 2)/(-1(-4x^2 - 1x + 2) + 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 4((-3(3sin(3\u03c0((1(-5x + 5) - 2)/(-2(-5x + 5) + 1)) - 2)) + 2)/(1(3sin(3\u03c0((1(-5x + 5) - 2)/(-2(-5x + 5) + 1)) - 2)) + 2)) + 2 and g(x) = -2(3cos(1\u03c0(5(4x^2 - 2x - 2) - 5) - 2) + 3) - 3 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": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1(5((1((-2((3x)/(2x - 3)) - 3)/(2((3x)/(2x - 3)) + 2)) + 3)/(2((-2((3x)/(2x - 3)) - 3)/(2((3x)/(2x - 3)) + 2)) - 1))^2 + 5((1((-2((3x)/(2x - 3)) - 3)/(2((3x)/(2x - 3)) + 2)) + 3)/(2((-2((3x)/(2x - 3)) - 3)/(2((3x)/(2x - 3)) + 2)) - 1)) + 4) - 5, g(x) = 2(1sin(2\u03c0((1(1x + 2) + 1)/(3(1x + 2))) - 3) - 2)^2 - 5(1sin(2\u03c0((1(1x + 2) + 1)/(3(1x + 2))) - 3) - 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": "-3.6", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1|(-1sin(1\u03c0((2((2(2|x + 3| + 2) + 2)/(-3(2|x + 3| + 2) - 1)) - 2)/(-3((2(2|x + 3| + 2) + 2)/(-3(2|x + 3| + 2) - 1)) - 2)) + 1) - 2) + 3| + 1 and g(x) = -1(1cos(1\u03c0((1(-2|x - 3| - 1) - 3)/(-1(-2|x - 3| - 1) - 3)) + 3) - 2) - 3 between the vertical lines x = 4.7 and x = 5.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2|(4(-2sin(1\u03c0(-1|(1x^2 - 5x - 3)|) + 2) - 2) - 4) + 2| - 2 and g(x) = 3|(3(-2|(-3sin(3\u03c0x - 2) - 1)| + 2) + 5) - 1| 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": "226.7", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3(-1sin(3\u03c0(-2(3(-2|x - 3| - 2)^2 + 2(-2|x - 3| - 2))^2 - 2(3(-2|x - 3| - 2)^2 + 2(-2|x - 3| - 2)) + 5) - 3) + 2)^2 - 5(-1sin(3\u03c0(-2(3(-2|x - 3| - 2)^2 + 2(-2|x - 3| - 2))^2 - 2(3(-2|x - 3| - 2)^2 + 2(-2|x - 3| - 2)) + 5) - 3) + 2) - 4, g(x) = 2cos(3\u03c0(-3(-3(1|x - 2| + 3)^2 - 4(1|x - 2| + 3) - 1)^2 - 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3(-2|(4(1|(2x + 1) + 2| - 2) + 1) + 1| + 3)^2 - 1(-2|(4(1|(2x + 1) + 2| - 2) + 1) + 1| + 3) + 2, g(x) = 1|(1cos(3\u03c0(4(3|x| + 3)^2 + 5(3|x| + 3) + 5) + 1) - 1) + 3| - 1, 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": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1(1(2|((-3(-1|x + 2| + 2) + 1)/(-3(-1|x + 2| + 2) + 4))| - 2)^2 - 5(2|((-3(-1|x + 2| + 2) + 1)/(-3(-1|x + 2| + 2) + 4))| - 2) + 2) - 4 and g(x) = -3(2cos(1\u03c0(-1|(-1|x + 3| - 1) - 3| + 2) + 3))^2 + 2(2cos(1\u03c0(-1|(-1|x + 3| - 1) - 3| + 2) + 3)) + 5 between the vertical lines x = 2.6 and x = 3.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1|(3(-5(-4(-2x - 1)^2 + 2(-2x - 1) + 1)^2 + 2(-4(-2x - 1)^2 + 2(-2x - 1) + 1) + 4)^2 + 2(-5(-4(-2x - 1)^2 + 2(-2x - 1) + 1)^2 + 2(-4(-2x - 1)^2 + 2(-2x - 1) + 1) + 4) + 1)| + 2 and g(x) = 2(-1e^(1(1(4x^2 + 3x - 1) - 2)))^2 - 1(-1e^(1(1(4x^2 + 3x - 1) - 2))) - 4 from x = -0.8 to x = -0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.4", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-2(1|(-2((-3(3x + 3) - 1)/(3(3x + 3) - 2)) + 1) - 3| + 1) + 1)/(-2(1|(-2((-3(3x + 3) - 1)/(3(3x + 3) - 2)) + 1) - 3| + 1) + 3) and g(x) = -1(-3sin(1\u03c0(-1(2x - 5) - 2) - 1) - 1)^2 + 1(-3sin(1\u03c0(-1(2x - 5) - 2) - 1) - 1) - 2 between the vertical lines x = 2.7 and x = 2.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1|(2cos(1\u03c0(1(-5(3x^2 + 5x - 1)^2 - 4(3x^2 + 5x - 1) - 4) - 5) - 2) - 1)| + 3 and g(x) = (-1(1sin(2\u03c0((-1(-1x^2 - 5x + 4) + 2)/(2(-1x^2 - 5x + 4) - 3)) + 1) + 1) - 3)/(-3(1sin(2\u03c0((-1(-1x^2 - 5x + 4) + 2)/(2(-1x^2 - 5x + 4) - 3)) + 1) + 1)) from x = 4.2 to 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": "Determine the area of the region enclosed by the graphs of f(x) = (2((-2((3(-5(1x^2 + 1x - 5)^2 - 3(1x^2 + 1x - 5) + 3) - 1)/(-1(-5(1x^2 + 1x - 5)^2 - 3(1x^2 + 1x - 5) + 3) - 3)) + 1)/(3((3(-5(1x^2 + 1x - 5)^2 - 3(1x^2 + 1x - 5) + 3) - 1)/(-1(-5(1x^2 + 1x - 5)^2 - 3(1x^2 + 1x - 5) + 3) - 3)) - 1)))/(3((-2((3(-5(1x^2 + 1x - 5)^2 - 3(1x^2 + 1x - 5) + 3) - 1)/(-1(-5(1x^2 + 1x - 5)^2 - 3(1x^2 + 1x - 5) + 3) - 3)) + 1)/(3((3(-5(1x^2 + 1x - 5)^2 - 3(1x^2 + 1x - 5) + 3) - 1)/(-1(-5(1x^2 + 1x - 5)^2 - 3(1x^2 + 1x - 5) + 3) - 3)) - 1)) + 3) and g(x) = -5(-2((2(-2sin(1\u03c0x) - 2) + 3)/(3(-2sin(1\u03c0x) - 2) - 2)) - 4) + 5 between the vertical lines x = -2.5 and x = 1.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "100.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -3((1((3(-1cos(1\u03c0(-5x) - 2)) + 2)/(3(-1cos(1\u03c0(-5x) - 2)) - 2)) - 2)/(1((3(-1cos(1\u03c0(-5x) - 2)) + 2)/(3(-1cos(1\u03c0(-5x) - 2)) - 2)) - 3)) + 2, g(x) = (-3(-3cos(2\u03c0(5((2x)/(1x))^2 + 3((2x)/(1x)) - 5) + 1) - 1) + 3)/(2(-3cos(2\u03c0(5((2x)/(1x))^2 + 3((2x)/(1x)) - 5) + 1) - 1) - 3), x = 0.5, and x = 0.