{"messages": [{"content": "How many local minima does the function f(x) = -2(1|((-3(1sin(2\u03c0(3(-4x + 5) - 4) - 3) - 3) - 2)/(-2(1sin(2\u03c0(3(-4x + 5) - 4) - 3) - 3) + 1)) + 3| + 1)^2 + 5(1|((-3(1sin(2\u03c0(3(-4x + 5) - 4) - 3) - 3) - 2)/(-2(1sin(2\u03c0(3(-4x + 5) - 4) - 3) - 3) + 1)) + 3| + 1) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "240", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -3(3|(-5(-2sin(1\u03c0(-2(-3x^2 - 1x + 2) - 4) + 2) + 1) - 4) - 3| - 2)^2 + 1(3|(-5(-2sin(1\u03c0(-2(-3x^2 - 1x + 2) - 4) + 2) + 1) - 4) - 3| - 2) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "168", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = 5(4((-2(-2sin(2\u03c0(-3|(-3x^2 - 4x + 4) - 2| + 3) - 3) + 1) + 1)/(1(-2sin(2\u03c0(-3|(-3x^2 - 4x + 4) - 2| + 3) - 3) + 1) - 3))^2 - 4((-2(-2sin(2\u03c0(-3|(-3x^2 - 4x + 4) - 2| + 3) - 3) + 1) + 1)/(1(-2sin(2\u03c0(-3|(-3x^2 - 4x + 4) - 2| + 3) - 3) + 1) - 3)) + 1) + 4 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "151", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -2((1(-5(2(5(1x^2 - 3x + 5) - 1)^2 - 4)^2 + 2(2(5(1x^2 - 3x + 5) - 1)^2 - 4) + 4) - 3)/(-3(-5(2(5(1x^2 - 3x + 5) - 1)^2 - 4)^2 + 2(2(5(1x^2 - 3x + 5) - 1)^2 - 4) + 4) + 1)) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -3(-3|((-3(-1(-1(-2cos(3\u03c0x + 2) + 3)^2 + 3(-2cos(3\u03c0x + 2) + 3) + 2) - 5) + 2)/(1(-1(-1(-2cos(3\u03c0x + 2) + 3)^2 + 3(-2cos(3\u03c0x + 2) + 3) + 2) - 5) - 3)) + 1| + 3)^2 + 5(-3|((-3(-1(-1(-2cos(3\u03c0x + 2) + 3)^2 + 3(-2cos(3\u03c0x + 2) + 3) + 2) - 5) + 2)/(1(-1(-1(-2cos(3\u03c0x + 2) + 3)^2 + 3(-2cos(3\u03c0x + 2) + 3) + 2) - 5) - 3)) + 1| + 3) - 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "252", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -4(-2(3((2(-1(-2sin(2\u03c0x + 1) - 2) - 5))/(-3(-1(-2sin(2\u03c0x + 1) - 2) - 5) + 1))^2 + 5((2(-1(-2sin(2\u03c0x + 1) - 2) - 5))/(-3(-1(-2sin(2\u03c0x + 1) - 2) - 5) + 1)) + 5)^2 + 1)^2 + 5(-2(3((2(-1(-2sin(2\u03c0x + 1) - 2) - 5))/(-3(-1(-2sin(2\u03c0x + 1) - 2) - 5) + 1))^2 + 5((2(-1(-2sin(2\u03c0x + 1) - 2) - 5))/(-3(-1(-2sin(2\u03c0x + 1) - 2) - 5) + 1)) + 5)^2 + 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 5(-1|(3|(1sin(2\u03c0((1((3x - 3)/(-1x + 3)) + 3)/(2((3x - 3)/(-1x + 3)) + 3)) - 2) + 2)|) - 3| - 2) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = (-2(2cos(2\u03c0((-1(-3(-4(-1|x + 1| + 1) - 3) - 2) + 2)/(-2(-3(-4(-1|x + 1| + 1) - 3) - 2) - 3)) + 1)) - 2)/(3(2cos(2\u03c0((-1(-3(-4(-1|x + 1| + 1) - 3) - 2) + 2)/(-2(-3(-4(-1|x + 1| + 1) - 3) - 2) - 3)) + 1))) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = (-1(1(-2cos(2\u03c0(1(-3(-2|x - 3|)^2 - 5(-2|x - 3|) - 1)) - 1) - 1)^2 - 1(-2cos(2\u03c0(1(-3(-2|x - 3|)^2 - 5(-2|x - 3|) - 1)) - 1) - 1) + 1) + 3)/(-3(1(-2cos(2\u03c0(1(-3(-2|x - 3|)^2 - 5(-2|x - 3|) - 1)) - 1) - 1)^2 - 1(-2cos(2\u03c0(1(-3(-2|x - 3|)^2 - 5(-2|x - 3|) - 1)) - 1) - 1) + 1)) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "461", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = (2(-2cos(3\u03c0(-1((-2((1(-2x - 5) - 2)/(-2(-2x - 5) - 2)) + 1)/(-2((1(-2x - 5) - 2)/(-2(-2x - 5) - 2))))) + 1) + 2) - 3)/(3(-2cos(3\u03c0(-1((-2((1(-2x - 5) - 2)/(-2(-2x - 5) - 2)) + 1)/(-2((1(-2x - 5) - 2)/(-2(-2x - 5) - 2))))) + 1) + 2) + 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = (-2((3(-1(-4((-1(1cos(2\u03c0x + 2)) - 1)/(-1(1cos(2\u03c0x + 2)) - 2)) - 2) + 3) + 2)/(-2(-1(-4((-1(1cos(2\u03c0x + 2)) - 1)/(-1(1cos(2\u03c0x + 2)) - 2)) - 2) + 3) - 2)) + 2)/(1((3(-1(-4((-1(1cos(2\u03c0x + 2)) - 1)/(-1(1cos(2\u03c0x + 2)) - 2)) - 2) + 3) + 2)/(-2(-1(-4((-1(1cos(2\u03c0x + 2)) - 1)/(-1(1cos(2\u03c0x + 2)) - 2)) - 2) + 3) - 2)) + 2) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -3|(4((2((2(2(-3|x + 1| + 3)^2 - 4(-3|x + 1| + 3) - 4) - 3)/(1(2(-3|x + 1| + 3)^2 - 4(-3|x + 1| + 3) - 4) + 2)) - 3)/(-2((2(2(-3|x + 1| + 3)^2 - 4(-3|x + 1| + 3) - 4) - 3)/(1(2(-3|x + 1| + 3)^2 - 4(-3|x + 1| + 3) - 4) + 2)) - 2)) - 1) + 2| - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = (-2(-4(-1((3(-5(-1e^(2x) + 1)^2 + 4(-1e^(2x) + 1) - 4) - 2)/(2(-5(-1e^(2x) + 1)^2 + 4(-1e^(2x) + 1) - 4) - 1)) + 5)^2 - 3(-1((3(-5(-1e^(2x) + 1)^2 + 4(-1e^(2x) + 1) - 4) - 2)/(2(-5(-1e^(2x) + 1)^2 + 4(-1e^(2x) + 1) - 4) - 1)) + 5) - 2) + 1)/(-3(-4(-1((3(-5(-1e^(2x) + 1)^2 + 4(-1e^(2x) + 1) - 4) - 2)/(2(-5(-1e^(2x) + 1)^2 + 4(-1e^(2x) + 1) - 4) - 1)) + 5)^2 - 3(-1((3(-5(-1e^(2x) + 1)^2 + 4(-1e^(2x) + 1) - 4) - 2)/(2(-5(-1e^(2x) + 1)^2 + 4(-1e^(2x) + 1) - 4) - 1)) + 5) - 2) - 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "27", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = (1((1(2(2e^(2(-1(-3|x + 2| + 3) + 4)) - 1) - 4) + 2)/(1(2(2e^(2(-1(-3|x + 2| + 3) + 4)) - 1) - 4) + 1)))/(-2((1(2(2e^(2(-1(-3|x + 2| + 3) + 4)) - 1) - 4) + 2)/(1(2(2e^(2(-1(-3|x + 2| + 3) + 4)) - 1) - 4) + 1)) + 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -2|(-4(2|((-3(-1|(-2x^2 + 5x + 5) + 2| + 2))/(-3(-1|(-2x^2 + 5x + 5) + 2| + 2) + 4)) - 2| + 3) + 2) - 2| - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 4(5(3|((-2(4((-2x - 2)/(1x))^2 + 5((-2x - 2)/(1x)) - 3) - 2)/(-3(4((-2x - 2)/(1x))^2 + 5((-2x - 2)/(1x)) - 3) + 1))| + 1)^2 - 2(3|((-2(4((-2x - 2)/(1x))^2 + 5((-2x - 2)/(1x)) - 3) - 2)/(-3(4((-2x - 2)/(1x))^2 + 5((-2x - 2)/(1x)) - 3) + 1))| + 1) + 2) - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = (3(5(-3(3(-1|(1x + 2) - 2| + 2)^2 + 1(-1|(1x + 2) - 2| + 2) + 4) + 1) - 4))/(1(5(-3(3(-1|(1x + 2) - 2| + 2)^2 + 1(-1|(1x + 2) - 2| + 2) + 4) + 1) - 4)) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "74", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 1sin(1\u03c0(2(-4(1|((-3(-3|x + 2| - 1) - 2)/(2(-3|x + 2| - 1))) + 3| + 2) + 2)^2 + 3)) + 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "138", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = (-1((-3(-3(-4(-3cos(1\u03c0(2|x| - 3) - 3))) + 3) + 1)/(1(-3(-4(-3cos(1\u03c0(2|x| - 3) - 3))) + 3) + 1)) + 2)/(-3((-3(-3(-4(-3cos(1\u03c0(2|x| - 3) - 3))) + 3) + 1)/(1(-3(-4(-3cos(1\u03c0(2|x| - 3) - 3))) + 3) + 1))) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 1(2|(2e^(-2((1(-1((2x + 3)/(-1x - 1))^2 - 3((2x + 3)/(-1x - 1)) - 3) + 2)/(-2(-1((2x + 3)/(-1x - 1))^2 - 3((2x + 3)/(-1x - 1)) - 3) - 2))) - 3) - 1| - 2)^2 + 1(2|(2e^(-2((1(-1((2x + 3)/(-1x - 1))^2 - 3((2x + 3)/(-1x - 1)) - 3) + 2)/(-2(-1((2x + 3)/(-1x - 1))^2 - 3((2x + 3)/(-1x - 1)) - 3) - 2))) - 3) - 1| - 2) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 2((-1(-2|(-1|(-5(4x - 5) - 2) + 2| + 3) - 3| - 1) - 1)/(-3(-2|(-1|(-5(4x - 5) - 2) + 2| + 3) - 3| - 1) - 3)) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "222", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 2|(1|((2(-1(-2cos(1\u03c0(-1x^2 - 1x + 2) - 1) + 3) - 4) + 3)/(3(-1(-2cos(1\u03c0(-1x^2 - 1x + 2) - 1) + 3) - 4) - 2)) - 1| + 1) - 1| + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "101", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -2cos(2\u03c0(3|(2(3|((3(2|x - 3| + 1) - 3)/(-1(2|x - 3| + 1) - 3)) + 2| - 1)^2 + 3(3|((3(2|x - 3| + 1) - 3)/(-1(2|x - 3| + 1) - 3)) + 2| - 1) - 3)| - 3) - 1) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "99", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = (-3(4((-2(2|((-3(-3sin(2\u03c0x - 2) - 1) - 3)/(-2(-3sin(2\u03c0x - 2) - 1))) - 3| + 1) - 3)/(3(2|((-3(-3sin(2\u03c0x - 2) - 1) - 3)/(-2(-3sin(2\u03c0x - 2) - 1))) - 3| + 1))) + 3) + 2)/(1(4((-2(2|((-3(-3sin(2\u03c0x - 2) - 1) - 3)/(-2(-3sin(2\u03c0x - 2) - 1))) - 3| + 1) - 3)/(3(2|((-3(-3sin(2\u03c0x - 2) - 1) - 3)/(-2(-3sin(2\u03c0x - 2) - 1))) - 3| + 1))) + 3) + 1) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "117", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 1(3cos(3\u03c0(3(-4(-4(-2|x - 2| + 2)^2 + 3(-2|x - 2| + 2)) + 3) + 3) + 1) - 3)^2 + 2(3cos(3\u03c0(3(-4(-4(-2|x - 2| + 2)^2 + 3(-2|x - 2| + 2)) + 3) + 3) + 1) - 3) - 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "133", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -1|(-2(1sin(1\u03c0(3(-5(-3|x - 3| - 2)^2 - 1)^2 + 1(-5(-3|x - 3| - 2)^2 - 1) + 3) + 3) + 2) - 1) - 3| + 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = -1(-3(-3|(-1((2((2x)/(1x - 2)) - 1)/(3((2x)/(1x - 2)) + 1))^2 - 4((2((2x)/(1x - 2)) - 1)/(3((2x)/(1x - 2)) + 1)) + 1)| + 1)^2 + 3(-3|(-1((2((2x)/(1x - 2)) - 1)/(3((2x)/(1x - 2)) + 1))^2 - 4((2((2x)/(1x - 2)) - 1)/(3((2x)/(1x - 2)) + 1)) + 1)| + 1) - 1) - 4 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 2(-4(2(1|(-1(1sin(1\u03c0x - 1) + 3)^2 + 2(1sin(1\u03c0x - 1) + 3) - 2) + 1| + 2) - 2)^2 - 3(2(1|(-1(1sin(1\u03c0x - 1) + 3)^2 + 2(1sin(1\u03c0x - 1) + 3) - 2) + 1| + 2) - 2) - 4)^2 - 3(-4(2(1|(-1(1sin(1\u03c0x - 1) + 3)^2 + 2(1sin(1\u03c0x - 1) + 3) - 2) + 1| + 2) - 2)^2 - 3(2(1|(-1(1sin(1\u03c0x - 1) + 3)^2 + 2(1sin(1\u03c0x - 1) + 3) - 2) + 1| + 2) - 2) - 4) + 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = (-1(5(3sin(1\u03c0(3((-1(-1|x + 2| - 2) + 2)/(-2(-1|x + 2| - 2) - 1)) - 1) - 1) - 2) + 3) - 2)/(2(5(3sin(1\u03c0(3((-1(-1|x + 2| - 2) + 2)/(-2(-1|x + 2| - 2) - 1)) - 1) - 1) - 2) + 3) - 1) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -1|(-1(-4(2sin(2\u03c0(-3|(4x) + 3| - 1) + 1) - 3)^2 + 1(2sin(2\u03c0(-3|(4x) + 3| - 1) + 1) - 3) - 3)^2 + 1) + 3| in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "477", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = (1(3|(1cos(2\u03c0((1(4(3x - 1) + 5) - 3)/(-2(4(3x - 1) + 5) - 3)) + 1) - 1) + 2| - 2) + 1)/(-2(3|(1cos(2\u03c0((1(4(3x - 1) + 5) - 3)/(-2(4(3x - 1) + 5) - 3)) + 1) - 1) + 2| - 2) - 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = (-2(5(1cos(2\u03c0(-2(4(-1x + 5) + 4) - 5) - 2) + 1)^2 + 4(1cos(2\u03c0(-2(4(-1x + 5) + 4) - 5) - 2) + 1) + 1) + 3)/(2(5(1cos(2\u03c0(-2(4(-1x + 5) + 4) - 5) - 2) + 1)^2 + 4(1cos(2\u03c0(-2(4(-1x + 5) + 4) - 5) - 2) + 1) + 1) - 1) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "320", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = (-3(2|(3((2(2(-1x^2 - 4x)^2 + 5(-1x^2 - 4x) - 1))/(-2(2(-1x^2 - 4x)^2 + 5(-1x^2 - 4x) - 1) - 2))^2 - 1((2(2(-1x^2 - 4x)^2 + 5(-1x^2 - 4x) - 1))/(-2(2(-1x^2 - 4x)^2 + 5(-1x^2 - 4x) - 1) - 2)) + 3) + 1| - 2) + 1)/(2(2|(3((2(2(-1x^2 - 4x)^2 + 5(-1x^2 - 4x) - 1))/(-2(2(-1x^2 - 4x)^2 + 5(-1x^2 - 4x) - 1) - 2))^2 - 1((2(2(-1x^2 - 4x)^2 + 5(-1x^2 - 4x) - 1))/(-2(2(-1x^2 - 4x)^2 + 5(-1x^2 - 4x) - 1) - 2)) + 3) + 1| - 2) + 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = (-1(-2sin(2\u03c0(-2(-1|(5(1|x - 2| - 3) - 1) - 1| - 2)^2 - 3(-1|(5(1|x - 2| - 3) - 1) - 1| - 2) + 2) + 2) + 1))/(2(-2sin(2\u03c0(-2(-1|(5(1|x - 2| - 3) - 1) - 1| - 2)^2 - 3(-1|(5(1|x - 2| - 3) - 1) - 1| - 2) + 2) + 2) + 1) + 1) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "335", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -2|((-2(-2sin(3\u03c0((-3(4(3x^2 - 4) - 4) + 3)/(1(4(3x^2 - 4) - 4) + 1)) + 1) - 2) - 1)/(3(-2sin(3\u03c0((-3(4(3x^2 - 4) - 4) + 3)/(1(4(3x^2 - 4) - 4) + 1)) + 1) - 2) + 1)) - 2| - 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = (1(-1(-2|((-1(3|(1sin(3\u03c0x + 3) + 2) + 1| - 2) - 2)/(2(3|(1sin(3\u03c0x + 3) + 2) + 1| - 2) + 1))| - 1)^2 - 5(-2|((-1(3|(1sin(3\u03c0x + 3) + 2) + 1| - 2) - 2)/(2(3|(1sin(3\u03c0x + 3) + 2) + 1| - 2) + 1))| - 1) + 3) + 2)/(-2(-1(-2|((-1(3|(1sin(3\u03c0x + 3) + 2) + 1| - 2) - 2)/(2(3|(1sin(3\u03c0x + 3) + 2) + 1| - 2) + 1))| - 1)^2 - 5(-2|((-1(3|(1sin(3\u03c0x + 3) + 2) + 1| - 2) - 2)/(2(3|(1sin(3\u03c0x + 3) + 2) + 1| - 2) + 1))| - 1) + 3) + 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -2|(3((3(1sin(3\u03c0(3(3x - 1)^2 - 1(3x - 1) - 5) + 2)) - 2)/(-3(1sin(3\u03c0(3(3x - 1)^2 - 1(3x - 1) - 5) + 2)) - 3)) - 3) + 2| + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = (-2((1(-3|(-1(-2sin(3\u03c0(1|x + 3| - 2) + 1)) - 5) - 2| - 1) + 1)/(2(-3|(-1(-2sin(3\u03c0(1|x + 3| - 2) + 1)) - 5) - 2| - 1) - 3)) + 3)/(-1((1(-3|(-1(-2sin(3\u03c0(1|x + 3| - 2) + 1)) - 5) - 2| - 1) + 1)/(2(-3|(-1(-2sin(3\u03c0(1|x + 3| - 2) + 1)) - 5) - 2| - 1) - 3)) - 3) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "61", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 3|((-3(4(2|(2cos(1\u03c0(2|x + 1| + 3) - 1) + 1) + 2| + 2)^2 + 5(2|(2cos(1\u03c0(2|x + 1| + 3) - 1) + 1) + 2| + 2) + 1) + 3)/(1(4(2|(2cos(1\u03c0(2|x + 1| + 3) - 1) + 1) + 2| + 2)^2 + 5(2|(2cos(1\u03c0(2|x + 1| + 3) - 1) + 1) + 2| + 2) + 1))) + 2| + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -2|((1(2sin(3\u03c0(1(-1(1x - 5) + 1) - 4) - 2) + 1) - 2)/(2(2sin(3\u03c0(1(-1(1x - 5) + 1) - 4) - 2) + 1))) + 2| - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -4(3|(2((3(1cos(3\u03c0(4x - 2) - 2) + 2) + 1)/(-3(1cos(3\u03c0(4x - 2) - 2) + 2) + 2))^2 - 2((3(1cos(3\u03c0(4x - 2) - 2) + 2) + 1)/(-3(1cos(3\u03c0(4x - 2) - 2) + 2) + 2)) + 2) + 1| + 3)^2 + 1(3|(2((3(1cos(3\u03c0(4x - 2) - 2) + 2) + 1)/(-3(1cos(3\u03c0(4x - 2) - 2) + 2) + 2))^2 - 2((3(1cos(3\u03c0(4x - 2) - 2) + 2) + 1)/(-3(1cos(3\u03c0(4x - 2) - 2) + 2) + 2)) + 2) + 1| + 3) + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "59", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -2(-3|(5(-3(-2e^(1(1x + 2)) + 2)^2 - 3(-2e^(1(1x + 2)) + 2) + 5)^2 + 1(-3(-2e^(1(1x + 2)) + 2)^2 - 3(-2e^(1(1x + 2)) + 2) + 5) + 1) - 2| + 1) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 3((-2(-2|(-1(4((2x)/(-2x - 3))^2 - 5((2x)/(-2x - 3)) - 2)^2 - 5(4((2x)/(-2x - 3))^2 - 5((2x)/(-2x - 3)) - 2) - 1) - 1| - 1) + 3)/(2(-2|(-1(4((2x)/(-2x - 3))^2 - 5((2x)/(-2x - 3)) - 2)^2 - 5(4((2x)/(-2x - 3))^2 - 5((2x)/(-2x - 3)) - 2) - 1) - 1| - 1) + 1))^2 - 4((-2(-2|(-1(4((2x)/(-2x - 3))^2 - 5((2x)/(-2x - 3)) - 2)^2 - 5(4((2x)/(-2x - 3))^2 - 5((2x)/(-2x - 3)) - 2) - 1) - 1| - 1) + 3)/(2(-2|(-1(4((2x)/(-2x - 3))^2 - 5((2x)/(-2x - 3)) - 2)^2 - 5(4((2x)/(-2x - 3))^2 - 5((2x)/(-2x - 3)) - 2) - 1) - 1| - 1) + 1)) + 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -2cos(3\u03c0(-2|((-2(-1(-5(2|x - 2| - 2)^2 + 1(2|x - 2| - 2) + 5) - 2) + 2)/(-3(-1(-5(2|x - 2| - 2)^2 + 1(2|x - 2| - 2) + 5) - 2) - 3))| - 3) - 2) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -2|((3(-1(3(-1sin(1\u03c0(3|x - 3| + 2) + 1) + 1)^2 - 2(-1sin(1\u03c0(3|x - 3| + 2) + 1) + 1) + 1)^2 + 5(3(-1sin(1\u03c0(3|x - 3| + 2) + 1) + 1)^2 - 2(-1sin(1\u03c0(3|x - 3| + 2) + 1) + 1) + 1) - 5) + 3)/(-2(-1(3(-1sin(1\u03c0(3|x - 3| + 2) + 1) + 1)^2 - 2(-1sin(1\u03c0(3|x - 3| + 2) + 1) + 1) + 1)^2 + 5(3(-1sin(1\u03c0(3|x - 3| + 2) + 1) + 1)^2 - 2(-1sin(1\u03c0(3|x - 3| + 2) + 1) + 1) + 1) - 5))) + 2| in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "268", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -5(-1(-1cos(1\u03c0(-1(1|(-5x - 3) - 1| + 1) - 3) + 2) + 3) - 4) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "51", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -3|(3(2cos(1\u03c0(-4((-1(3x^2 - 5) - 1)/(-2(3x^2 - 5) - 1))^2 + 4((-1(3x^2 - 5) - 1)/(-2(3x^2 - 5) - 1)) + 5) - 2) + 2) - 5) - 3| + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -1(3|(2|(-2cos(2\u03c0(5(1|x - 3| + 2) + 1) - 2)) + 1| - 1) + 3| + 1)^2 + 3(3|(2|(-2cos(2\u03c0(5(1|x - 3| + 2) + 1) - 2)) + 1| - 1) + 3| + 1) + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "365", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 1|(-3|(1|(-2|(-4(1x^2 - 1x - 2) - 2) - 3| + 3) + 3| - 2) + 2|)| - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 3(-2|((-1(-3cos(1\u03c0((3(-3x^2 + 5x - 1) + 2)/(2(-3x^2 + 5x - 1) + 1)) + 3) + 3) - 2)/(-3(-3cos(1\u03c0((3(-3x^2 + 5x - 1) + 2)/(2(-3x^2 + 5x - 1) + 1)) + 3) + 3) + 2)) + 1|) - 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -2sin(2\u03c0(5(-5(1(-3|(-1x^2 - 5x + 2) + 2| + 1)^2 + 1(-3|(-1x^2 - 5x + 2) + 2| + 1) + 2) + 1) + 1) - 2) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "63", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = (-3(1|((-3(-2(-5(1x^2 - 1x - 3)^2 + 4)^2 - 5(-5(1x^2 - 1x - 3)^2 + 4) - 1) + 3)/(1(-2(-5(1x^2 - 1x - 3)^2 + 4)^2 - 5(-5(1x^2 - 1x - 3)^2 + 4) - 1) + 3)) + 2| - 2) - 2)/(2(1|((-3(-2(-5(1x^2 - 1x - 3)^2 + 4)^2 - 5(-5(1x^2 - 1x - 3)^2 + 4) - 1) + 3)/(1(-2(-5(1x^2 - 1x - 3)^2 + 4)^2 - 5(-5(1x^2 - 1x - 3)^2 + 4) - 1) + 3)) + 2| - 2) - 1) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -5((1((-2(1sin(3\u03c0(-1(-2x^2 + 4x)) - 2) + 1) + 3)/(3(1sin(3\u03c0(-1(-2x^2 + 4x)) - 2) + 1))) - 1)/(-2((-2(1sin(3\u03c0(-1(-2x^2 + 4x)) - 2) + 1) + 3)/(3(1sin(3\u03c0(-1(-2x^2 + 4x)) - 2) + 1))))) - 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "466", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -4(-4(1sin(3\u03c0(-3|(-3((3x - 2)/(-1x + 2))) + 3| - 2) - 2) + 3)^2 + 3(1sin(3\u03c0(-3|(-3((3x - 2)/(-1x + 2))) + 3| - 2) - 2) + 3)) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "86", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = 1(-5(3(1(-2(5x^2 - 1x - 1)^2 - 4(5x^2 - 1x - 1) - 5) + 4)^2 + 2(1(-2(5x^2 - 1x - 1)^2 - 4(5x^2 - 1x - 1) - 5) + 4) - 3)^2 - 5)^2 - 4(-5(3(1(-2(5x^2 - 1x - 1)^2 - 4(5x^2 - 1x - 1) - 5) + 4)^2 + 2(1(-2(5x^2 - 1x - 1)^2 - 4(5x^2 - 1x - 1) - 5) + 4) - 3)^2 - 5) - 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 1(-3sin(3\u03c0(1|(-1|(-2(-3|x + 1| + 2) - 1) - 3|)| + 2) - 3) - 2) + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "181", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 2(4(-1(2cos(1\u03c0((1(-3x - 4) + 2)/(-2(-3x - 4) - 1)) - 3))^2 - 2(2cos(1\u03c0((1(-3x - 4) + 2)/(-2(-3x - 4) - 1)) - 3)) - 3) - 3)^2 - 4(4(-1(2cos(1\u03c0((1(-3x - 4) + 2)/(-2(-3x - 4) - 1)) - 3))^2 - 2(2cos(1\u03c0((1(-3x - 4) + 2)/(-2(-3x - 4) - 1)) - 3)) - 3) - 3) - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -2(1(1(1sin(3\u03c0(-1|(3|x + 3| - 1)| + 2) + 1) - 1)^2 + 5(1sin(3\u03c0(-1|(3|x + 3| - 1)| + 2) + 1) - 1) - 3)) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "90", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -3|(4(3((3(-3sin(2\u03c0(1|x - 1| - 2) + 2) + 2) - 3)/(1(-3sin(2\u03c0(1|x - 1| - 2) + 2) + 2) + 3))^2 + 4((3(-3sin(2\u03c0(1|x - 1| - 2) + 2) + 2) - 3)/(1(-3sin(2\u03c0(1|x - 1| - 2) + 2) + 2) + 3)) - 5)^2 - 5(3((3(-3sin(2\u03c0(1|x - 1| - 2) + 2) + 2) - 3)/(1(-3sin(2\u03c0(1|x - 1| - 2) + 2) + 2) + 3))^2 + 4((3(-3sin(2\u03c0(1|x - 1| - 2) + 2) + 2) - 3)/(1(-3sin(2\u03c0(1|x - 1| - 2) + 2) + 2) + 3)) - 5) + 5) - 2| + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "159", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -2|((-1(2cos(1\u03c0(-3|((-2(2x - 3) + 2)/(2(2x - 3) + 2)) + 1|) + 2) + 1) + 1)/(1(2cos(1\u03c0(-3|((-2(2x - 3) + 2)/(2(2x - 