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3e^(1(-2(2((-1(-4x - 3) + 1)/(3(-4x - 3) - 1)) - 3)^2 + 3(2((-1(-4x - 3) + 1)/(3(-4x - 3) - 1)) - 3) + 2)) + 1, g(x) = 1(-4(-1e^(-2(-3x - 3)) + 1) - 2)^2 + 5(-4(-1e^(-2(-3x - 3)) + 1) - 2) + 3, x = -1.2, and x = -1.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-3(2|((3(-5(-3x - 2) - 4) + 2)/(-2(-5(-3x - 2) - 4) - 3)) + 3| + 3) - 2)/(-2(2|((3(-5(-3x - 2) - 4) + 2)/(-2(-5(-3x - 2) - 4) - 3)) + 3| + 3)), g(x) = (2(3((1(1sin(2\u03c0x)))/(-1(1sin(2\u03c0x)) - 1))^2 - 4((1(1sin(2\u03c0x)))/(-1(1sin(2\u03c0x)) - 1))) - 2)/(1(3((1(1sin(2\u03c0x)))/(-1(1sin(2\u03c0x)) - 1))^2 - 4((1(1sin(2\u03c0x)))/(-1(1sin(2\u03c0x)) - 1))) + 3), 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 3|(-3cos(2\u03c0(1|(-1(1x^2 + 5x - 4) + 5)| - 3) - 3) + 2) + 1| - 1 and g(x) = (-1((1(-3((1x + 1)/(1x + 1)) - 3) - 1)/(-3(-3((1x + 1)/(1x + 1)) - 3) - 3)) + 2)/(-1((1(-3((1x + 1)/(1x + 1)) - 3) - 1)/(-3(-3((1x + 1)/(1x + 1)) - 3) - 3)) + 2) between the vertical lines x = 3.4 and x = 3.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.7", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3(1((-3(-2|(2|x| + 2) + 1| + 1) - 1)/(-1(-2|(2|x| + 2) + 1| + 1) - 3))^2 - 2((-3(-2|(2|x| + 2) + 1| + 1) - 1)/(-1(-2|(2|x| + 2) + 1| + 1) - 3)) - 4) + 4, g(x) = 5(-3cos(2\u03c0(5(1x + 5)^2 + 4(1x + 5) - 3) - 2) + 1) - 5, x = 3.9, and x = 4.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1(4((1((-3((1x - 3)/(-2x - 1)) - 3)/(-2((1x - 3)/(-2x - 1)) + 3)) - 3)/(-2((-3((1x - 3)/(-2x - 1)) - 3)/(-2((1x - 3)/(-2x - 1)) + 3))))^2 - 4((1((-3((1x - 3)/(-2x - 1)) - 3)/(-2((1x - 3)/(-2x - 1)) + 3)) - 3)/(-2((-3((1x - 3)/(-2x - 1)) - 3)/(-2((1x - 3)/(-2x - 1)) + 3)))) + 3) + 1, g(x) = -4(3(2sin(1\u03c0(2|x - 3| + 1) - 2) - 1) + 4)^2 - 3(3(2sin(1\u03c0(2|x - 3| + 1) - 2) - 1) + 4) + 2, x = 4.3, and x = 4.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -4((2(-1cos(1\u03c0(1|(-3x^2 - 5x - 1) - 1| - 2)) + 3))/(2(-1cos(1\u03c0(1|(-3x^2 - 5x - 1) - 1| - 2)) + 3) + 1))^2 - 2((2(-1cos(1\u03c0(1|(-3x^2 - 5x - 1) - 1| - 2)) + 3))/(2(-1cos(1\u03c0(1|(-3x^2 - 5x - 1) - 1| - 2)) + 3) + 1)) + 3 and g(x) = 3(3|((1(4x^2 - 1x - 5) - 1)/(3(4x^2 - 1x - 5) + 1))| - 3) + 3 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": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (3(1|(-3(-2((-3x + 3)/(3x))^2 + 5((-3x + 3)/(3x)) + 1) - 3) - 1| - 2) + 3)/(-2(1|(-3(-2((-3x + 3)/(3x))^2 + 5((-3x + 3)/(3x)) + 1) - 3) - 1| - 2) - 1), g(x) = -2|(-1(-2|(-1cos(1\u03c0x - 3) - 2) + 1| + 1)^2 + 3(-2|(-1cos(1\u03c0x - 3) - 2) + 1| + 1) - 1) + 3| + 1, 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-2(-1(-3(-4(4x^2 - 3x + 3) + 2)^2 + 2(-4(4x^2 - 3x + 3) + 2) - 3) - 2) - 1)/(2(-1(-3(-4(4x^2 - 3x + 3) + 2)^2 + 2(-4(4x^2 - 3x + 3) + 2) - 3) - 2) - 1), g(x) = 1(-3(3cos(1\u03c0(3|x|) + 2) + 1)^2 + 5)^2 + 3(-3(3cos(1\u03c0(3|x|) + 2) + 1)^2 + 5) - 1, x = 0.7, and x = 0.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1((-2(1(5(1x^2 + 1x + 5))^2 + 1(5(1x^2 + 1x + 5)) - 5) + 2)/(-3(1(5(1x^2 + 1x + 5))^2 + 1(5(1x^2 + 1x + 5)) - 5)))^2 + 5((-2(1(5(1x^2 + 1x + 5))^2 + 1(5(1x^2 + 1x + 5)) - 5) + 2)/(-3(1(5(1x^2 + 1x + 5))^2 + 1(5(1x^2 + 1x + 5)) - 5))) - 3 and g(x) = -1(2(1(-5x + 4)^2 - 4(-5x + 4) - 3) - 2)^2 + 3(2(1(-5x + 4)^2 - 4(-5x + 4) - 3) - 2) between the vertical lines x = -0.2 and x = 1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "191.6", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 3(1|(-1cos(1\u03c0((3(1|x + 3| + 2) + 1)/(3(1|x + 3| + 2) - 2)) + 3) + 3) - 1|) - 1 and g(x) = 3|(1(1(3x - 4) - 4) - 3) - 2| - 1 between the vertical lines x = 4.0 and x = 4.7. 