3) + 2)) + 1|) + 2) + 1) + 2))| + 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "48", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -1cos(1\u03c0(-2|(-3|(-1(-2(-1x + 3)^2 + 1) - 3) - 1|) - 2|) - 3) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "252", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -1(-1((-2(5((-1(-2sin(3\u03c0x) + 3) + 1)/(-3(-2sin(3\u03c0x) + 3) + 4))^2 - 3((-1(-2sin(3\u03c0x) + 3) + 1)/(-3(-2sin(3\u03c0x) + 3) + 4)) + 2))/(-2(5((-1(-2sin(3\u03c0x) + 3) + 1)/(-3(-2sin(3\u03c0x) + 3) + 4))^2 - 3((-1(-2sin(3\u03c0x) + 3) + 1)/(-3(-2sin(3\u03c0x) + 3) + 4)) + 2) - 3)) + 5) + 5 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = (-1(2(2|(-2(2|(-3sin(3\u03c0x - 2) + 1)|)^2 - 4(2|(-3sin(3\u03c0x - 2) + 1)|) + 2) + 3| + 3) + 2) - 3)/(-2(2(2|(-2(2|(-3sin(3\u03c0x - 2) + 1)|)^2 - 4(2|(-3sin(3\u03c0x - 2) + 1)|) + 2) + 3| + 3) + 2) - 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "192", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -3(2e^(2(-5(2((2(2x + 2) + 1)/(1(2x + 2) - 2))^2 - 5((2(2x + 2) + 1)/(1(2x + 2) - 2)) + 3) + 3)) + 3)^2 + 4(2e^(2(-5(2((2(2x + 2) + 1)/(1(2x + 2) - 2))^2 - 5((2(2x + 2) + 1)/(1(2x + 2) - 2)) + 3) + 3)) + 3) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = 4(-1(2|((-2(-1|(-1cos(2\u03c0x) - 1)| + 3) - 2)/(1(-1|(-1cos(2\u03c0x) - 1)| + 3) + 3)) - 1| + 3)^2 - 2(2|((-2(-1|(-1cos(2\u03c0x) - 1)| + 3) - 2)/(1(-1|(-1cos(2\u03c0x) - 1)| + 3) + 3)) - 1| + 3) - 2)^2 - 1(-1(2|((-2(-1|(-1cos(2\u03c0x) - 1)| + 3) - 2)/(1(-1|(-1cos(2\u03c0x) - 1)| + 3) + 3)) - 1| + 3)^2 - 2(2|((-2(-1|(-1cos(2\u03c0x) - 1)| + 3) - 2)/(1(-1|(-1cos(2\u03c0x) - 1)| + 3) + 3)) - 1| + 3) - 2) + 5 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = (1(3(-2e^(1(5(-2((-1x + 2)/(1x + 1)) - 5))) - 1)^2 - 1(-2e^(1(5(-2((-1x + 2)/(1x + 1)) - 5))) - 1) - 5) + 3)/(3(3(-2e^(1(5(-2((-1x + 2)/(1x + 1)) - 5))) - 1)^2 - 1(-2e^(1(5(-2((-1x + 2)/(1x + 1)) - 5))) - 1) - 5) - 1) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 3((-3(-2|(1|(2sin(3\u03c0((-1x + 2)/(3x + 3)) - 1) - 3) - 3| + 1) + 3| - 3) + 1)/(1(-2|(1|(2sin(3\u03c0((-1x + 2)/(3x + 3)) - 1) - 3) - 3| + 1) + 3| - 3)))^2 + 3((-3(-2|(1|(2sin(3\u03c0((-1x + 2)/(3x + 3)) - 1) - 3) - 3| + 1) + 3| - 3) + 1)/(1(-2|(1|(2sin(3\u03c0((-1x + 2)/(3x + 3)) - 1) - 3) - 3| + 1) + 3| - 3))) - 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 1(4((2((1(-2((-3x - 1)/(1x - 3))^2 + 2) + 1)/(2(-2((-3x - 1)/(1x - 3))^2 + 2) - 1)) + 1)/(-2((1(-2((-3x - 1)/(1x - 3))^2 + 2) + 1)/(2(-2((-3x - 1)/(1x - 3))^2 + 2) - 1)) + 1))^2)^2 - 3(4((2((1(-2((-3x - 1)/(1x - 3))^2 + 2) + 1)/(2(-2((-3x - 1)/(1x - 3))^2 + 2) - 1)) + 1)/(-2((1(-2((-3x - 1)/(1x - 3))^2 + 2) + 1)/(2(-2((-3x - 1)/(1x - 3))^2 + 2) - 1)) + 1))^2) - 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -2e^(1(-1(1(2((1(4x^2 - 2x - 5) - 1)/(1(4x^2 - 2x - 5) + 1))^2 + 5((1(4x^2 - 2x - 5) - 1)/(1(4x^2 - 2x - 5) + 1)) - 3)^2 - 2(2((1(4x^2 - 2x - 5) - 1)/(1(4x^2 - 2x - 5) + 1))^2 + 5((1(4x^2 - 2x - 5) - 1)/(1(4x^2 - 2x - 5) + 1)) - 3) + 4) - 3)) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -5(-2cos(1\u03c0(-3(-3|(5(-1|x - 1| - 2) + 1) + 2| - 3)^2 + 4(-3|(5(-1|x - 1| - 2) + 1) + 2| - 3) + 4) + 2) + 1)^2 + 4(-2cos(1\u03c0(-3(-3|(5(-1|x - 1| - 2) + 1) + 2| - 3)^2 + 4(-3|(5(-1|x - 1| - 2) + 1) + 2| - 3) + 4) + 2) + 1) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "73", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -3(4(3sin(2\u03c0(-2|(-1(3x + 1)^2 + 3(3x + 1) + 1) - 3|) - 1) + 1)^2 - 4(3sin(2\u03c0(-2|(-1(3x + 1)^2 + 3(3x + 1) + 1) - 3|) - 1) + 1) + 1) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "200", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -1(2(3((3(-2((1x - 1)/(2x))^2 + 1((1x - 1)/(2x)) + 3) + 1)/(-1(-2((1x - 1)/(2x))^2 + 1((1x - 1)/(2x)) + 3) - 1)) + 3) - 1)^2 + 4(2(3((3(-2((1x - 1)/(2x))^2 + 1((1x - 1)/(2x)) + 3) + 1)/(-1(-2((1x - 1)/(2x))^2 + 1((1x - 1)/(2x)) + 3) - 1)) + 3) - 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 1(-3|(2(-5(-2(-1cos(3\u03c0x - 1))^2 + 4(-1cos(3\u03c0x - 1)) - 3)^2 + 3(-2(-1cos(3\u03c0x - 1))^2 + 4(-1cos(3\u03c0x - 1)) - 3) + 1) + 3) - 1| - 1) + 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 1(-1((-2(-3((-1(1x + 1))/(-2(1x + 1) + 1))^2 + 4((-1(1x + 1))/(-2(1x + 1) + 1)) + 5) + 3)/(-3(-3((-1(1x + 1))/(-2(1x + 1) + 1))^2 + 4((-1(1x + 1))/(-2(1x + 1) + 1)) + 5) + 2))^2 - 2((-2(-3((-1(1x + 1))/(-2(1x + 1) + 1))^2 + 4((-1(1x + 1))/(-2(1x + 1) + 1)) + 5) + 3)/(-3(-3((-1(1x + 1))/(-2(1x + 1) + 1))^2 + 4((-1(1x + 1))/(-2(1x + 1) + 1)) + 5) + 2)) + 3)^2 + 1(-1((-2(-3((-1(1x + 1))/(-2(1x + 1) + 1))^2 + 4((-1(1x + 1))/(-2(1x + 1) + 1)) + 5) + 3)/(-3(-3((-1(1x + 1))/(-2(1x + 1) + 1))^2 + 4((-1(1x + 1))/(-2(1x + 1) + 1)) + 5) + 2))^2 - 2((-2(-3((-1(1x + 1))/(-2(1x + 1) + 1))^2 + 4((-1(1x + 1))/(-2(1x + 1) + 1)) + 5) + 3)/(-3(-3((-1(1x + 1))/(-2(1x + 1) + 1))^2 + 4((-1(1x + 1))/(-2(1x + 1) + 1)) + 5) + 2)) + 3) - 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = -3((1(1|((-3(-1|(1cos(3\u03c0x + 3) - 1) + 3|) - 1)/(3(-1|(1cos(3\u03c0x + 3) - 1) + 3|) + 2)) + 2| + 1) + 2)/(2(1|((-3(-1|(1cos(3\u03c0x + 3) - 1) + 3|) - 1)/(3(-1|(1cos(3\u03c0x + 3) - 1) + 3|) + 2)) + 2| + 1) + 1))^2 - 1((1(1|((-3(-1|(1cos(3\u03c0x + 3) - 1) + 3|) - 1)/(3(-1|(1cos(3\u03c0x + 3) - 1) + 3|) + 2)) + 2| + 1) + 2)/(2(1|((-3(-1|(1cos(3\u03c0x + 3) - 1) + 3|) - 1)/(3(-1|(1cos(3\u03c0x + 3) - 1) + 3|) + 2)) + 2| + 1) + 1)) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 3(-2(3cos(1\u03c0(4((3(2x^2 - 1x - 5))/(3(2x^2 - 1x - 5) - 1)) - 2) + 1) - 1) + 1)^2 + 1(-2(3cos(1\u03c0(4((3(2x^2 - 1x - 5))/(3(2x^2 - 1x - 5) - 1)) - 2) + 1) - 1) + 1) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 1(3|((-3((-3(3|(2cos(1\u03c0x - 1) - 3) - 3| - 2) - 1)/(3(3|(2cos(1\u03c0x - 1) - 3) - 3| - 2))) + 1)/(-1((-3(3|(2cos(1\u03c0x - 1) - 3) - 3| - 2) - 1)/(3(3|(2cos(1\u03c0x - 1) - 3) - 3| - 2))) - 2)) + 1| + 3) - 5 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = 1|(-3|(-1cos(1\u03c0(1(2|((2x + 3)/(-3x + 1)) + 2|)^2 + 5(2|((2x + 3)/(-3x + 1)) + 2|) - 1) + 2) + 2) - 2| + 1) + 3| - 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "130", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 5((-2(3sin(1\u03c0(5(-5(5x - 5))^2 - 3(-5(5x - 5)) + 3) - 2)) - 1)/(1(3sin(1\u03c0(5(-5(5x - 5))^2 - 3(-5(5x - 5)) + 3) - 2)) + 3))^2 + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "45", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = 1(-3((2(-2(-2((-2x + 1)/(-3x - 3))^2 + 3((-2x + 1)/(-3x - 3)) + 1)^2 - 2(-2((-2x + 1)/(-3x - 3))^2 + 3((-2x + 1)/(-3x - 3)) + 1) + 3) - 2)/(1(-2(-2((-2x + 1)/(-3x - 3))^2 + 3((-2x + 1)/(-3x - 3)) + 1)^2 - 2(-2((-2x + 1)/(-3x - 3))^2 + 3((-2x + 1)/(-3x - 3)) + 1) + 3) + 2))^2 + 3((2(-2(-2((-2x + 1)/(-3x - 3))^2 + 3((-2x + 1)/(-3x - 3)) + 1)^2 - 2(-2((-2x + 1)/(-3x - 3))^2 + 3((-2x + 1)/(-3x - 3)) + 1) + 3) - 2)/(1(-2(-2((-2x + 1)/(-3x - 3))^2 + 3((-2x + 1)/(-3x - 3)) + 1)^2 - 2(-2((-2x + 1)/(-3x - 3))^2 + 3((-2x + 1)/(-3x - 3)) + 1) + 3) + 2)) + 3) - 4 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 3(-1((-3(-3(1|(-2cos(3\u03c0x - 3) - 1) + 3| + 1) - 1) - 1)/(-2(-3(1|(-2cos(3\u03c0x - 3) - 1) + 3| + 1) - 1) - 2))^2 - 1((-3(-3(1|(-2cos(3\u03c0x - 3) - 1) + 3| + 1) - 1) - 1)/(-2(-3(1|(-2cos(3\u03c0x - 3) - 1) + 3| + 1) - 1) - 2)) + 3)^2 + 3(-1((-3(-3(1|(-2cos(3\u03c0x - 3) - 1) + 3| + 1) - 1) - 1)/(-2(-3(1|(-2cos(3\u03c0x - 3) - 1) + 3| + 1) - 1) - 2))^2 - 1((-3(-3(1|(-2cos(3\u03c0x - 3) - 1) + 3| + 1) - 1) - 1)/(-2(-3(1|(-2cos(3\u03c0x - 3) - 1) + 3| + 1) - 1) - 2)) + 3) + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -2|(2((-1(-1(2|(-2sin(2\u03c0x - 1) + 1) + 3| + 3) - 3) + 1)/(3(-1(2|(-2sin(2\u03c0x - 1) + 1) + 3| + 3) - 3) + 3))^2 + 4((-1(-1(2|(-2sin(2\u03c0x - 1) + 1) + 3| + 3) - 3) + 1)/(3(-1(2|(-2sin(2\u03c0x - 1) + 1) + 3| + 3) - 3) + 3)) - 3) - 3| - 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 1(-3(3(-1(-5(-2sin(3\u03c0x - 1) + 3) + 5)^2 + 1(-5(-2sin(3\u03c0x - 1) + 3) + 5) - 5)^2 - 1(-1(-5(-2sin(3\u03c0x - 1) + 3) + 5)^2 + 1(-5(-2sin(3\u03c0x - 1) + 3) + 5) - 5) - 2))^2 + 5(-3(3(-1(-5(-2sin(3\u03c0x - 1) + 3) + 5)^2 + 1(-5(-2sin(3\u03c0x - 1) + 3) + 5) - 5)^2 - 1(-1(-5(-2sin(3\u03c0x - 1) + 3) + 5)^2 + 1(-5(-2sin(3\u03c0x - 1) + 3) + 5) - 5) - 2)) - 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "54", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 2(1sin(1\u03c0((-1(-3|((-2(4x - 2) + 2)/(-3(4x - 2) - 1)) - 2| + 3) + 1)/(3(-3|((-2(4x - 2) + 2)/(-3(4x - 2) - 1)) - 2| + 3) + 1)) + 3))^2 + 2(1sin(1\u03c0((-1(-3|((-2(4x - 2) + 2)/(-3(4x - 2) - 1)) - 2| + 3) + 1)/(3(-3|((-2(4x - 2) + 2)/(-3(4x - 2) - 1)) - 2| + 3) + 1)) + 3)) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = 1(2sin(1\u03c0(3|(2|(-2(5x - 2)^2 - 4(5x - 2) - 3) - 2| - 1)| - 2) + 1) + 2)^2 + 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "136", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = (3(1e^(1(4(2|(-4(5x)^2 + 3(5x) + 1) - 3| + 1)^2 - 3(2|(-4(5x)^2 + 3(5x) + 1) - 3| + 1) + 1)) - 3) - 2)/(-1(1e^(1(4(2|(-4(5x)^2 + 3(5x) + 1) - 3| + 1)^2 - 3(2|(-4(5x)^2 + 3(5x) + 1) - 3| + 1) + 1)) - 3) + 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = (-1((-2((2(4(-1|(-1cos(3\u03c0x + 1) + 1) + 2| + 1)^2 + 2(-1|(-1cos(3\u03c0x + 1) + 1) + 2| + 1) + 3) + 2)/(2(4(-1|(-1cos(3\u03c0x + 1) + 1) + 2| + 1)^2 + 2(-1|(-1cos(3\u03c0x + 1) + 1) + 2| + 1) + 3) + 3)) + 1)/(-2((2(4(-1|(-1cos(3\u03c0x + 1) + 1) + 2| + 1)^2 + 2(-1|(-1cos(3\u03c0x + 1) + 1) + 2| + 1) + 3) + 2)/(2(4(-1|(-1cos(3\u03c0x + 1) + 1) + 2| + 1)^2 + 2(-1|(-1cos(3\u03c0x + 1) + 1) + 2| + 1) + 3) + 3)) + 3)) - 2)/(-3((-2((2(4(-1|(-1cos(3\u03c0x + 1) + 1) + 2| + 1)^2 + 2(-1|(-1cos(3\u03c0x + 1) + 1) + 2| + 1) + 3) + 2)/(2(4(-1|(-1cos(3\u03c0x + 1) + 1) + 2| + 1)^2 + 2(-1|(-1cos(3\u03c0x + 1) + 1) + 2| + 1) + 3) + 3)) + 1)/(-2((2(4(-1|(-1cos(3\u03c0x + 1) + 1) + 2| + 1)^2 + 2(-1|(-1cos(3\u03c0x + 1) + 1) + 2| + 1) + 3) + 2)/(2(4(-1|(-1cos(3\u03c0x + 1) + 1) + 2| + 1)^2 + 2(-1|(-1cos(3\u03c0x + 1) + 1) + 2| + 1) + 3) + 3)) + 3)) - 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 1(5(1(1|(-2|(2x - 2) + 2| + 3) + 1| - 1) - 3))^2 + 2(5(1(1|(-2|(2x - 2) + 2| + 3) + 1| - 1) - 3)) - 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 1|(1|((2(-4(-3|(1cos(3\u03c0x - 2) + 1)| + 3)^2 + 3) - 3)/(3(-4(-3|(1cos(3\u03c0x - 2) + 1)| + 3)^2 + 3) - 1))|)| - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "102", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 4(2|(-2|(1(2|(5x^2 - 5x - 3)| + 2)^2 - 3(2|(5x^2 - 5x - 3)| + 2) - 4) - 2| + 3) - 3| + 2) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = 2((3(-5((3(-2sin(3\u03c0((1x + 1)/(-3x - 2)) + 2) + 1) + 1)/(-1(-2sin(3\u03c0((1x + 1)/(-3x - 2)) + 2) + 1) + 2))^2 + 3) - 3)/(2(-5((3(-2sin(3\u03c0((1x + 1)/(-3x - 2)) + 2) + 1) + 1)/(-1(-2sin(3\u03c0((1x + 1)/(-3x - 2)) + 2) + 1) + 2))^2 + 3) + 1))^2 + 4((3(-5((3(-2sin(3\u03c0((1x + 1)/(-3x - 2)) + 2) + 1) + 1)/(-1(-2sin(3\u03c0((1x + 1)/(-3x - 2)) + 2) + 1) + 2))^2 + 3) - 3)/(2(-5((3(-2sin(3\u03c0((1x + 1)/(-3x - 2)) + 2) + 1) + 1)/(-1(-2sin(3\u03c0((1x + 1)/(-3x - 2)) + 2) + 1) + 2))^2 + 3) + 1)) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 4(1sin(3\u03c0(4(-5(-1|(-1|x + 2| + 2) + 1| - 2) - 5)^2 - 4(-5(-1|(-1|x + 2| + 2) + 1| - 2) - 5) - 5) + 3) - 2) + 5 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "371", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = (-1((2(-1|(-3|(-1sin(2\u03c0(-4x - 3)) + 2) - 2|) - 3|) + 2)/(3(-1|(-3|(-1sin(2\u03c0(-4x - 3)) + 2) - 2|) - 3|) + 3)) - 1)/(-2((2(-1|(-3|(-1sin(2\u03c0(-4x - 3)) + 2) - 2|) - 3|) + 2)/(3(-1|(-3|(-1sin(2\u03c0(-4x - 3)) + 2) - 2|) - 3|) + 3)) + 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "268", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = (-1(-2|(-2cos(3\u03c0(4(2(-3x^2 + 2x - 4) - 2) + 1)) - 3) - 1| + 3) + 1)/(2(-2|(-2cos(3\u03c0(4(2(-3x^2 + 2x - 4) - 2) + 1)) - 3) - 1| + 3) - 3) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "364", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = 1(5(-1(-1|(-4((2x + 3)/(3x))^2 + 4((2x + 3)/(3x)) + 3) + 1| + 2)^2 + 1(-1|(-4((2x + 3)/(3x))^2 + 4((2x + 3)/(3x)) + 3) + 1| + 2) - 5)^2 + 5(-1(-1|(-4((2x + 3)/(3x))^2 + 4((2x + 3)/(3x)) + 3) + 1| + 2)^2 + 1(-1|(-4((2x + 3)/(3x))^2 + 4((2x + 3)/(3x)) + 3) + 1| + 2) - 5) - 4) - 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = (1(3cos(1\u03c0(-3(-4(2|(-5x - 3) + 3| - 1)^2 + 2(2|(-5x - 3) + 3| - 1) + 4)^2 + 4(-4(2|(-5x - 3) + 3| - 1)^2 + 2(2|(-5x - 3) + 3| - 1) + 4) - 4) - 3)) + 3)/(1(3cos(1\u03c0(-3(-4(2|(-5x - 3) + 3| - 1)^2 + 2(2|(-5x - 3) + 3| - 1) + 4)^2 + 4(-4(2|(-5x - 3) + 3| - 1)^2 + 2(2|(-5x - 3) + 3| - 1) + 4) - 4) - 3)) - 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 2sin(1\u03c0((-2(2(-1(-4((-2x - 3)/(-3x - 2))^2 + 5((-2x - 3)/(-3x - 2)) + 4) + 1)^2 - 3(-1(-4((-2x - 3)/(-3x - 2))^2 + 5((-2x - 3)/(-3x - 2)) + 4) + 1) - 2) + 2)/(-1(2(-1(-4((-2x - 3)/(-3x - 2))^2 + 5((-2x - 3)/(-3x - 2)) + 4) + 1)^2 - 3(-1(-4((-2x - 3)/(-3x - 2))^2 + 5((-2x - 3)/(-3x - 2)) + 4) + 1) - 2) + 2)) - 2) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = (-3(4(-1(-1sin(2\u03c0(-5(5x - 5) + 5) - 2)))^2 + 2(-1(-1sin(2\u03c0(-5(5x - 5) + 5) - 2))) - 5) + 2)/(-3(4(-1(-1sin(2\u03c0(-5(5x - 5) + 5) - 2)))^2 + 2(-1(-1sin(2\u03c0(-5(5x - 5) + 5) - 2))) - 5) + 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "164", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 2(-1cos(2\u03c0((-2(-1(-1|(1|x - 1| - 1) - 2| + 2)^2 - 4(-1|(1|x - 1| - 1) - 2| + 2)) - 3)/(-2(-1(-1|(1|x - 1| - 1) - 2| + 2)^2 - 4(-1|(1|x - 1| - 1) - 2| + 2)) + 3)) - 2) - 3)^2 + 4(-1cos(2\u03c0((-2(-1(-1|(1|x - 1| - 1) - 2| + 2)^2 - 4(-1|(1|x - 1| - 1) - 2| + 2)) - 3)/(-2(-1(-1|(1|x - 1| - 1) - 2| + 2)^2 - 4(-1|(1|x - 1| - 1) - 2| + 2)) + 3)) - 2) - 3) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "150", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 3|(-1(4(-1((2(-2sin(2\u03c0x + 2) - 2) - 1)/(-1(-2sin(2\u03c0x + 2) - 2) - 2)) - 5) - 5)^2 - 3(4(-1((2(-2sin(2\u03c0x + 2) - 2) - 1)/(-1(-2sin(2\u03c0x + 2) - 2) - 2)) - 5) - 5) - 4)| have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "99", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = -3((-2(-3cos(2\u03c0(4(-2|(5x - 1) - 2|) + 4)) + 3) + 3)/(2(-3cos(2\u03c0(4(-2|(5x - 1) - 2|) + 4)) + 3)))^2 + 5 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "468", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 4((3(2(3(-1cos(2\u03c0(-4x)) + 1) - 4)^2 + 3(3(-1cos(2\u03c0(-4x)) + 1) - 4) + 5) + 1)/(-1(2(3(-1cos(2\u03c0(-4x)) + 1) - 4)^2 + 3(3(-1cos(2\u03c0(-4x)) + 1) - 4) + 5)))^2 + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "126", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = -1cos(2\u03c0(2|(-2((-2((-2(-4x - 4) - 1)/(-3(-4x - 4) + 2)))/(-2((-2(-4x - 4) - 1)/(-3(-4x - 4) + 2)) + 3)) + 3) + 3| - 1) - 1) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = (3(-1cos(2\u03c0((1((-2(3(2|x - 2| - 3) + 1))/(-1(3(2|x - 2| - 3) + 1) + 2)) + 1)/(-3((-2(3(2|x - 2| - 3) + 1))/(-1(3(2|x - 2| - 3) + 1) + 2)) + 2)) - 2) + 2))/(-1(-1cos(2\u03c0((1((-2(3(2|x - 2| - 3) + 1))/(-1(3(2|x - 2| - 3) + 1) + 2)) + 1)/(-3((-2(3(2|x - 2| - 3) + 1))/(-1(3(2|x - 2| - 3) + 1) + 2)) + 2)) - 2) + 2)) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = (-1(1(5(2(-1(-5x^2 - 3x - 1)^2 + 5(-5x^2 - 3x - 1) + 5) - 4)^2 + 5(2(-1(-5x^2 - 3x - 1)^2 + 5(-5x^2 - 3x - 1) + 5) - 4) - 1) - 3) - 3)/(-3(1(5(2(-1(-5x^2 - 3x - 1)^2 + 5(-5x^2 - 3x - 1) + 5) - 4)^2 + 5(2(-1(-5x^2 - 3x - 1)^2 + 5(-5x^2 - 3x - 1) + 5) - 4) - 1) - 3) + 4) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -3(3cos(1\u03c0(-1|(1|(-1|(1|x + 1| + 2) + 2| + 3) + 2| + 2) + 3| + 2) - 2) - 2) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = (1(4((-2(-1sin(3\u03c0(-2|(-5x - 4) - 3| + 2) - 1) - 1) + 3)/(1(-1sin(3\u03c0(-2|(-5x - 4) - 3| + 2) - 1) - 1) + 3)) - 2) + 1)/(-3(4((-2(-1sin(3\u03c0(-2|(-5x - 4) - 3| + 2) - 1) - 1) + 3)/(1(-1sin(3\u03c0(-2|(-5x - 4) - 3| + 2) - 1) - 1) + 3)) - 2) - 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "213", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -1cos(3\u03c0((2(-1|(1(-5((2x - 1)/(1x + 2)) - 4)^2 - 4(-5((2x - 1)/(1x + 2)) - 4) + 1)| + 1) - 1)/(2(-1|(1(-5((2x - 1)/(1x + 2)) - 4)^2 - 4(-5((2x - 1)/(1x + 2)) - 4) + 1)| + 1) + 3))) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -4(1|(-1(-2cos(3\u03c0((-2(5x^2 - 4x + 1) - 3)/(-2(5x^2 - 4x + 1))) - 2) - 3)^2 - 2) - 3|)^2 - 2(1|(-1(-2cos(3\u03c0((-2(5x^2 - 4x + 1) - 3)/(-2(5x^2 - 4x + 1))) - 2) - 3)^2 - 2) - 3|) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "24", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 2|((-3(2(3(1|(-1|x| + 2)|)^2 - 1(1|(-1|x| + 2)|) - 3) - 4) - 1)/(2(2(3(1|(-1|x| + 2)|)^2 - 1(1|(-1|x| + 2)|) - 3) - 4) - 1)) + 2| - 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = 1|(-2sin(2\u03c0(2((-3((1(-3x - 1) + 1)/(-3(-3x - 1) + 4)) + 2)/(3((1(-3x - 1) + 1)/(-3(-3x - 1) + 4)) + 1)) + 2) + 2)) - 1| - 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "617", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -1|(-1sin(3\u03c0(2|(-3|(2(1x + 2) - 5) + 2| + 1) - 3| + 3) - 2)) + 1| + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "360", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 1(5(2(1|(1(2x^2 + 4x - 5) + 4) - 1| - 3) - 4) - 2)^2 + 3(5(2(1|(1(2x^2 + 4x - 5) + 4) - 1| - 3) - 4) - 2) + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -1|((-3(1|((1((1(-2sin(3\u03c0x + 3) + 2) + 2)/(1(-2sin(3\u03c0x + 3) + 2) + 3)) + 3)/(3((1(-2sin(3\u03c0x + 3) + 2) + 2)/(1(-2sin(3\u03c0x + 3) + 2) + 3)))) - 2| + 2) + 1)/(-2(1|((1((1(-2sin(3\u03c0x + 3) + 2) + 2)/(1(-2sin(3\u03c0x + 3) + 2) + 3)) + 3)/(3((1(-2sin(3\u03c0x + 3) + 2) + 2)/(1(-2sin(3\u03c0x + 3) + 2) + 3)))) - 2| + 2) - 1)) + 2| - 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 3(2|(2cos(3\u03c0(-2|((3((2x + 2)/(-3x)) + 2)/(3((2x + 2)/(-3x)) - 2)) + 3| + 1) - 3) + 1) - 3| + 1) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -1((-3(1(1(-2(3cos(3\u03c0x - 3) + 1) + 2) - 5)^2 - 1(1(-2(3cos(3\u03c0x - 3) + 1) + 2) - 5) - 1) + 3)/(3(1(1(-2(3cos(3\u03c0x - 3) + 1) + 2) - 5)^2 - 1(1(-2(3cos(3\u03c0x - 3) + 1) + 2) - 5) - 1) - 2)) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -3|(-1(3|((2(1((3x + 3)/(2x + 2))))/(3(1((3x + 3)/(2x + 2))) - 2)) + 2| + 2) + 3) + 1| in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = (-3(1|(-2cos(2\u03c0(1|(5((1x + 