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) = 2|((1((1((1(-5x^2 + 5x) + 1)/(3(-5x^2 + 5x) + 1)) + 2)/(-2((1(-5x^2 + 5x) + 1)/(3(-5x^2 + 5x) + 1)) + 3)) - 2)/(3((1((1(-5x^2 + 5x) + 1)/(3(-5x^2 + 5x) + 1)) + 2)/(-2((1(-5x^2 + 5x) + 1)/(3(-5x^2 + 5x) + 1)) + 3)) + 1)) + 3| + 1 and g(x) = 2|(-2e^(2(1(-1x^2 + 3x - 1))) - 3) - 3| + 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": "1.6", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -4((-1(-2cos(1\u03c0((-1((-1x + 2)/(3x - 2)) - 1)/(3((-1x + 2)/(3x - 2)) - 2)) + 3) - 1) - 2)/(2(-2cos(1\u03c0((-1((-1x + 2)/(3x - 2)) - 1)/(3((-1x + 2)/(3x - 2)) - 2)) + 3) - 1) - 3)) + 2, g(x) = (-2((1((-2(-2e^(1x) - 1) + 2)/(3(-2e^(1x) - 1) + 2)) + 1)/(-1((-2(-2e^(1x) - 1) + 2)/(3(-2e^(1x) - 1) + 2)) - 3)) - 3)/(-2((1((-2(-2e^(1x) - 1) + 2)/(3(-2e^(1x) - 1) + 2)) + 1)/(-1((-2(-2e^(1x) - 1) + 2)/(3(-2e^(1x) - 1) + 2)) - 3)) + 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": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -3(5((2(-3sin(2\u03c0((-1x - 1)/(2x + 2))) + 2) - 3)/(-3(-3sin(2\u03c0((-1x - 1)/(2x + 2))) + 2) + 4)) + 1) - 5, g(x) = -1sin(3\u03c0(3(-2|(-5x^2 - 1x - 4) + 1| + 1)^2 + 1(-2|(-5x^2 - 1x - 4) + 1| + 1) - 5) + 2), x = -4.9, 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (2((2(3(-2|(-1e^(-2x) + 2) - 1| + 3)^2 + 1(-2|(-1e^(-2x) + 2) - 1| + 3) - 5) + 2)/(2(3(-2|(-1e^(-2x) + 2) - 1| + 3)^2 + 1(-2|(-1e^(-2x) + 2) - 1| + 3) - 5) - 1)) + 1)/(3((2(3(-2|(-1e^(-2x) + 2) - 1| + 3)^2 + 1(-2|(-1e^(-2x) + 2) - 1| + 3) - 5) + 2)/(2(3(-2|(-1e^(-2x) + 2) - 1| + 3)^2 + 1(-2|(-1e^(-2x) + 2) - 1| + 3) - 5) - 1)) - 2) and g(x) = 2|(-3(2(-2x - 4)^2 + 5(-2x - 4) - 5) + 2) + 2| - 3 between the vertical lines x = -0.5 and x = -0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-1(-2|((-2(-3|((3x)/(-1x - 3)) - 3| + 2) - 3)/(2(-3|((3x)/(-1x - 3)) - 3| + 2) - 1)) + 1| + 3) + 1)/(2(-2|((-2(-3|((3x)/(-1x - 3)) - 3| + 2) - 3)/(2(-3|((3x)/(-1x - 3)) - 3| + 2) - 1)) + 1| + 3) - 1) and g(x) = -1((-2(3((-2x + 1)/(2x - 3)) - 2) + 3)/(-2(3((-2x + 1)/(2x - 3)) - 2) + 1))^2 - 5((-2(3((-2x + 1)/(2x - 3)) - 2) + 3)/(-2(3((-2x + 1)/(2x - 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": "64.5", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -5((2((-2(3|(-2x + 4) - 2| + 3) - 3)/(-1(3|(-2x + 4) - 2| + 3) + 2)) + 2)/(2((-2(3|(-2x + 4) - 2| + 3) - 3)/(-1(3|(-2x + 4) - 2| + 3) + 2)) - 3)), g(x) = -4(2e^(2(3((3x + 1)/(-1x - 2))^2 - 4((3x + 1)/(-1x - 2)) - 5)) + 1)^2 + 3(2e^(2(3((3x + 1)/(-1x - 2))^2 - 4((3x + 1)/(-1x - 2)) - 5)) + 1) + 3, x = -1.0, 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": "20.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-2(-5(-4(2|(1|x - 1| + 3) - 1| - 3)^2 - 2(2|(1|x - 1| + 3) - 1| - 3) - 3) - 2) + 1)/(-2(-5(-4(2|(1|x - 1| + 3) - 1| - 3)^2 - 2(2|(1|x - 1| + 3) - 1| - 3) - 3) - 2) - 2) and g(x) = -5((-2((1(3cos(1\u03c0x - 2)) + 3)/(-3(3cos(1\u03c0x - 2)))) + 3)/(2((1(3cos(1\u03c0x - 2)) + 3)/(-3(3cos(1\u03c0x - 2)))) + 1)) + 2 between the vertical lines x = -1.9 and x = -0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38.7", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -4(-2|(-3sin(1\u03c0((-2(-1x^2 + 4x + 4) - 1)/(-1(-1x^2 + 4x + 4) + 3)) - 1) - 1) + 3| - 3)^2 - 4(-2|(-3sin(1\u03c0((-2(-1x^2 + 4x + 4) - 1)/(-1(-1x^2 + 4x + 4) + 3)) - 1) - 1) + 3| - 3) + 5, g(x) = 5(-1((-3((-3x - 2)/(2x - 3)))/(-1((-3x - 2)/(2x - 3)) - 2))) - 1, 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": "22.6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3e^(-1(3(1(-1((-2x)/(1x - 2)) - 3) - 3) - 4)) and g(x) = -1|(1cos(1\u03c0(-4(-4x^2 + 2x - 4)^2 - 1(-4x^2 + 2x - 4) + 1) - 3) - 3) - 3| 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": "1.6", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3(-3(-3((2(-1|x - 2| - 2) - 2)/(-3(-1|x - 2| - 2) - 2))^2 + 1) - 4)^2 + 5(-3(-3((2(-1|x - 2| - 2) - 2)/(-3(-1|x - 2| - 2) - 2))^2 + 1) - 4) + 2 and g(x) = 2(-3(-3|(-5x^2)| + 2) + 4) + 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (1((-2((-2(-1(-2sin(1\u03c0x - 2) + 2)^2 - 1(-2sin(1\u03c0x - 2) + 2) - 3) - 3)/(-2(-1(-2sin(1\u03c0x - 2) + 2)^2 - 1(-2sin(1\u03c0x - 2) + 2) - 3) + 3)) + 2)/(1((-2(-1(-2sin(1\u03c0x - 2) + 2)^2 - 1(-2sin(1\u03c0x - 2) + 2) - 3) - 3)/(-2(-1(-2sin(1\u03c0x - 2) + 2)^2 - 1(-2sin(1\u03c0x - 2) + 2) - 3) + 3)))))/(2((-2((-2(-1(-2sin(1\u03c0x - 2) + 2)^2 - 1(-2sin(1\u03c0x - 2) + 2) - 3) - 3)/(-2(-1(-2sin(1\u03c0x - 2) + 2)^2 - 1(-2sin(1\u03c0x - 2) + 2) - 3) + 3)) + 2)/(1((-2(-1(-2sin(1\u03c0x - 2) + 2)^2 - 1(-2sin(1\u03c0x - 2) + 2) - 3) - 3)/(-2(-1(-2sin(1\u03c0x - 2) + 2)^2 - 1(-2sin(1\u03c0x - 2) + 2) - 3) + 3)))) + 1) and g(x) = 3|(-5(2|(4x + 3) - 1|)^2 + 4(2|(4x + 3) - 1|) + 4) - 2| - 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": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1cos(2\u03c0(-1((1(-1(1x^2 - 2x + 2) - 5) + 1)/(1(-1(1x^2 - 2x + 2) - 5))) - 4) - 2) - 1 and g(x) = 2((1(-2(1x^2 + 1x - 1)^2 + 4(1x^2 + 1x - 1) + 3) + 1)/(-1(-2(1x^2 + 1x - 1)^2 + 4(1x^2 + 1x - 1) + 3) - 3))^2 - 5((1(-2(1x^2 + 1x - 1)^2 + 4(1x^2 + 1x - 1) + 3) + 1)/(-1(-2(1x^2 + 1x - 1)^2 + 4(1x^2 + 1x - 1) + 3) - 3)) - 5 from x = -1.6 to x = -1.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2|(2(-3((-2(5x - 3) + 2)/(-2(5x - 3) + 3)) - 1) - 4) + 3| - 1 and g(x) = 1((3(1sin(3\u03c0(2|x - 1| - 3) - 3) + 2) + 3)/(-2(1sin(3\u03c0(2|x - 1| - 3) - 3) + 2)))^2 + 4((3(1sin(3\u03c0(2|x - 1| - 3) - 3) + 2) + 3)/(-2(1sin(3\u03c0(2|x - 1| - 3) - 3) + 2))) - 2 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": "Determine the area of the region enclosed by the graphs of f(x) = -2e^(-1(2|((-1((-3((3x - 3)/(-1x + 2)) + 1)/(-3((3x - 3)/(-1x + 2)) - 1)) + 3)/(1((-3((3x - 3)/(-1x + 2)) + 1)/(-3((3x - 3)/(-1x + 2)) - 1)) - 3)) + 2| + 1)) + 1 and g(x) = -2|((-3((2(1x^2 - 2x - 3) - 3)/(-2(1x^2 - 2x - 3))) + 3)/(3((2(1x^2 - 2x - 3) - 3)/(-2(1x^2 - 2x - 3))) + 1)) + 2| + 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": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3|(4((1((-2(-2x + 4) + 3)/(2(-2x + 4))) - 1)/(3((-2(-2x + 4) + 3)/(2(-2x + 4))) + 2)) + 3) - 2| + 1 and g(x) = 3cos(2\u03c0(5(-2|((-1x + 2)/(-3x + 4)) - 3| + 3)) + 1) from x = 1.3 to x = 1.4000000000000001. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-1(1((2(-5(2|x + 1| - 3)^2 - 3(2|x + 1| - 3) + 3) - 1)/(2(-5(2|x + 1| - 3)^2 - 3(2|x + 1| - 3) + 3) - 3)) - 5) + 3)/(-3(1((2(-5(2|x + 1| - 3)^2 - 3(2|x + 1| - 3) + 3) - 1)/(2(-5(2|x + 1| - 3)^2 - 3(2|x + 1| - 3) + 3) - 3)) - 5) + 1) and g(x) = -3(5(1(1|x - 1| - 2) + 1)^2 + 1(1(1|x - 1| - 2) + 1) - 4)^2 + 3(5(1(1|x - 1| - 2) + 1)^2 + 1(1(1|x - 1| - 2) + 1) - 4) + 5 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": "54.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -4((-2(3(3((-2x + 2)/(-3x - 1)) + 1)^2 - 4(3((-2x + 2)/(-3x - 1)) + 1) + 3) - 3)/(3(3(3((-2x + 2)/(-3x - 1)) + 1)^2 - 4(3((-2x + 2)/(-3x - 1)) + 1) + 3) - 1))^2 - 3((-2(3(3((-2x + 2)/(-3x - 1)) + 1)^2 - 4(3((-2x + 2)/(-3x - 1)) + 1) + 3) - 3)/(3(3(3((-2x + 2)/(-3x - 1)) + 1)^2 - 4(3((-2x + 2)/(-3x - 1)) + 1) + 3) - 1)) + 4, g(x) = 3cos(3\u03c0((-1(5(-3x^2 - 4x - 1) - 1) + 2)/(2(5(-3x^2 - 4x - 1) - 1))) + 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1|(4(-3cos(2\u03c0(3|(2|x - 3| - 3) + 3| - 1) + 2))) + 2| + 1 and g(x) = -3sin(2\u03c0(5(1|((2x - 2)/(-1x + 3)) - 2| + 1) + 3) + 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": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2(-2e^(1(-2|(-3((-3x + 1)/(2x - 1)) - 5)| - 3)) - 3)^2 + 2(-2e^(1(-2|(-3((-3x + 1)/(2x - 1)) - 5)| - 3)) - 3) + 3, g(x) = -1((2(2|(5x + 1)|) - 2)/(-3(2|(5x + 1)|) + 2))^2 - 4((2(2|(5x + 1)|) - 2)/(-3(2|(5x + 1)|) + 2)) - 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": "2.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1(2sin(3\u03c0((2(-4(-3x^2 + 5x - 1) + 1) - 1)/(-1(-4(-3x^2 + 5x - 1) + 1) + 2)) + 1) - 2) + 3, g(x) = (-3(2(2sin(2\u03c0(1|x - 3| + 1) + 2) + 1) - 1) - 1)/(-2(2(2sin(2\u03c0(1|x - 3| + 1) + 2) + 1) - 1) + 3), x = -4.8, 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": "8.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-3(-1((-2(1cos(2\u03c0(1x - 4) - 2) + 1) + 2)/(2(1cos(2\u03c0(1x - 4) - 2) + 1) + 1)) + 2) + 1)/(3(-1((-2(1cos(2\u03c0(1x - 4) - 2) + 1) + 2)/(2(1cos(2\u03c0(1x - 4) - 2) + 1) + 1)) + 2) - 2) and g(x) = 2|((2(-1|((1x)/(-2x - 1)) + 2| + 3))/(-1(-1|((1x)/(-2x - 1)) + 2| + 3) + 2)) - 3| + 3 from x = 1.9 to x = 2.7. 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": "Calculate the area enclosed between the functions f(x) = (2(1|(-1sin(1\u03c0(-4((-3x + 3)/(2x - 3))^2 + 5((-3x + 3)/(2x - 3))) + 1) - 3) - 2| - 3) + 3)/(1(1|(-1sin(1\u03c0(-4((-3x + 3)/(2x - 3))^2 + 5((-3x + 3)/(2x - 3))) + 1) - 3) - 2| - 3) + 2) and g(x) = -2|(-3(5(-1x^2 + 4x - 2) - 3)^2 + 4(5(-1x^2 + 4x - 2) - 3) - 2) + 3| + 2 from x = 3.0 to x = 3.1. 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": "Calculate the area enclosed between the functions f(x) = -3(-2(1sin(2\u03c0(3((-1x + 1)/(3x + 1)) - 5) - 3)) + 2)^2 - 4(-2(1sin(2\u03c0(3((-1x + 1)/(3x + 1)) - 5) - 3)) + 2) + 5 and g(x) = (1(-3(-2cos(3\u03c0(2|x + 1| + 1) + 1) - 2) - 1))/(-2(-3(-2cos(3\u03c0(2|x + 1| + 1) + 1) - 2) - 1) + 1) 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": "2.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (2(1(-2(1(5x + 3)^2 + 2(5x + 3) - 2)^2 + 2(1(5x + 3)^2 + 2(5x + 3) - 2) - 3)^2 + 1) + 1)/(-2(1(-2(1(5x + 3)^2 + 2(5x + 3) - 2)^2 + 2(1(5x + 3)^2 + 2(5x + 3) - 2) - 3)^2 + 1)) and g(x) = -1sin(2\u03c0(-3|(-1|(-4x^2 + 1x) - 3| + 1) + 1| - 3) - 2) - 2 from x = 3.8 to x = 3.