1)/(1x))^2 - 3) + 3| + 1) - 2) + 1)| - 2) - 1)/(2(1|(-2cos(2\u03c0(1|(5((1x + 1)/(1x))^2 - 3) + 3| + 1) - 2) + 1)| - 2) + 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "55", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -3|(-1|((2(-4(4(4x^2 - 5x + 3)^2 - 3(4x^2 - 5x + 3) + 1)^2 - 2(4(4x^2 - 5x + 3)^2 - 3(4x^2 - 5x + 3) + 1) + 2) - 3)/(-1(-4(4(4x^2 - 5x + 3)^2 - 3(4x^2 - 5x + 3) + 1)^2 - 2(4(4x^2 - 5x + 3)^2 - 3(4x^2 - 5x + 3) + 1) + 2) - 3)) - 2| + 2)| - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 5(-3(-4(-1|(2e^(2(2x + 3)) - 3)|)^2 + 2(-1|(2e^(2(2x + 3)) - 3)|) - 1) - 3) - 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = (-2(-1(2|(2e^(1(-1(-3|x + 3|)^2 + 4)) + 3)| + 1)^2 - 3) - 2)/(-3(-1(2|(2e^(1(-1(-3|x + 3|)^2 + 4)) + 3)| + 1)^2 - 3) + 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 5(3cos(3\u03c0(2((3(2|(-5x^2 - 3x + 5) - 2|) + 2)/(2(2|(-5x^2 - 3x + 5) - 2|) + 1))^2 - 1((3(2|(-5x^2 - 3x + 5) - 2|) + 2)/(2(2|(-5x^2 - 3x + 5) - 2|) + 1)) + 4) - 1) + 2)^2 + 5(3cos(3\u03c0(2((3(2|(-5x^2 - 3x + 5) - 2|) + 2)/(2(2|(-5x^2 - 3x + 5) - 2|) + 1))^2 - 1((3(2|(-5x^2 - 3x + 5) - 2|) + 2)/(2(2|(-5x^2 - 3x + 5) - 2|) + 1)) + 4) - 1) + 2) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = 1(-4(-3|(3|(-2sin(1\u03c0(2x + 4) - 1) + 1) - 3|) + 1| - 3) + 5) + 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -1(5((1(3(1(2|x + 2|) - 2) - 2) + 2)/(-1(3(1(2|x + 2|) - 2) - 2) + 2))^2 + 2((1(3(1(2|x + 2|) - 2) - 2) + 2)/(-1(3(1(2|x + 2|) - 2) - 2) + 2)) - 3)^2 + 1(5((1(3(1(2|x + 2|) - 2) - 2) + 2)/(-1(3(1(2|x + 2|) - 2) - 2) + 2))^2 + 2((1(3(1(2|x + 2|) - 2) - 2) + 2)/(-1(3(1(2|x + 2|) - 2) - 2) + 2)) - 3) + 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -1(-2cos(1\u03c0(-1(-2((-3(3x^2 - 5x + 3) - 2)/(2(3x^2 - 5x + 3) - 3))^2 - 3)^2 + 2(-2((-3(3x^2 - 5x + 3) - 2)/(2(3x^2 - 5x + 3) - 3))^2 - 3) + 3) + 2) - 1) - 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "147", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = (2(-2((3(-1(-1(3x^2 - 3x - 4)^2 + 1) - 3) + 3)/(1(-1(-1(3x^2 - 3x - 4)^2 + 1) - 3)))^2 - 3((3(-1(-1(3x^2 - 3x - 4)^2 + 1) - 3) + 3)/(1(-1(-1(3x^2 - 3x - 4)^2 + 1) - 3))) + 1))/(3(-2((3(-1(-1(3x^2 - 3x - 4)^2 + 1) - 3) + 3)/(1(-1(-1(3x^2 - 3x - 4)^2 + 1) - 3)))^2 - 3((3(-1(-1(3x^2 - 3x - 4)^2 + 1) - 3) + 3)/(1(-1(-1(3x^2 - 3x - 4)^2 + 1) - 3))) + 1) + 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = 1(3cos(3\u03c0((1((-2(-2|(-1|x| + 3)| - 3) + 2)/(2(-2|(-1|x| + 3)| - 3) - 1)) - 3)/(2((-2(-2|(-1|x| + 3)| - 3) + 2)/(2(-2|(-1|x| + 3)| - 3) - 1)) + 2)) + 1) - 1) + 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "239", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 1(2(4((2(-3(3x + 4)^2 + 1(3x + 4) + 2) - 2)/(1(-3(3x + 4)^2 + 1(3x + 4) + 2) + 1)) + 5)^2 + 5)^2 - 2(2(4((2(-3(3x + 4)^2 + 1(3x + 4) + 2) - 2)/(1(-3(3x + 4)^2 + 1(3x + 4) + 2) + 1)) + 5)^2 + 5) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = 4((2((3(2((1(3|x - 2| - 3) + 1)/(2(3|x - 2| - 3) - 3))^2 - 2) + 2)/(1(2((1(3|x - 2| - 3) + 1)/(2(3|x - 2| - 3) - 3))^2 - 2) + 1)) + 2)/(2((3(2((1(3|x - 2| - 3) + 1)/(2(3|x - 2| - 3) - 3))^2 - 2) + 2)/(1(2((1(3|x - 2| - 3) + 1)/(2(3|x - 2| - 3) - 3))^2 - 2) + 1)) + 1))^2 - 2((2((3(2((1(3|x - 2| - 3) + 1)/(2(3|x - 2| - 3) - 3))^2 - 2) + 2)/(1(2((1(3|x - 2| - 3) + 1)/(2(3|x - 2| - 3) - 3))^2 - 2) + 1)) + 2)/(2((3(2((1(3|x - 2| - 3) + 1)/(2(3|x - 2| - 3) - 3))^2 - 2) + 2)/(1(2((1(3|x - 2| - 3) + 1)/(2(3|x - 2| - 3) - 3))^2 - 2) + 1)) + 1)) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -3|(-3(2((-1((2(-1x^2 + 4x + 2))/(2(-1x^2 + 4x + 2) + 2)) - 2)/(1((2(-1x^2 + 4x + 2))/(2(-1x^2 + 4x + 2) + 2)) - 2)) + 2)^2 + 3(2((-1((2(-1x^2 + 4x + 2))/(2(-1x^2 + 4x + 2) + 2)) - 2)/(1((2(-1x^2 + 4x + 2))/(2(-1x^2 + 4x + 2) + 2)) - 2)) + 2) + 3) - 2| - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -2|((-1(1(1e^(-1(-1((-3x - 3)/(-1x + 2)) - 5)) - 3)) - 1)/(-2(1(1e^(-1(-1((-3x - 3)/(-1x + 2)) - 5)) - 3)) + 3)) + 2| + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = 4(2|((-1(2(-4(-3cos(1\u03c0x + 1) - 1)^2 - 5(-3cos(1\u03c0x + 1) - 1) + 1) + 4) + 1)/(1(2(-4(-3cos(1\u03c0x + 1) - 1)^2 - 5(-3cos(1\u03c0x + 1) - 1) + 1) + 4) + 3)) - 3| + 2)^2 - 3(2|((-1(2(-4(-3cos(1\u03c0x + 1) - 1)^2 - 5(-3cos(1\u03c0x + 1) - 1) + 1) + 4) + 1)/(1(2(-4(-3cos(1\u03c0x + 1) - 1)^2 - 5(-3cos(1\u03c0x + 1) - 1) + 1) + 4) + 3)) - 3| + 2) - 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 2|((2(1|(1(2|(-3|x - 3| + 1) - 1|) - 2) - 1| - 3))/(2(1|(1(2|(-3|x - 3| + 1) - 1|) - 2) - 1| - 3) - 1)) + 3| + 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -3((-3(3e^(1(4(1|(-2|x - 1| + 1) - 3| - 3)^2 + 3(1|(-2|x - 1| + 1) - 3| - 3) - 2)) + 1) - 3)/(2(3e^(1(4(1|(-2|x - 1| + 1) - 3| - 3)^2 + 3(1|(-2|x - 1| + 1) - 3| - 3) - 2)) + 1) + 1))^2 - 5((-3(3e^(1(4(1|(-2|x - 1| + 1) - 3| - 3)^2 + 3(1|(-2|x - 1| + 1) - 3| - 3) - 2)) + 1) - 3)/(2(3e^(1(4(1|(-2|x - 1| + 1) - 3| - 3)^2 + 3(1|(-2|x - 1| + 1) - 3| - 3) - 2)) + 1) + 1)) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -3(-3|((-1(-3|(1(2x - 5)^2 - 3(2x - 5) + 1) - 3| + 1))/(-1(-3|(1(2x - 5)^2 - 3(2x - 5) + 1) - 3| + 1) - 3)) + 3| + 1) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = 2((2(3|(3(3|(-2sin(3\u03c0x + 1) - 2) + 2| - 1) - 3) + 2| + 1) - 3)/(-3(3|(3(3|(-2sin(3\u03c0x + 1) - 2) + 2| - 1) - 3) + 2| + 1) + 4)) + 4 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "232", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -2sin(1\u03c0(-4((-2(-1(-1(3|x - 2|)^2 + 4(3|x - 2|) + 3) - 5) + 2)/(1(-1(-1(3|x - 2|)^2 + 4(3|x - 2|) + 3) - 5) + 1))^2 - 1((-2(-1(-1(3|x - 2|)^2 + 4(3|x - 2|) + 3) - 5) + 2)/(1(-1(-1(3|x - 2|)^2 + 4(3|x - 2|) + 3) - 5) + 1)) - 4) + 2) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = (3((3(3|(-5(-2|(-4x + 2) + 1| + 3)^2 + 3) + 2| - 3) + 1)/(1(3|(-5(-2|(-4x + 2) + 1| + 3)^2 + 3) + 2| - 3))) - 3)/(2((3(3|(-5(-2|(-4x + 2) + 1| + 3)^2 + 3) + 2| - 3) + 1)/(1(3|(-5(-2|(-4x + 2) + 1| + 3)^2 + 3) + 2| - 3)))) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -1(-5(3|((-3(5(-3sin(3\u03c0x + 1) + 2) - 3) - 2)/(1(5(-3sin(3\u03c0x + 1) + 2) - 3) + 3)) - 1| + 3) + 1)^2 - 2(-5(3|((-3(5(-3sin(3\u03c0x + 1) + 2) - 3) - 2)/(1(5(-3sin(3\u03c0x + 1) + 2) - 3) + 3)) - 1| + 3) + 1) + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "115", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 5(2(-3(-1sin(1\u03c0(-1(-2|x - 3| - 3) - 4) + 1) - 3) - 1) - 2)^2 + 4(2(-3(-1sin(1\u03c0(-1(-2|x - 3| - 3) - 4) + 1) - 3) - 1) - 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = -1|(1((3((-3(2(-2sin(3\u03c0x - 3) + 3)^2 + 5(-2sin(3\u03c0x - 3) + 3) + 4) - 2)/(1(2(-2sin(3\u03c0x - 3) + 3)^2 + 5(-2sin(3\u03c0x - 3) + 3) + 4))) + 2)/(3((-3(2(-2sin(3\u03c0x - 3) + 3)^2 + 5(-2sin(3\u03c0x - 3) + 3) + 4) - 2)/(1(2(-2sin(3\u03c0x - 3) + 3)^2 + 5(-2sin(3\u03c0x - 3) + 3) + 4))) + 1)) + 3) + 1| + 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -1|(3(2(1(-2|(-1cos(1\u03c0x - 1) + 3)| + 3) - 2) + 2) - 5) + 2| + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = (3(-1|(-3|(1cos(1\u03c0(3(1x^2 + 5x + 1)^2 - 1(1x^2 + 5x + 1)) + 1) + 3) + 2| - 2) - 1| + 2) + 1)/(1(-1|(-3|(1cos(1\u03c0(3(1x^2 + 5x + 1)^2 - 1(1x^2 + 5x + 1)) + 1) + 3) + 2| - 2) - 1| + 2) + 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "321", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 3cos(3\u03c0(-3(-3|(-4((1(-4x))/(2(-4x) - 1)) - 3) - 2| + 1) - 5) + 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "54", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = (2(-4(1(-2sin(2\u03c0((-2(5x^2 + 3x - 4) - 1)/(1(5x^2 + 3x - 4) - 3)) + 3)) - 3)^2 - 3(1(-2sin(2\u03c0((-2(5x^2 + 3x - 4) - 1)/(1(5x^2 + 3x - 4) - 3)) + 3)) - 3) + 3) + 2)/(-3(-4(1(-2sin(2\u03c0((-2(5x^2 + 3x - 4) - 1)/(1(5x^2 + 3x - 4) - 3)) + 3)) - 3)^2 - 3(1(-2sin(2\u03c0((-2(5x^2 + 3x - 4) - 1)/(1(5x^2 + 3x - 4) - 3)) + 3)) - 3) + 3)) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = (-1((1(-2|(-2(5(1cos(1\u03c0x + 1) + 2)^2 + 2(1cos(1\u03c0x + 1) + 2) - 1)^2 - 5(5(1cos(1\u03c0x + 1) + 2)^2 + 2(1cos(1\u03c0x + 1) + 2) - 1) - 3) - 3|) + 3)/(-2(-2|(-2(5(1cos(1\u03c0x + 1) + 2)^2 + 2(1cos(1\u03c0x + 1) + 2) - 1)^2 - 5(5(1cos(1\u03c0x + 1) + 2)^2 + 2(1cos(1\u03c0x + 1) + 2) - 1) - 3) - 3|) + 1)) + 1)/(2((1(-2|(-2(5(1cos(1\u03c0x + 1) + 2)^2 + 2(1cos(1\u03c0x + 1) + 2) - 1)^2 - 5(5(1cos(1\u03c0x + 1) + 2)^2 + 2(1cos(1\u03c0x + 1) + 2) - 1) - 3) - 3|) + 3)/(-2(-2|(-2(5(1cos(1\u03c0x + 1) + 2)^2 + 2(1cos(1\u03c0x + 1) + 2) - 1)^2 - 5(5(1cos(1\u03c0x + 1) + 2)^2 + 2(1cos(1\u03c0x + 1) + 2) - 1) - 3) - 3|) + 1))) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = -5(-4(-2|(1(4(-1cos(2\u03c0x - 2) - 2)^2 + 1(-1cos(2\u03c0x - 2) - 2) + 2) + 5) - 2| + 1) + 1)^2 - 2(-4(-2|(1(4(-1cos(2\u03c0x - 2) - 2)^2 + 1(-1cos(2\u03c0x - 2) - 2) + 2) + 5) - 2| + 1) + 1) - 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = (-1(-5(-5(-1cos(1\u03c0(-2(-3|x - 3|) - 2) - 2) - 3) + 1) - 5) + 3)/(-2(-5(-5(-1cos(1\u03c0(-2(-3|x - 3|) - 2) - 2) - 3) + 1) - 5) + 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "61", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -2sin(3\u03c0(-2|((-1((-3(4((2x)/(3x - 2)) - 4) - 2)/(-1(4((2x)/(3x - 2)) - 4))) - 2)/(-2((-3(4((2x)/(3x - 2)) - 4) - 2)/(-1(4((2x)/(3x - 2)) - 4))))) - 2| - 3) + 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 2(3((3(-3((-2(-2x^2 - 5x + 5) - 2)/(-2(-2x^2 - 5x + 5) - 3))^2 + 4((-2(-2x^2 - 5x + 5) - 2)/(-2(-2x^2 - 5x + 5) - 3)) + 3) + 3)/(-2(-3((-2(-2x^2 - 5x + 5) - 2)/(-2(-2x^2 - 5x + 5) - 3))^2 + 4((-2(-2x^2 - 5x + 5) - 2)/(-2(-2x^2 - 5x + 5) - 3)) + 3) - 2))^2 - 4((3(-3((-2(-2x^2 - 5x + 5) - 2)/(-2(-2x^2 - 5x + 5) - 3))^2 + 4((-2(-2x^2 - 5x + 5) - 2)/(-2(-2x^2 - 5x + 5) - 3)) + 3) + 3)/(-2(-3((-2(-2x^2 - 5x + 5) - 2)/(-2(-2x^2 - 5x + 5) - 3))^2 + 4((-2(-2x^2 - 5x + 5) - 2)/(-2(-2x^2 - 5x + 5) - 3)) + 3) - 2)) + 1) - 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "234", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = (3(2|(2((-3(-1(1sin(2\u03c0x + 2) - 2) + 2) - 1)/(2(-1(1sin(2\u03c0x + 2) - 2) + 2) - 1)) + 2) - 3| - 2) + 3)/(-2(2|(2((-3(-1(1sin(2\u03c0x + 2) - 2) + 2) - 1)/(2(-1(1sin(2\u03c0x + 2) - 2) + 2) - 1)) + 2) - 3| - 2) + 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 4((2(4(-3e^(-1(2|(-5x) - 2| + 2)) - 1) + 2) - 2)/(-1(4(-3e^(-1(2|(-5x) - 2| + 2)) - 1) + 2) - 2))^2 + 4((2(4(-3e^(-1(2|(-5x) - 2| + 2)) - 1) + 2) - 2)/(-1(4(-3e^(-1(2|(-5x) - 2| + 2)) - 1) + 2) - 2)) + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = (3(4(5(-1|(-2sin(2\u03c0(3x^2 - 2x + 1) - 1) + 2) - 1| + 1) + 1)^2 - 1(5(-1|(-2sin(2\u03c0(3x^2 - 2x + 1) - 1) + 2) - 1| + 1) + 1) + 1) + 2)/(3(4(5(-1|(-2sin(2\u03c0(3x^2 - 2x + 1) - 1) + 2) - 1| + 1) + 1)^2 - 1(5(-1|(-2sin(2\u03c0(3x^2 - 2x + 1) - 1) + 2) - 1| + 1) + 1) + 1) - 2) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "485", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = 1cos(3\u03c0(-5((-3(2|((-3((2x + 3)/(-3x - 3)) - 1)/(3((2x + 3)/(-3x - 3)) - 2)) - 1| + 3) - 3)/(-2(2|((-3((2x + 3)/(-3x - 3)) - 1)/(3((2x + 3)/(-3x - 3)) - 2)) - 1| + 3) + 1)) + 1) + 3) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -5((2(1(4(1(-1x^2 + 5) + 1) - 5)^2 - 4(4(1(-1x^2 + 5) + 1) - 5) - 5) + 2)/(3(1(4(1(-1x^2 + 5) + 1) - 5)^2 - 4(4(1(-1x^2 + 5) + 1) - 5) - 5) - 2))^2 + 4((2(1(4(1(-1x^2 + 5) + 1) - 5)^2 - 4(4(1(-1x^2 + 5) + 1) - 5) - 5) + 2)/(3(1(4(1(-1x^2 + 5) + 1) - 5)^2 - 4(4(1(-1x^2 + 5) + 1) - 5) - 5) - 2)) - 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = (2((2(3|(-1|((3(2cos(1\u03c0x - 3) + 2) - 1)/(-3(2cos(1\u03c0x - 3) + 2) + 2)) - 3| - 3) - 2| - 1))/(-2(3|(-1|((3(2cos(1\u03c0x - 3) + 2) - 1)/(-3(2cos(1\u03c0x - 3) + 2) + 2)) - 3| - 3) - 2| - 1) + 1)) + 2)/(1((2(3|(-1|((3(2cos(1\u03c0x - 3) + 2) - 1)/(-3(2cos(1\u03c0x - 3) + 2) + 2)) - 3| - 3) - 2| - 1))/(-2(3|(-1|((3(2cos(1\u03c0x - 3) + 2) - 1)/(-3(2cos(1\u03c0x - 3) + 2) + 2)) - 3| - 3) - 2| - 1) + 1)) + 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "55", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = (-2(2|(-1(-2cos(1\u03c0(2|(-2|x - 3| + 2) + 3| - 3) - 1)) - 2) + 1| + 2) + 2)/(-2(2|(-1(-2cos(1\u03c0(2|(-2|x - 3| + 2) + 3| - 3) - 1)) - 2) + 1| + 2) + 1) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "161", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = (-1(1((3((2(1|(5x^2 + 2x - 3) + 1| - 2) + 2)/(3(1|(5x^2 + 2x - 3) + 1| - 2) + 3)) + 2)/(-3((2(1|(5x^2 + 2x - 3) + 1| - 2) + 2)/(3(1|(5x^2 + 2x - 3) + 1| - 2) + 3)) + 1))^2 + 3((3((2(1|(5x^2 + 2x - 3) + 1| - 2) + 2)/(3(1|(5x^2 + 2x - 3) + 1| - 2) + 3)) + 2)/(-3((2(1|(5x^2 + 2x - 3) + 1| - 2) + 2)/(3(1|(5x^2 + 2x - 3) + 1| - 2) + 3)) + 1)) - 4) + 3)/(2(1((3((2(1|(5x^2 + 2x - 3) + 1| - 2) + 2)/(3(1|(5x^2 + 2x - 3) + 1| - 2) + 3)) + 2)/(-3((2(1|(5x^2 + 2x - 3) + 1| - 2) + 2)/(3(1|(5x^2 + 2x - 3) + 1| - 2) + 3)) + 1))^2 + 3((3((2(1|(5x^2 + 2x - 3) + 1| - 2) + 2)/(3(1|(5x^2 + 2x - 3) + 1| - 2) + 3)) + 2)/(-3((2(1|(5x^2 + 2x - 3) + 1| - 2) + 2)/(3(1|(5x^2 + 2x - 3) + 1| - 2) + 3)) + 1)) - 4) + 1) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -1|(-3|(3cos(3\u03c0(2|(-5(-2x - 2)^2 - 3(-2x - 2) + 2)| - 1) + 3) - 2) - 1|)| + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "211", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 5(-5(-3sin(2\u03c0(-3(1((2x + 3)/(3x - 2))^2 + 1((2x + 3)/(3x - 2)) + 5) - 5)) - 2)^2 - 4(-3sin(2\u03c0(-3(1((2x + 3)/(3x - 2))^2 + 1((2x + 3)/(3x - 2)) + 5) - 5)) - 2) + 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "43", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 1sin(1\u03c0(5(1(3|((1((-3x + 1)/(1x + 1)) + 2)/(2((-3x + 1)/(1x + 1)) - 3)) - 1| - 2) + 2)^2 + 1(1(3|((1((-3x + 1)/(1x + 1)) + 2)/(2((-3x + 1)/(1x + 1)) - 3)) - 1| - 2) + 2) - 1) - 3) - 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "102", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -5(-2cos(3\u03c0(5(5((1(-3|x - 1| + 3) + 1)/(2(-3|x - 1| + 3) + 3))^2 - 4((1(-3|x - 1| + 3) + 1)/(2(-3|x - 1| + 3) + 3)) - 2) - 4) + 2) - 2) + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "26", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = (-2(1(3(1|(3sin(1\u03c0(-4x^2 + 3x - 1) - 3) - 3) + 1| - 1) - 3)^2 + 5(3(1|(3sin(1\u03c0(-4x^2 + 3x - 1) - 3) - 3) + 1| - 1) - 3) - 5) - 1)/(-3(1(3(1|(3sin(1\u03c0(-4x^2 + 3x - 1) - 3) - 3) + 1| - 1) - 3)^2 + 5(3(1|(3sin(1\u03c0(-4x^2 + 3x - 1) - 3) - 3) + 1| - 1) - 3) - 5) + 1) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "239", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = (3((-3(3|(2|(3(1|x + 1| + 1)^2 + 3(1|x + 1| + 1) - 2) + 3| + 2) + 3| - 2) - 2)/(-2(3|(2|(3(1|x + 1| + 1)^2 + 3(1|x + 1| + 1) - 2) + 3| + 2) + 3| - 2) - 1)) + 3)/(-2((-3(3|(2|(3(1|x + 1| + 1)^2 + 3(1|x + 1| + 1) - 2) + 3| + 2) + 3| - 2) - 2)/(-2(3|(2|(3(1|x + 1| + 1)^2 + 3(1|x + 1| + 1) - 2) + 3| + 2) + 3| - 2) - 1)) - 2) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "229", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -5(1|(1(3((3(1x^2 - 3x) + 2)/(2(1x^2 - 3x) + 3))^2 + 3((3(1x^2 - 3x) + 2)/(2(1x^2 - 3x) + 3)) + 4) + 2) + 2| - 1)^2 + 5(1|(1(3((3(1x^2 - 3x) + 2)/(2(1x^2 - 3x) + 3))^2 + 3((3(1x^2 - 3x) + 2)/(2(1x^2 - 3x) + 3)) + 4) + 2) + 2| - 1) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -2cos(1\u03c0(-3(-3|((3(-1((2x)/(2x + 1)) + 5) + 1)/(2(-1((2x)/(2x + 1)) + 5) + 1)) - 1|)^2 + 5(-3|((3(-1((2x)/(2x + 1)) + 5) + 1)/(2(-1((2x)/(2x + 1)) + 5) + 1)) - 1|) + 3) - 3) - 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = (-3(-1(-1((3(-2|((-1x - 3)/(-1x + 2)) - 3| + 1) + 3)/(3(-2|((-1x - 3)/(-1x + 2)) - 3| + 1) - 2))^2 - 1((3(-2|((-1x - 3)/(-1x + 2)) - 3| + 1) + 3)/(3(-2|((-1x - 3)/(-1x + 2)) - 3| + 1) - 2)) + 2)^2 - 1(-1((3(-2|((-1x - 3)/(-1x + 2)) - 3| + 1) + 3)/(3(-2|((-1x - 3)/(-1x + 2)) - 3| + 1) - 2))^2 - 1((3(-2|((-1x - 3)/(-1x + 2)) - 3| + 1) + 3)/(3(-2|((-1x - 3)/(-1x + 2)) - 3| + 1) - 2)) + 2) - 2) + 2)/(2(-1(-1((3(-2|((-1x - 3)/(-1x + 2)) - 3| + 1) + 3)/(3(-2|((-1x - 3)/(-1x + 2)) - 3| + 1) - 2))^2 - 1((3(-2|((-1x - 3)/(-1x + 2)) - 3| + 1) + 3)/(3(-2|((-1x - 3)/(-1x + 2)) - 3| + 1) - 2)) + 2)^2 - 1(-1((3(-2|((-1x - 3)/(-1x + 2)) - 3| + 1) + 3)/(3(-2|((-1x - 3)/(-1x + 2)) - 3| + 1) - 2))^2 - 1((3(-2|((-1x - 3)/(-1x + 2)) - 3| + 1) + 3)/(3(-2|((-1x - 3)/(-1x + 2)) - 3| + 1) - 2)) + 2) - 2) + 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = -1cos(3\u03c0((2(-1(-1|(-1|(-2|x|) + 1| - 1) - 1| + 3)^2 - 4(-1|(-1|(-2|x|) + 1| - 1) - 1| + 3) + 2) + 3)/(-1(-1(-1|(-1|(-2|x|) + 1| - 1) - 1| + 3)^2 - 4(-1|(-1|(-2|x|) + 1| - 1) - 1| + 3) + 2) - 2))) - 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = 1(-1|(2sin(3\u03c0((2(2|(1|x + 3| - 2) + 2|) - 1)/(-3(2|(1|x + 3| - 2) + 2|))) + 2) - 2) - 3| + 3) + 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 5(3|(4((-2(2e^(1((3x - 1)/(2x - 1))) - 2) + 2)/(2(2e^(1((3x - 1)/(2x - 1))) - 2) + 1))^2 - 3((-2(2e^(1((3x - 1)/(2x - 1))) - 2) + 2)/(2(2e^(1((3x - 1)/(2x - 1))) - 2) + 1)) - 2) - 1| + 2)^2 - 3(3|(4((-2(2e^(1((3x - 1)/(2x - 1))) - 2) + 2)/(2(2e^(1((3x - 1)/(2x - 1))) - 2) + 1))^2 - 3((-2(2e^(1((3x - 1)/(2x - 1))) - 2) + 2)/(2(2e^(1((3x - 1)/(2x - 1))) - 2) + 1)) - 2) - 1| + 2) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -2(-1e^(1(4(-3|(-2(-5x^2 + 4x + 5)^2 - 2(-5x^2 + 4x + 5) + 2) + 3| + 1))) + 3) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 4(3|(3(2(-4(-1sin(2\u03c0x + 2) + 2)^2 + 1(-1sin(2\u03c0x + 2) + 2) - 4) + 1) + 3) + 3| - 2)^2 - 1(3|(3(2(-4(-1sin(2\u03c0x + 2) + 2)^2 + 1(-1sin(2\u03c0x + 2) + 2) - 4) + 1) + 3) + 3| - 2) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = (-1(-1(5(-2(-2|(3x^2 - 4x - 3) + 3| + 1)^2 - 1(-2|(3x^2 - 4x - 3) + 3| + 1) - 5) - 3) - 3) + 3)/(3(-1(5(-2(-2|(3x^2 - 4x - 3) + 3| + 1)^2 - 1(-2|(3x^2 - 4x - 3) + 3| + 1) - 5) - 3) - 3) - 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -3sin(1\u03c0(2|((-3((-1(4(-2|x + 2|)^2 + 2(-2|x + 2|) - 3) - 1)/(-1(4(-2|x + 2|)^2 + 2(-2|x + 2|) - 3) - 2)) + 1)/(2((-1(4(-2|x + 2|)^2 + 2(-2|x + 2|) - 3) - 1)/(-1(4(-2|x + 2|)^2 + 2(-2|x + 2|) - 3) - 2)) - 1)) - 1| - 3) - 3) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = (-3(-1(5(1(-1(-3x^2 + 1x + 3) + 5)^2 - 3(-1(-3x^2 + 1x + 3) + 5) + 5)^2 - 1(1(-1(-3x^2 + 1x + 3) + 5)^2 - 3(-1(-3x^2 + 1x + 3) + 5) + 5) + 4)) - 1)/(1(-1(5(1(-1(-3x^2 + 1x + 3) + 5)^2 - 3(-1(-3x^2 + 1x + 3) + 5) + 5)^2 - 1(1(-1(-3x^2 + 1x + 3) + 5)^2 - 3(-1(-3x^2 + 1x + 3) + 5) + 5) + 4))) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = (2(1(-3(1sin(1\u03c0(-4(2x + 2)^2 - 