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (3((1(-2|(-3((3x - 2)/(-2x + 3))^2 - 4((3x - 2)/(-2x + 3))) - 2| - 2) + 3)/(3(-2|(-3((3x - 2)/(-2x + 3))^2 - 4((3x - 2)/(-2x + 3))) - 2| - 2) - 2)) + 3)/(-2((1(-2|(-3((3x - 2)/(-2x + 3))^2 - 4((3x - 2)/(-2x + 3))) - 2| - 2) + 3)/(3(-2|(-3((3x - 2)/(-2x + 3))^2 - 4((3x - 2)/(-2x + 3))) - 2| - 2) - 2)) - 2) and g(x) = -2sin(3\u03c0(-1(-1|((2x - 3)/(3x + 3))| + 2)) + 1) - 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1|(-3(2|(3(1cos(2\u03c0x + 1) - 1) + 2) + 2| + 2)^2 + 2) + 1| - 2 and g(x) = 5(-2|(-3e^(-1(-2|x + 1| + 3)) + 1) - 1| + 1) - 4 between the vertical lines x = -2.9 and x = -2.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2(-2sin(1\u03c0((-1(-3(-4x + 4)^2 - 1(-4x + 4) + 5))/(2(-3(-4x + 4)^2 - 1(-4x + 4) + 5) - 1)) - 2) + 1)^2 - 2(-2sin(1\u03c0((-1(-3(-4x + 4)^2 - 1(-4x + 4) + 5))/(2(-3(-4x + 4)^2 - 1(-4x + 4) + 5) - 1)) - 2) + 1) + 4 and g(x) = 1|((3(-2(-5x - 2)^2 + 4(-5x - 2) - 3) - 3)/(-2(-2(-5x - 2)^2 + 4(-5x - 2) - 3) - 2)) + 2| + 3 from x = -0.8 to x = -0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1(-3|(-2|((1(-1x^2 + 4x - 5) + 3)/(-1(-1x^2 + 4x - 5)))| + 2) - 2|)^2 - 3(-3|(-2|((1(-1x^2 + 4x - 5) + 3)/(-1(-1x^2 + 4x - 5)))| + 2) - 2|) - 5 and g(x) = -5((-1(2(-1x^2 + 5x + 2)^2 + 2(-1x^2 + 5x + 2) + 3) - 2)/(-1(2(-1x^2 + 5x + 2)^2 + 2(-1x^2 + 5x + 2) + 3) - 3))^2 + 3((-1(2(-1x^2 + 5x + 2)^2 + 2(-1x^2 + 5x + 2) + 3) - 2)/(-1(2(-1x^2 + 5x + 2)^2 + 2(-1x^2 + 5x + 2) + 3) - 3)) - 4 from x = 1.0 to x = 3.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "98.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 3(3(1(4(4x^2 - 4x + 1)^2 + 2(4x^2 - 4x + 1) - 4)^2 + 1(4(4x^2 - 4x + 1)^2 + 2(4x^2 - 4x + 1) - 4) - 3)^2 + 4(1(4(4x^2 - 4x + 1)^2 + 2(4x^2 - 4x + 1) - 4)^2 + 1(4(4x^2 - 4x + 1)^2 + 2(4x^2 - 4x + 1) - 4) - 3) - 1)^2 - 5(3(1(4(4x^2 - 4x + 1)^2 + 2(4x^2 - 4x + 1) - 4)^2 + 1(4(4x^2 - 4x + 1)^2 + 2(4x^2 - 4x + 1) - 4) - 3)^2 + 4(1(4(4x^2 - 4x + 1)^2 + 2(4x^2 - 4x + 1) - 4)^2 + 1(4(4x^2 - 4x + 1)^2 + 2(4x^2 - 4x + 1) - 4) - 3) - 1) + 1 and g(x) = 2(-1|(2e^(1(3x^2 + 1x - 3)) + 3)| + 3) + 3 between the vertical lines x = 0.0 and x = 0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "48.7", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -4((-2(2|(-3(-3e^(1x)) - 5) - 2| - 3) - 2)/(2(2|(-3(-3e^(1x)) - 5) - 2| - 3) + 3)) + 4, g(x) = -2e^(1(-1(3|(-3|x + 3| + 3) - 3| - 1)^2 - 4(3|(-3|x + 3| + 3) - 3| - 1) + 1)) + 3, x = -0.4, and x = -0.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2e^(-1(1(-2(-2|((-2x - 1)/(-1x - 1)) - 3| - 1)^2 - 5(-2|((-2x - 1)/(-1x - 1)) - 3| - 1)) + 4)) + 1 and g(x) = 3sin(1\u03c0(1(-1|((-1x + 2)/(1x)) - 1| - 1)^2 + 1(-1|((-1x + 2)/(1x)) - 1| - 1) - 1) - 2) between the vertical lines x = -4.3 and x = -3.0. 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) = 5(-4(1((1(5x - 1) - 2)/(1(5x - 1) - 3))^2 - 5((1(5x - 1) - 2)/(1(5x - 1) - 3)) + 1) + 5)^2 - 1(-4(1((1(5x - 1) - 2)/(1(5x - 1) - 3))^2 - 5((1(5x - 1) - 2)/(1(5x - 1) - 3)) + 1) + 5) - 5 and g(x) = 3cos(2\u03c0(2(-3|(2x - 2) + 3| + 1)^2 - 1(-3|(2x - 2) + 3| + 1) + 1) - 2) - 1 from x = 0.6 to x = 0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "51.5", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1|(-3(-2(3|((-1x + 1)/(1x + 2)) + 2| - 2) + 1)^2 + 5(-2(3|((-1x + 1)/(1x + 2)) + 2| - 2) + 1) + 4) - 2| - 2, g(x) = (3((1(-5((-3x - 3)/(3x - 1)) + 1) + 2)/(3(-5((-3x - 3)/(3x - 1)) + 1) - 1)) + 3)/(-3((1(-5((-3x - 3)/(3x - 1)) + 1) + 2)/(3(-5((-3x - 3)/(3x - 1)) + 1) - 1)) - 3), x = -3.6, and x = -3.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1(1sin(3\u03c0(4(-2|(-1x - 2)| - 1)^2 + 1) + 3) + 1)^2 + 3(1sin(3\u03c0(4(-2|(-1x - 2)| - 1)^2 + 1) + 3) + 1) - 3 and g(x) = 4(-3(-3(-5x + 2)^2 - 1(-5x + 2) + 1)) + 4 from x = 0.6 to x = 0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3|((1(2(3|((-2x - 2)/(-2x)) + 3| - 1)^2 - 4(3|((-2x - 2)/(-2x)) + 3| - 1) - 4) - 1)/(-1(2(3|((-2x - 2)/(-2x)) + 3| - 1)^2 - 4(3|((-2x - 2)/(-2x)) + 3| - 1) - 4) + 2))| + 1 and g(x) = (1(1|(-3cos(1\u03c0(-2x^2 - 4x - 3) + 3) + 1) - 3| + 1))/(2(1|(-3cos(1\u03c0(-2x^2 - 4x - 3) + 3) + 1) - 3| + 1)) from x = -0.4 to x = -0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (1(4((-3(2|(5x + 3) - 1| + 2) - 1)/(2(2|(5x + 3) - 1| + 2) + 3))^2 - 5((-3(2|(5x + 3) - 1| + 2) - 1)/(2(2|(5x + 3) - 1| + 2) + 3)) + 3) + 1)/(1(4((-3(2|(5x + 3) - 1| + 2) - 1)/(2(2|(5x + 3) - 1| + 2) + 3))^2 - 5((-3(2|(5x + 3) - 1| + 2) - 1)/(2(2|(5x + 3) - 1| + 2) + 3)) + 3) + 3) and g(x) = -2(-2sin(3\u03c0((2((2x + 2)/(-3x + 1)) - 2)/(2((2x + 2)/(-3x + 1))))) + 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": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1((-3(-3|(-1(1|x - 1| + 3) + 4) + 1| - 1))/(1(-3|(-1(1|x - 1| + 3) + 4) + 1| - 1) + 3))^2 - 5((-3(-3|(-1(1|x - 1| + 3) + 4) + 1| - 1))/(1(-3|(-1(1|x - 1| + 3) + 4) + 1| - 1) + 3)) and g(x) = (1(-3cos(3\u03c0(-1(4x^2 + 4x + 3) - 2) - 2) + 1) - 2)/(-1(-3cos(3\u03c0(-1(4x^2 + 4x + 3) - 2) - 2) + 1) - 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": "1.6", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1|((-1(-1sin(2\u03c0((-2(4x^2 + 2x + 5) + 1)/(3(4x^2 + 2x + 5) - 2)))))/(3(-1sin(2\u03c0((-2(4x^2 + 2x + 5) + 1)/(3(4x^2 + 2x + 5) - 2)))) - 1)) + 2| - 2 and g(x) = -4((-2(2((3x + 1)/(1x + 1)) - 1))/(2(2((3x + 1)/(1x + 1)) - 1) - 3))^2 + 3((-2(2((3x + 1)/(1x + 1)) - 1))/(2(2((3x + 1)/(1x + 1)) - 1) - 3)) + 4 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": "1.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2(1|(-1|(1(1sin(3\u03c0x - 3))^2 + 1(1sin(3\u03c0x - 3))) + 2| - 1) - 1| - 1) - 5 and g(x) = (1(2|((-3(3cos(3\u03c0x) - 2) - 1)/(3(3cos(3\u03c0x) - 2) - 2)) + 3| - 3) - 1)/(-2(2|((-3(3cos(3\u03c0x) - 2) - 1)/(3(3cos(3\u03c0x) - 2) - 2)) + 3| - 3)) between the vertical lines x = -2.0 and x = 2.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "46.9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3(-2(3|((1(-2x) + 3)/(-1(-2x) + 3)) + 1|) - 1) + 3 and g(x) = 4((1(-1|(-1|x - 3| + 3) + 3|) - 2)/(-1(-1|(-1|x - 3| + 3) + 3|) - 1)) + 5 from x = -3.6 to x = -2.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1|((2(2|((1(2x + 1) + 3)/(3(2x + 1))) - 2|) + 3)/(-3(2|((1(2x + 1) + 3)/(3(2x + 1))) - 2|) - 1)) + 3| + 2 and g(x) = -5((2(4(-1|x - 3|)^2 + 2(-1|x - 3|) + 2))/(-2(4(-1|x - 3|)^2 + 2(-1|x - 3|) + 2) + 3)) - 5 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1(4(1sin(2\u03c0(-2|(3|x + 1| - 3) + 1| - 1)) + 1) - 3) - 2 and g(x) = (2((-2(-5(-4x^2 + 4x + 4)^2 + 1(-4x^2 + 4x + 4) - 1) + 3)/(2(-5(-4x^2 + 4x + 4)^2 + 1(-4x^2 + 4x + 4) - 1))) + 1)/(-1((-2(-5(-4x^2 + 4x + 4)^2 + 1(-4x^2 + 4x + 4) - 1) + 3)/(2(-5(-4x^2 + 4x + 4)^2 + 1(-4x^2 + 4x + 4) - 1))) - 1) between the vertical lines x = -0.6 and x = 1.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "94.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (1(3|(-3|(2cos(1\u03c0(5x^2 - 2x - 5) - 1) - 1) + 2| + 1)| + 3) + 2)/(1(3|(-3|(2cos(1\u03c0(5x^2 - 2x - 5) - 1) - 1) + 2| + 1)| + 3) - 3), g(x) = 2(-4(3((-3x - 2)/(-2x - 3))^2 + 5((-3x - 2)/(-2x - 3)) - 4) - 5)^2 - 2(-4(3((-3x - 2)/(-2x - 3))^2 + 5((-3x - 2)/(-2x - 3)) - 4) - 5), x = -0.4, and x = -0.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 3((-2(-1|(-4(-3x + 2) - 5) - 2| + 2) + 2)/(1(-1|(-4(-3x + 2) - 5) - 2| + 2) + 2)) - 2 and g(x) = 2|(-3|(4(1|x - 2| + 3) - 1) + 1| + 3) - 1| between the vertical lines x = 0.9 and x = 1.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "91.8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -4(-1(-2((1((-2x - 1)/(2x + 2)) + 1)/(2((-2x - 1)/(2x + 2)) - 1)) - 2)^2 + 1(-2((1((-2x - 1)/(2x + 2)) + 1)/(2((-2x - 1)/(2x + 2)) - 1)) - 2) + 5)^2 + 2(-1(-2((1((-2x - 1)/(2x + 2)) + 1)/(2((-2x - 1)/(2x + 2)) - 1)) - 2)^2 + 1(-2((1((-2x - 1)/(2x + 2)) + 1)/(2((-2x - 1)/(2x + 2)) - 1)) - 2) + 5) + 3 and g(x) = -3|(1cos(2\u03c0((-2(3|x - 2| + 2) - 3)/(-2(3|x - 2| + 2))) - 1) - 3) - 1| + 1 from x = -0.6 to x = -0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3(-1|(1|(-2(4x + 4) + 3)| + 1) - 1|) + 1, g(x) = -1|(1|(-4(1e^(2x))^2 + 5(1e^(2x)) + 1) + 1| + 3) + 3| + 3, x = -0.9, and x = -0.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1(-5(1cos(1\u03c0(3|(3|x - 3| - 2) - 3| + 3) - 1) + 1)^2 - 1(1cos(1\u03c0(3|(3|x - 3| - 2) - 3| + 3) - 1) + 1) - 2) + 5 and g(x) = -3((-1(-2e^(2(-1x^2 + 5x + 1)) + 2) - 1)/(-3(-2e^(2(-1x^2 + 5x + 1)) + 2) + 2)) + 3 between the vertical lines x = -0.1 and x = -0.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2sin(1\u03c0((-1(5(-4((1x + 3)/(3x - 2))^2 + 4) + 3) + 3)/(-1(5(-4((1x + 3)/(3x - 2))^2 + 4) + 3) + 2)) - 1) - 2 and g(x) = 1|(-2|(-4(-3e^(1x)) - 3) - 1| + 1) - 1| - 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": "1.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 3|(-2|((1(5(-4x^2 - 2x + 5) - 5) - 1)/(-2(5(-4x^2 - 2x + 5) - 5) - 1)) - 1| - 1) + 2| - 1 and g(x) = 3|((-1(-2sin(2\u03c0((3x + 3)/(-3x + 1)) + 2) - 2) - 1)/(3(-2sin(2\u03c0((3x + 3)/(-3x + 1)) + 2) - 2) + 3)) - 2| + 3 between the vertical lines x = -1.3 and x = 0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15.4", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2sin(1\u03c0(1|((-1(-1|(1|x| + 2) - 3| - 1) - 2)/(2(-1|(1|x| + 2) - 3| - 1) + 2))|) + 2) - 1 and g(x) = (2(2e^(-2(-2((2x - 2)/(-1x - 3))^2 - 5((2x - 2)/(-1x - 3)) + 1)) - 2) - 2)/(2(2e^(-2(-2((2x - 2)/(-1x - 3))^2 - 5((2x - 2)/(-1x - 3)) + 1)) - 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -5(1(-3(-2|(-2|x + 3| - 2) + 3| + 2)^2 + 5(-2|(-2|x + 3| - 2) + 3| + 2)) + 3) + 4, g(x) = 1(4(1(1|x - 1| - 2)) - 1) + 2, x = -4.2, 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": "53.4", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -3|(3|(1(3(-2|x - 3| + 1)^2 + 2(-2|x - 3| + 1) - 1) - 2)| - 1) + 1| + 1, g(x) = (-3((2(-3e^(-2(-3|x - 1| + 3)) - 3) - 2)/(1(-3e^(-2(-3|x - 1| + 3)) - 3) - 3)) - 2)/(2((2(-3e^(-2(-3|x - 1| + 3)) - 3) - 2)/(1(-3e^(-2(-3|x - 1| + 3)) - 3) - 3)) + 2), x = 3.2, and x = 4.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18.6", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -3((1(-4(-3cos(1\u03c0(1x^2 + 1x + 4) - 3) - 1) - 5) + 3)/(2(-4(-3cos(1\u03c0(1x^2 + 1x + 4) - 3) - 1) - 5) - 1)) + 3, g(x) = 3((3(-3(-2sin(3\u03c0x - 1) - 1) - 5) - 2)/(3(-3(-2sin(3\u03c0x - 1) - 1) - 5) + 1))^2 - 4((3(-3(-2sin(3\u03c0x - 1) - 1) - 5) - 2)/(3(-3(-2sin(3\u03c0x - 1) - 1) - 5) + 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": "25.7", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2e^(-1(2|(-2|(2|((-2x - 2)/(1x)) + 3| - 2) - 2| + 3) + 3| - 3)) - 3 and g(x) = -1(1sin(2\u03c0(2((-1x - 2)/(2x)) - 2) + 1) + 1)^2 + 3(1sin(2\u03c0(2((-1x - 2)/(2x)) - 2) + 1) + 1) - 2 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": "2.7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2((-2(3|((-1((-2x)/(-1x - 3)) + 1)/(-1((-2x)/(-1x - 3)) + 3)) + 2| + 1) - 2)/(-2(3|((-1((-2x)/(-1x - 3)) + 1)/(-1((-2x)/(-1x - 3)) + 3)) + 2| + 1) - 3))^2 + 2((-2(3|((-1((-2x)/(-1x - 3)) + 1)/(-1((-2x)/(-1x - 3)) + 3)) + 2| + 1) - 2)/(-2(3|((-1((-2x)/(-1x - 3)) + 1)/(-1((-2x)/(-1x - 3)) + 3)) + 2| + 1) - 3)) + 2 and g(x) = (2(-3|(3cos(2\u03c0(-2|x + 1| + 2)) + 1)| + 2) - 1)/(3(-3|(3cos(2\u03c0(-2|x + 1| + 2)) + 1)| + 2) + 2) 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": "Calculate the area enclosed between the functions f(x) = -3|((1(4(1((2x + 1)/(2x)) - 5)^2 + 1(1((2x + 1)/(2x)) - 5) + 5) + 2)/(-1(4(1((2x + 1)/(2x)) - 5)^2 + 1(1((2x + 1)/(2x)) - 5) + 5) + 3))| - 1 and g(x) = (-3(-3|(1|(-3x^2 - 2x - 2) - 1| - 1) - 3| + 3) + 2)/(-3(-3|(1|(-3x^2 - 2x - 2) - 1| - 1) - 3| + 3)) 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": "5.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (2(-3((2(-1sin(1\u03c0(4x - 5) - 1) - 1) + 2)/(3(-1sin(1\u03c0(4x - 5) - 1) - 1)))^2 - 1((2(-1sin(1\u03c0(4x - 5) - 1) - 1) + 2)/(3(-1sin(1\u03c0(4x - 5) - 1) - 1))) - 4) - 1)/(1(-3((2(-1sin(1\u03c0(4x - 5) - 1) - 1) + 2)/(3(-1sin(1\u03c0(4x - 5) - 1) - 1)))^2 - 1((2(-1sin(1\u03c0(4x - 5) - 1) - 1) + 2)/(3(-1sin(1\u03c0(4x - 5) - 1) - 1))) - 4)), g(x) = -2|((3((-1((1x)/(-3x + 4)) + 1)/(-2((1x)/(-3x + 4)) + 3)) + 2)/(-3((-1((1x)/(-3x + 4)) + 1)/(-2((1x)/(-3x + 4)) + 3)) + 1)) - 3| + 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3(-5(2cos(2\u03c0(2|(-4x + 3) + 2| - 1) - 3)) + 3) - 3, g(x) = 5((3(2((2x - 2)/(-2x + 1)) + 3) - 2)/(3(2((2x - 2)/(-2x + 1)) + 3) - 2)) + 4, x = 4.9, and x = 5.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 5(-1|((-1(2|(2|x - 2| - 1) - 1| - 3) + 3)/(3(2|(2|x - 2| - 1) - 1| - 3) - 2)) - 3| + 1) + 2 and g(x) = 1(1(-3|(-1x - 5) - 2| + 2)) - 1 from x = 2.1 to x = 2.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2(-2sin(3\u03c0(2|(-5(-1x + 5)^2 - 4(-1x + 5) + 3)| - 1) - 1) + 2)^2 - 4(-2sin(3\u03c0(2|(-5(-1x + 5)^2 - 4(-1x + 5) + 3)| - 1) - 1) + 2) + 1 and g(x) = 2cos(2\u03c0(-1|(3|((3x - 2)/(-1x - 3)) + 2| + 1) + 1| - 1)) + 1 from x = 3.8 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": "Calculate the area enclosed between the functions f(x) = 1|(-1(1|(-3(2|x| + 2)^2 + 2(2|x| + 2) - 2)| - 2) + 3)| - 2 and g(x) = -2(-1|(-2(1x^2 + 4x - 2) + 2) - 2| + 2) + 1 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": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1(5(-1sin(1\u03c0(3(3|x| + 1)^2 + 5(3|x| + 1) - 3) + 1) + 2)^2 - 4(-1sin(1\u03c0(3(3|x| + 1)^2 + 5(3|x| + 1) - 3) + 1) + 2) + 4)^2 + 5(5(-1sin(1\u03c0(3(3|x| + 1)^2 + 5(3|x| + 1) - 3) + 1) + 2)^2 - 4(-1sin(1\u03c0(3(3|x| + 1)^2 + 5(3|x| + 1) - 3) + 1) + 2) + 4) - 4 and g(x) = 4(4(1|(-2sin(1\u03c0x - 1) + 2) - 3| + 1)^2 - 2(1|(-2sin(1\u03c0x - 1) + 2) - 3| + 1) - 4) - 3 between the vertical lines x = -0.5 and x = 0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "244.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3cos(2\u03c0(-3|(2|(-1(1|x - 3| - 1) + 1)| - 1)| - 1)) + 3 and g(x) = (1(2|(-1e^(-2(-1|x| - 3)) - 3) + 2| + 3) + 2)/(3(2|(-1e^(-2(-1|x| - 3)) - 3) + 2| + 3) + 2) between the vertical lines x = -0.5 and x = -0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2cos(3\u03c0(2((-1((3(-1x^2 + 4x + 1) + 1)/(2(-1x^2 + 4x + 1) - 1)))/(-3((3(-1x^2 + 4x + 1) + 1)/(2(-1x^2 + 4x + 1) - 1)) - 3))^2 + 5((-1((3(-1x^2 + 4x + 1) + 1)/(2(-1x^2 + 4x + 1) - 1)))/(-3((3(-1x^2 + 4x + 1) + 1)/(2(-1x^2 + 4x + 1) - 1)) - 3)) + 4) + 3) - 2 and g(x) = 2(5(-2cos(2\u03c0(-5x + 2) + 2) - 1))^2 - 5(5(-2cos(2\u03c0(-5x + 2) + 2) - 1)) - 3 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": "31.8", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-3((-2(-3e^(-1(-4(-3x + 4) - 1)) + 2))/(3(-3e^(-1(-4(-3x + 4) - 1)) + 2) + 1)) + 1)/(-3((-2(-3e^(-1(-4(-3x + 4) - 1)) + 2))/(3(-3e^(-1(-4(-3x + 4) - 1)) + 2) + 1)) - 1), g(x) = 1(2|(2|(-5x + 1)|) - 3| + 2)^2 - 5(2|(2|(-5x + 1)|) - 3| + 2) + 2, 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": "1.9", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2|(-2e^(-1(2((3(2|x + 3| - 3) - 2)/(3(2|x + 3| - 3) - 2))^2 + 5((3(2|x + 3| - 3) - 2)/(3(2|x + 3| - 3) - 2)) + 5)) - 1) + 2| + 2, g(x) = 1(-1(3(-3x^2 - 4x + 1) - 1)^2 + 1)^2 - 3(-1(3(-3x^2 - 4x + 1) - 1)^2 + 1) - 5, 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": "1.8", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -3|(-2|((3(-2|(-1cos(2\u03c0x - 2) + 1) - 2| + 2) - 2)/(2(-2|(-1cos(2\u03c0x - 2) + 1) - 2| + 2))) + 2| + 2) + 2| - 2, g(x) = -4((2((-3(3sin(1\u03c0x + 2) - 3))/(-3(3sin(1\u03c0x + 2) - 3) + 1)) + 1)/(-1((-3(3sin(1\u03c0x + 2) - 3))/(-3(3sin(1\u03c0x + 2) - 3) + 1)) + 3))^2 + 1((2((-3(3sin(1\u03c0x + 2) - 3))/(-3(3sin(1\u03c0x + 2) - 3) + 1)) + 1)/(-1((-3(3sin(1\u03c0x + 2) - 3))/(-3(3sin(1\u03c0x + 2) - 3) + 1)) + 3)) - 1, x = 0.6, and x = 0.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -4(-2sin(2\u03c0(-1(-1(-3x^2 - 3)^2 - 1(-3x^2 - 3) + 3)^2 - 4(-1(-3x^2 - 3)^2 - 1(-3x^2 - 3) + 3) + 2) + 1) - 2) and g(x) = -1(3(-3((1x - 2)/(-3x - 3)) - 1) - 1)^2 - 4(3(-3((1x - 2)/(-3x - 3)) - 1) - 1) + 2 between the vertical lines x = 1.7 and x = 1.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (1(-2((-2(-5(-3|x - 1| + 1)^2 + 2(-3|x - 1| + 1) + 3) - 3)/(-1(-5(-3|x - 1| + 1)^2 + 2(-3|x - 1| + 1) + 3) - 2))^2 - 1((-2(-5(-3|x - 1| + 1)^2 + 2(-3|x - 1| + 1) + 3) - 3)/(-1(-5(-3|x - 1| + 1)^2 + 2(-3|x - 1| + 1) + 3) - 2)) + 4) + 3)/(3(-2((-2(-5(-3|x - 1| + 1)^2 + 2(-3|x - 1| + 1) + 3) - 3)/(-1(-5(-3|x - 1| + 1)^2 + 2(-3|x - 1| + 1) + 3) - 2))^2 - 1((-2(-5(-3|x - 1| + 1)^2 + 2(-3|x - 1| + 1) + 3) - 3)/(-1(-5(-3|x - 1| + 1)^2 + 2(-3|x - 1| + 1) + 3) - 2)) + 4) - 2) and g(x) = 1|(-5((3((-3x + 3)/(1x + 2)) - 3)/(-2((-3x + 3)/(1x + 2)) - 2))) + 1| - 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": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (1(2|(-1(1(5x + 2) + 5)^2 - 3(1(5x + 2) + 5) - 2) + 2|) - 2)/(1(2|(-1(1(5x + 2) + 5)^2 - 3(1(5x + 2) + 5) - 2) + 2|) - 3), g(x) = 2(-2cos(2\u03c0(-5(-3|x - 1| + 3)^2 + 4(-3|x - 1| + 3) - 4)) - 2) + 5, 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": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -3(-3cos(2\u03c0(-1|((2(-3x^2 - 4x) + 3)/(1(-3x^2 - 4x) + 3)) - 3|) - 3) + 2)^2 - 1(-3cos(2\u03c0(-1|((2(-3x^2 - 4x) + 3)/(1(-3x^2 - 4x) + 3)) - 3|) - 3) + 2), g(x) = -2cos(1\u03c0(-4((-2((1x - 1)/(3x - 1)) + 1)/(-2((1x - 1)/(3x - 1)) + 3))) + 1) + 1, 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": "2.9", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2|(2|((-1(-2|((1x)/(-3x + 1)) + 2| + 1) + 3)/(-3(-2|((1x)/(-3x + 1)) + 2| + 1))) + 3| + 1) + 3| - 3, g(x) = (3(-3(3(1x^2 - 4x + 4)^2 + 3(1x^2 - 4x + 4) - 5) - 1) + 3)/(-2(-3(3(1x^2 - 4x + 4)^2 + 3(1x^2 - 4x + 4) - 5) - 1)), 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": "39.4", "dataset": "MATH"}