4(2x + 2) + 4) - 3) - 1)^2 - 3(1sin(1\u03c0(-4(2x + 2)^2 - 4(2x + 2) + 4) - 3) - 1) + 1)^2 + 2(-3(1sin(1\u03c0(-4(2x + 2)^2 - 4(2x + 2) + 4) - 3) - 1)^2 - 3(1sin(1\u03c0(-4(2x + 2)^2 - 4(2x + 2) + 4) - 3) - 1) + 1) + 1) + 1)/(3(1(-3(1sin(1\u03c0(-4(2x + 2)^2 - 4(2x + 2) + 4) - 3) - 1)^2 - 3(1sin(1\u03c0(-4(2x + 2)^2 - 4(2x + 2) + 4) - 3) - 1) + 1)^2 + 2(-3(1sin(1\u03c0(-4(2x + 2)^2 - 4(2x + 2) + 4) - 3) - 1)^2 - 3(1sin(1\u03c0(-4(2x + 2)^2 - 4(2x + 2) + 4) - 3) - 1) + 1) + 1) + 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "124", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = (-3(-3|(-3|((1(1(1cos(3\u03c0x + 3) - 2) - 4) + 2)/(-1(1(1cos(3\u03c0x + 3) - 2) - 4) + 2)) + 2| - 1) + 2| + 3) - 1)/(1(-3|(-3|((1(1(1cos(3\u03c0x + 3) - 2) - 4) + 2)/(-1(1(1cos(3\u03c0x + 3) - 2) - 4) + 2)) + 2| - 1) + 2| + 3)) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -1(-2|((-3(-5(-1cos(1\u03c0(3|x - 3| + 1) + 3) - 2) - 3) + 2)/(2(-5(-1cos(1\u03c0(3|x - 3| + 1) + 3) - 2) - 3) - 1)) - 2|)^2 - 4(-2|((-3(-5(-1cos(1\u03c0(3|x - 3| + 1) + 3) - 2) - 3) + 2)/(2(-5(-1cos(1\u03c0(3|x - 3| + 1) + 3) - 2) - 3) - 1)) - 2|) + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = 3cos(2\u03c0(5((2(3|(-3(-2|x + 2|)^2 + 3(-2|x + 2|) + 4) + 3| + 3))/(1(3|(-3(-2|x + 2|)^2 + 3(-2|x + 2|) + 4) + 3| + 3) + 2)) + 1) - 2) - 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 1|((-1(-3sin(2\u03c0(-4(1|(3|x - 3| - 1) - 3| + 3) + 2) - 1) - 2) - 2)/(-3(-3sin(2\u03c0(-4(1|(3|x - 3| - 1) - 3| + 3) + 2) - 1) - 2) - 1)) + 1| - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "479", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 2((3(3e^(1(-1(-1|(-5x^2 + 3x - 3) - 2| - 2) + 4)) - 3) - 1)/(3(3e^(1(-1(-1|(-5x^2 + 3x - 3) - 2| - 2) + 4)) - 3))) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 5(5(2(1|(5((3x - 1)/(-3x + 4))^2 + 1((3x - 1)/(-3x + 4)) - 1) - 2| - 3) - 3) + 2)^2 + 4(5(2(1|(5((3x - 1)/(-3x + 4))^2 + 1((3x - 1)/(-3x + 4)) - 1) - 2| - 3) - 3) + 2) - 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = 2((3(-1|(1(2|(-2cos(2\u03c0x - 2) - 2) - 1| - 3) - 5) + 1| + 1) + 3)/(-3(-1|(1(2|(-2cos(2\u03c0x - 2) - 2) - 1| - 3) - 5) + 1| + 1) + 2)) + 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = 3sin(2\u03c0(5(4(2|(4(-4x + 2)^2 + 3(-4x + 2) - 4)| + 1) - 5) - 1) - 2) - 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "50", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 1(5(1|(3|(-1sin(3\u03c0((1x)/(-2x + 1)) + 2)) + 3| + 3)| - 2)^2 + 1(1|(3|(-1sin(3\u03c0((1x)/(-2x + 1)) + 2)) + 3| + 3)| - 2) - 3)^2 + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -5((2(-3sin(1\u03c0((-2(-1(3|x - 3| + 2) + 3) - 1)/(-2(-1(3|x - 3| + 2) + 3) - 3))) - 3) + 3)/(1(-3sin(1\u03c0((-2(-1(3|x - 3| + 2) + 3) - 1)/(-2(-1(3|x - 3| + 2) + 3) - 3))) - 3) - 2)) + 4 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = (3(1|((-2(3|(-2(2cos(1\u03c0x - 1) - 2) + 5) - 2| - 1) + 1)/(3(3|(-2(2cos(1\u03c0x - 1) - 2) + 5) - 2| - 1) + 3)) + 1| - 2) - 2)/(2(1|((-2(3|(-2(2cos(1\u03c0x - 1) - 2) + 5) - 2| - 1) + 1)/(3(3|(-2(2cos(1\u03c0x - 1) - 2) + 5) - 2| - 1) + 3)) + 1| - 2)) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = (2(-3|(-2|(2|(-1(1x - 3)^2 - 4(1x - 3) - 2) + 1| - 1) - 3| - 1) + 3| - 1) - 3)/(2(-3|(-2|(2|(-1(1x - 3)^2 - 4(1x - 3) - 2) + 1| - 1) - 3| - 1) + 3| - 1) - 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = 4((1(1(2|(2(-1x - 4)^2 - 4(-1x - 4) + 1) + 1| - 1)^2 + 1(2|(2(-1x - 4)^2 - 4(-1x - 4) + 1) + 1| - 1) - 4) + 3)/(-1(1(2|(2(-1x - 4)^2 - 4(-1x - 4) + 1) + 1| - 1)^2 + 1(2|(2(-1x - 4)^2 - 4(-1x - 4) + 1) + 1| - 1) - 4)))^2 - 5((1(1(2|(2(-1x - 4)^2 - 4(-1x - 4) + 1) + 1| - 1)^2 + 1(2|(2(-1x - 4)^2 - 4(-1x - 4) + 1) + 1| - 1) - 4) + 3)/(-1(1(2|(2(-1x - 4)^2 - 4(-1x - 4) + 1) + 1| - 1)^2 + 1(2|(2(-1x - 4)^2 - 4(-1x - 4) + 1) + 1| - 1) - 4))) + 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -5(-1(-3(1((-3((-3x - 2)/(-3x + 4)) - 2)/(-3((-3x - 2)/(-3x + 4)) - 1)) - 2)^2 - 4(1((-3((-3x - 2)/(-3x + 4)) - 2)/(-3((-3x - 2)/(-3x + 4)) - 1)) - 2) - 2)^2 - 5(-3(1((-3((-3x - 2)/(-3x + 4)) - 2)/(-3((-3x - 2)/(-3x + 4)) - 1)) - 2)^2 - 4(1((-3((-3x - 2)/(-3x + 4)) - 2)/(-3((-3x - 2)/(-3x + 4)) - 1)) - 2) - 2) - 1) - 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = 3(2|(5(-3(-2cos(1\u03c0(-3x + 4) - 1) + 3)^2 + 4(-2cos(1\u03c0(-3x + 4) - 1) + 3) + 1) + 2) + 3| + 1)^2 - 2(2|(5(-3(-2cos(1\u03c0(-3x + 4) - 1) + 3)^2 + 4(-2cos(1\u03c0(-3x + 4) - 1) + 3) + 1) + 2) + 3| + 1) + 4 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = -2(-4(-3(-1cos(3\u03c0((1(-2x^2 + 4x + 3) + 3)/(-1(-2x^2 + 4x + 3) + 3))) + 2) + 3) - 3)^2 + 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "46", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -3|(-2|((-3(-2((-3(1cos(2\u03c0x - 3) + 2) + 2)/(-2(1cos(2\u03c0x - 3) + 2) - 3)) - 4) - 3)/(1(-2((-3(1cos(2\u03c0x - 3) + 2) + 2)/(-2(1cos(2\u03c0x - 3) + 2) - 3)) - 4))) + 3| + 1) + 1| - 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -2|(2sin(1\u03c0(-1(-1|(2(-1|x + 3| + 2) + 1) + 3| - 2)^2 - 4(-1|(2(-1|x + 3| + 2) + 1) + 3| - 2) - 3) + 1) - 1)| + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "477", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = 1sin(2\u03c0(1|(2|(-1(-4(3|x + 2| + 3) - 4)) - 2| - 1) + 1| + 2)) - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "477", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = (-1(-2(-1|((3(-5((2x + 1)/(2x + 2))^2 - 3((2x + 1)/(2x + 2)) + 1) - 2)/(2(-5((2x + 1)/(2x + 2))^2 - 3((2x + 1)/(2x + 2)) + 1) - 1))| - 3)^2 + 4(-1|((3(-5((2x + 1)/(2x + 2))^2 - 3((2x + 1)/(2x + 2)) + 1) - 2)/(2(-5((2x + 1)/(2x + 2))^2 - 3((2x + 1)/(2x + 2)) + 1) - 1))| - 3) + 1) - 2)/(2(-2(-1|((3(-5((2x + 1)/(2x + 2))^2 - 3((2x + 1)/(2x + 2)) + 1) - 2)/(2(-5((2x + 1)/(2x + 2))^2 - 3((2x + 1)/(2x + 2)) + 1) - 1))| - 3)^2 + 4(-1|((3(-5((2x + 1)/(2x + 2))^2 - 3((2x + 1)/(2x + 2)) + 1) - 2)/(2(-5((2x + 1)/(2x + 2))^2 - 3((2x + 1)/(2x + 2)) + 1) - 1))| - 3) + 1) - 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = 2(-1(4((-1(-1cos(2\u03c0(-1x^2 + 5x) + 1)) - 1)/(-2(-1cos(2\u03c0(-1x^2 + 5x) + 1)) - 3)) + 3) + 1) + 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "316", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 3|(-5(-1(-1|(2sin(1\u03c0((1x - 1)/(1x + 1)) - 1)) + 3| + 3)^2 - 5(-1|(2sin(1\u03c0((1x - 1)/(1x + 1)) - 1)) + 3| + 3) + 2)^2 - 2(-1(-1|(2sin(1\u03c0((1x - 1)/(1x + 1)) - 1)) + 3| + 3)^2 - 5(-1|(2sin(1\u03c0((1x - 1)/(1x + 1)) - 1)) + 3| + 3) + 2) - 1) - 1| - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = (1(-1(2|((1(-1(-3cos(2\u03c0x - 1) + 1)^2 - 3(-3cos(2\u03c0x - 1) + 1) + 4) + 3)/(1(-1(-3cos(2\u03c0x - 1) + 1)^2 - 3(-3cos(2\u03c0x - 1) + 1) + 4) - 2)) - 3| - 2)^2 - 3(2|((1(-1(-3cos(2\u03c0x - 1) + 1)^2 - 3(-3cos(2\u03c0x - 1) + 1) + 4) + 3)/(1(-1(-3cos(2\u03c0x - 1) + 1)^2 - 3(-3cos(2\u03c0x - 1) + 1) + 4) - 2)) - 3| - 2) + 1) - 2)/(-1(-1(2|((1(-1(-3cos(2\u03c0x - 1) + 1)^2 - 3(-3cos(2\u03c0x - 1) + 1) + 4) + 3)/(1(-1(-3cos(2\u03c0x - 1) + 1)^2 - 3(-3cos(2\u03c0x - 1) + 1) + 4) - 2)) - 3| - 2)^2 - 3(2|((1(-1(-3cos(2\u03c0x - 1) + 1)^2 - 3(-3cos(2\u03c0x - 1) + 1) + 4) + 3)/(1(-1(-3cos(2\u03c0x - 1) + 1)^2 - 3(-3cos(2\u03c0x - 1) + 1) + 4) - 2)) - 3| - 2) + 1) - 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "160", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 4(4(5(-4(2|((-2x)/(2x - 3)) - 3| - 3)^2 - 5(2|((-2x)/(2x - 3)) - 3| - 3) - 1)^2 - 4(-4(2|((-2x)/(2x - 3)) - 3| - 3)^2 - 5(2|((-2x)/(2x - 3)) - 3| - 3) - 1))^2 - 4(5(-4(2|((-2x)/(2x - 3)) - 3| - 3)^2 - 5(2|((-2x)/(2x - 3)) - 3| - 3) - 1)^2 - 4(-4(2|((-2x)/(2x - 3)) - 3| - 3)^2 - 5(2|((-2x)/(2x - 3)) - 3| - 3) - 1)) - 1)^2 + 2(4(5(-4(2|((-2x)/(2x - 3)) - 3| - 3)^2 - 5(2|((-2x)/(2x - 3)) - 3| - 3) - 1)^2 - 4(-4(2|((-2x)/(2x - 3)) - 3| - 3)^2 - 5(2|((-2x)/(2x - 3)) - 3| - 3) - 1))^2 - 4(5(-4(2|((-2x)/(2x - 3)) - 3| - 3)^2 - 5(2|((-2x)/(2x - 3)) - 3| - 3) - 1)^2 - 4(-4(2|((-2x)/(2x - 3)) - 3| - 3)^2 - 5(2|((-2x)/(2x - 3)) - 3| - 3) - 1)) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -1|(3sin(3\u03c0(4(-2((-1(1x^2 - 5x - 4))/(-1(1x^2 - 5x - 4) + 3))^2 + 3((-1(1x^2 - 5x - 4))/(-1(1x^2 - 5x - 4) + 3)) - 1)^2 + 5(-2((-1(1x^2 - 5x - 4))/(-1(1x^2 - 5x - 4) + 3))^2 + 3((-1(1x^2 - 5x - 4))/(-1(1x^2 - 5x - 4) + 3)) - 1) + 2) + 1) - 3) - 2| - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "66", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = (2(-4(1(5(4(-1sin(2\u03c0x + 2) - 3)^2 + 2(-1sin(2\u03c0x + 2) - 3)) - 1) + 1) + 2) - 2)/(-3(-4(1(5(4(-1sin(2\u03c0x + 2) - 3)^2 + 2(-1sin(2\u03c0x + 2) - 3)) - 1) + 1) + 2) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -2(3(2sin(1\u03c0((-2((1(2x) + 2)/(3(2x) - 2)) - 1)/(-3((1(2x) + 2)/(3(2x) - 2)) + 2)) + 2) + 1) - 2) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -1|((2((1((-2(3(-3sin(1\u03c0x - 1) - 3) + 4) + 3)/(1(3(-3sin(1\u03c0x - 1) - 3) + 4) + 1)) - 1)/(-2((-2(3(-3sin(1\u03c0x - 1) - 3) + 4) + 3)/(1(3(-3sin(1\u03c0x - 1) - 3) + 4) + 1)) + 1)) - 3)/(1((1((-2(3(-3sin(1\u03c0x - 1) - 3) + 4) + 3)/(1(3(-3sin(1\u03c0x - 1) - 3) + 4) + 1)) - 1)/(-2((-2(3(-3sin(1\u03c0x - 1) - 3) + 4) + 3)/(1(3(-3sin(1\u03c0x - 1) - 3) + 4) + 1)) + 1)))) - 2| - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "51", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = 4(-2(1(-1|(-4(1cos(1\u03c0x - 3)) + 4) + 1| - 2)^2 - 5(-1|(-4(1cos(1\u03c0x - 3)) + 4) + 1| - 2) - 2) - 4)^2 - 5(-2(1(-1|(-4(1cos(1\u03c0x - 3)) + 4) + 1| - 2)^2 - 5(-1|(-4(1cos(1\u03c0x - 3)) + 4) + 1| - 2) - 2) - 4) - 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 2|(-4(3(-1(2|(-1cos(3\u03c0x - 1) + 3) + 2| + 1)) + 3)^2 - 5(3(-1(2|(-1cos(3\u03c0x - 1) + 3) + 2| + 1)) + 3)) + 1| - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = (1(-1((-2(2cos(2\u03c0(-5((2x + 3)/(3x - 2)) - 2) + 2) + 3) - 3)/(-2(2cos(2\u03c0(-5((2x + 3)/(3x - 2)) - 2) + 2) + 3) - 1)) + 4) + 3)/(-3(-1((-2(2cos(2\u03c0(-5((2x + 3)/(3x - 2)) - 2) + 2) + 3) - 3)/(-2(2cos(2\u03c0(-5((2x + 3)/(3x - 2)) - 2) + 2) + 3) - 1)) + 4) - 3) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "25", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -1|(-1(-3|((3(-3sin(2\u03c0((2x - 3)/(-2x))) + 2) + 1)/(-2(-3sin(2\u03c0((2x - 3)/(-2x))) + 2))) - 1| - 3)^2 + 4(-3|((3(-3sin(2\u03c0((2x - 3)/(-2x))) + 2) + 1)/(-2(-3sin(2\u03c0((2x - 3)/(-2x))) + 2))) - 1| - 3) + 3) + 3| where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "49", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -1(2(5((-3(-5(-3x^2 + 4x + 5) - 2) + 2)/(-3(-5(-3x^2 + 4x + 5) - 2) - 2)) + 3) + 4)^2 + 3(2(5((-3(-5(-3x^2 + 4x + 5) - 2) + 2)/(-3(-5(-3x^2 + 4x + 5) - 2) - 2)) + 3) + 4) - 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 3(-2|(-3|(-3(-1|(1cos(3\u03c0x - 3) - 2) + 3| - 1) + 4) + 3| + 1) - 3| - 1)^2 + 3(-2|(-3|(-3(-1|(1cos(3\u03c0x - 3) - 2) + 3| - 1) + 4) + 3| + 1) - 3| - 1) + 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = 1|(3cos(3\u03c0(1|(3(3(-4x^2 - 2x + 4)^2 + 4(-4x^2 - 2x + 4) + 5) + 1) - 2| - 3) + 3) - 3)| + 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "51", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -1|(-1(1(-4(-1((-2x - 1)/(-2x + 3))^2 + 2((-2x - 1)/(-2x + 3)))^2 - 2(-1((-2x - 1)/(-2x + 3))^2 + 2((-2x - 1)/(-2x + 3))) + 2)^2 - 4)^2 + 5)| + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "25", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -1(2sin(2\u03c0(3(-3(1((1x + 3)/(1x))) + 1) - 2) - 3) - 1)^2 - 5(2sin(2\u03c0(3(-3(1((1x + 3)/(1x))) + 1) - 2) - 3) - 1) - 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "87", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 2|((-3(-1(3(2e^(2(-1x^2 + 5x + 2)) - 1) + 2)^2 - 4(3(2e^(2(-1x^2 + 5x + 2)) - 1) + 2) - 2) + 3)/(3(-1(3(2e^(2(-1x^2 + 5x + 2)) - 1) + 2)^2 - 4(3(2e^(2(-1x^2 + 5x + 2)) - 1) + 2) - 2) - 1)) + 1| - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = 1(-2|(1sin(1\u03c0((-1(2(-3x + 2) + 4) - 3)/(-1(2(-3x + 2) + 4) - 1)) + 3) + 3) - 1| + 3) + 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 3sin(2\u03c0((-1(2|(-2|((-2(2x - 5) - 1)/(-1(2x - 5) - 3)) - 2| + 3) + 2| - 3) + 2)/(-3(2|(-2|((-2(2x - 5) - 1)/(-1(2x - 5) - 3)) - 2| + 3) + 2| - 3) + 4)) + 2) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = 1(4((1(-2|(3(-3|x + 3| + 2) + 4) + 3| + 2) + 3)/(-1(-2|(3(-3|x + 3| + 2) + 4) + 3| + 2) + 3)) - 1)^2 + 3(4((1(-2|(3(-3|x + 3| + 2) + 4) + 3| + 2) + 3)/(-1(-2|(3(-3|x + 3| + 2) + 4) + 3| + 2) + 3)) - 1) - 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -1|(2(-3(-1|(2(1sin(3\u03c0x - 1)) - 2) - 2| + 2)^2 - 3(-1|(2(1sin(3\u03c0x - 1)) - 2) - 2| + 2) + 3)^2 - 5(-3(-1|(2(1sin(3\u03c0x - 1)) - 2) - 2| + 2)^2 - 3(-1|(2(1sin(3\u03c0x - 1)) - 2) - 2| + 2) + 3)) + 2| have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "180", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = (1(-4(2|(-3(-2cos(1\u03c0(4x^2 + 1) - 1) - 2)^2 - 1(-2cos(1\u03c0(4x^2 + 1) - 1) - 2) - 1)| - 1)^2 + 2(2|(-3(-2cos(1\u03c0(4x^2 + 1) - 1) - 2)^2 - 1(-2cos(1\u03c0(4x^2 + 1) - 1) - 2) - 1)| - 1)) - 1)/(-1(-4(2|(-3(-2cos(1\u03c0(4x^2 + 1) - 1) - 2)^2 - 1(-2cos(1\u03c0(4x^2 + 1) - 1) - 2) - 1)| - 1)^2 + 2(2|(-3(-2cos(1\u03c0(4x^2 + 1) - 1) - 2)^2 - 1(-2cos(1\u03c0(4x^2 + 1) - 1) - 2) - 1)| - 1)) + 3) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "98", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 3(-2(2|(-1|(-2(-3x^2 + 3x + 4) + 1) - 2| + 3) - 3| - 1)^2 + 3)^2 - 1(-2(2|(-1|(-2(-3x^2 + 3x + 4) + 1) - 2| + 3) - 3| - 1)^2 + 3) - 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 1(-3(-2sin(2\u03c0((-2(2(-3x)^2 + 1(-3x) - 3) + 2)/(-2(2(-3x)^2 + 1(-3x) - 3) - 2)) - 1) - 3)^2 - 2(-2sin(2\u03c0((-2(2(-3x)^2 + 1(-3x) - 3) + 2)/(-2(2(-3x)^2 + 1(-3x) - 3) - 2)) - 1) - 3) - 2)^2 - 4(-3(-2sin(2\u03c0((-2(2(-3x)^2 + 1(-3x) - 3) + 2)/(-2(2(-3x)^2 + 1(-3x) - 3) - 2)) - 1) - 3)^2 - 2(-2sin(2\u03c0((-2(2(-3x)^2 + 1(-3x) - 3) + 2)/(-2(2(-3x)^2 + 1(-3x) - 3) - 2)) - 1) - 3) - 2) - 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 1((-2(-1sin(2\u03c0(1((-1(1x - 4))/(2(1x - 4) - 1))^2 - 3((-1(1x - 4))/(2(1x - 4) - 1)) - 1) + 2) + 3) - 1)/(-1(-1sin(2\u03c0(1((-1(1x - 4))/(2(1x - 4) - 1))^2 - 3((-1(1x - 4))/(2(1x - 4) - 1)) - 1) + 2) + 3) - 2)) + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = (3(2|(-3|(1(-1(-5x - 3)^2 + 4(-5x - 3) + 3)^2 + 5(-1(-5x - 3)^2 + 4(-5x - 3) + 3) + 2)| + 2)|) - 3)/(-1(2|(-3|(1(-1(-5x - 3)^2 + 4(-5x - 3) + 3)^2 + 5(-1(-5x - 3)^2 + 4(-5x - 3) + 3) + 2)| + 2)|)) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 2(1|(1(2((3(-2x^2 + 1x + 2))/(-1(-2x^2 + 1x + 2) + 3))^2 - 3((3(-2x^2 + 1x + 2))/(-1(-2x^2 + 1x + 2) + 3)) - 3)^2 - 1(2((3(-2x^2 + 1x + 2))/(-1(-2x^2 + 1x + 2) + 3))^2 - 3((3(-2x^2 + 1x + 2))/(-1(-2x^2 + 1x + 2) + 3)) - 3) - 5) - 3| - 1)^2 + 5(1|(1(2((3(-2x^2 + 1x + 2))/(-1(-2x^2 + 1x + 2) + 3))^2 - 3((3(-2x^2 + 1x + 2))/(-1(-2x^2 + 1x + 2) + 3)) - 3)^2 - 1(2((3(-2x^2 + 1x + 2))/(-1(-2x^2 + 1x + 2) + 3))^2 - 3((3(-2x^2 + 1x + 2))/(-1(-2x^2 + 1x + 2) + 3)) - 3) - 5) - 3| - 1) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -3(-2(-3((-1(-2(3x + 3)^2 - 3(3x + 3) + 2) + 2)/(3(-2(3x + 3)^2 - 3(3x + 3) + 2) - 2)) + 2))^2 - 1(-2(-3((-1(-2(3x + 3)^2 - 3(3x + 3) + 2) + 2)/(3(-2(3x + 3)^2 - 3(3x + 3) + 2) - 2)) + 2)) - 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = 3|(3((-3((2(-1(-2|x - 3| + 1)^2 - 2(-2|x - 3| + 1) + 2) - 3)/(-3(-1(-2|x - 3| + 1)^2 - 2(-2|x - 3| + 1) + 2) + 2)) + 2)/(2((2(-1(-2|x - 3| + 1)^2 - 2(-2|x - 3| + 1) + 2) - 3)/(-3(-1(-2|x - 3| + 1)^2 - 2(-2|x - 3| + 1) + 2) + 2)))) + 2)| - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -1(-4((-2(-3((1(4x^2 + 3x) - 1)/(2(4x^2 + 3x) + 2))^2 + 3((1(4x^2 + 3x) - 1)/(2(4x^2 + 3x) + 2)) + 2))/(-2(-3((1(4x^2 + 3x) - 1)/(2(4x^2 + 3x) + 2))^2 + 3((1(4x^2 + 3x) - 1)/(2(4x^2 + 3x) + 2)) + 2) + 3))^2 - 2)^2 - 2(-4((-2(-3((1(4x^2 + 3x) - 1)/(2(4x^2 + 3x) + 2))^2 + 3((1(4x^2 + 3x) - 1)/(2(4x^2 + 3x) + 2)) + 2))/(-2(-3((1(4x^2 + 3x) - 1)/(2(4x^2 + 3x) + 2))^2 + 3((1(4x^2 + 3x) - 1)/(2(4x^2 + 3x) + 2)) + 2) + 3))^2 - 2) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -4((1(-3(-2sin(3\u03c0(2|((3x + 2)/(-2x + 3)) - 3| - 2) + 2)) - 5) - 1)/(1(-3(-2sin(3\u03c0(2|((3x + 2)/(-2x + 3)) - 3| - 2) + 2)) - 5))) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "53", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 2|(3(-1cos(3\u03c0(-2(-3(5x^2 + 5x + 3)^2 - 2(5x^2 + 5x + 3) - 4) - 2) - 1) - 1)^2 + 2(-1cos(3\u03c0(-2(-3(5x^2 + 5x + 3)^2 - 2(5x^2 + 5x + 3) - 4) - 2) - 1) - 1) - 4) + 1| + 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "64", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -1(-1(-1(3cos(2\u03c0((1((1x + 2)/(-2x - 1)))/(2((1x + 2)/(-2x - 1)) + 1)) + 3) + 2) - 2) + 2)^2 - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 1((-3((-3((1(1sin(3\u03c0(-1|x + 1| + 1) - 1) + 1) + 3)/(-1(1sin(3\u03c0(-1|x + 1| + 1) - 1) + 1) + 2)) - 2)/(3((1(1sin(3\u03c0(-1|x + 1| + 1) - 1) + 1) + 3)/(-1(1sin(3\u03c0(-1|x + 1| + 1) - 1) + 1) + 2)) + 3)) + 3)/(3((-3((1(1sin(3\u03c0(-1|x + 1| + 1) - 1) + 1) + 3)/(-1(1sin(3\u03c0(-1|x + 1| + 1) - 1) + 1) + 2)) - 2)/(3((1(1sin(3\u03c0(-1|x + 1| + 1) - 1) + 1) + 3)/(-1(1sin(3\u03c0(-1|x + 1| + 1) - 1) + 1) + 2)) + 3)) + 2)) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 1cos(3\u03c0((-2(2|(-2|((-2(2|x| - 2) + 3)/(-2(2|x| - 2) - 3)) - 1| + 1) - 1| - 3) + 3)/(-2(2|(-2|((-2(2|x| - 2) + 3)/(-2(2|x| - 2) - 3)) - 1| + 1) - 1| - 3) - 3)) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "180", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = 1|(2|((1((-2(-4(1cos(2\u03c0x - 3) - 3) + 2) + 1)/(-1(-4(1cos(2\u03c0x - 3) - 3) + 2) + 2)) - 3)/(3((-2(-4(1cos(2\u03c0x - 3) - 3) + 2) + 1)/(-1(-4(1cos(2\u03c0x - 3) - 3) + 2) + 2)) + 3))| + 1) - 3| + 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = (2((-3(2|(2|((3(1|x + 3| - 3) - 2)/(-1(1|x + 3| - 3) + 2)) - 2| + 1) - 2| + 2) - 1)/(2(2|(2|((3(1|x + 3| - 3) - 2)/(-1(1|x + 3| - 3) + 2)) - 2| + 1) - 2| + 2) + 3)) + 1)/(3((-3(2|(2|((3(1|x + 3| - 3) - 2)/(-1(1|x + 3| - 3) + 2)) - 2| + 1) - 2| + 2) - 1)/(2(2|(2|((3(1|x + 3| - 3) - 2)/(-1(1|x + 3| - 3) + 2)) - 2| + 1) - 2| + 2) + 3)) + 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = (-1(-1|(-1(1(-1(-5x + 5) - 1)^2 - 5(-1(-5x + 5) - 1) + 2)^2 + 5) + 1| - 2))/(3(-1|(-1(1(-1(-5x + 5) - 1)^2 - 5(-1(-5x + 5) - 1) + 2)^2 + 5) + 1| - 2) - 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 3((-1(1(1(1sin(2\u03c0(-1|x - 3| + 1) + 2) + 1) - 1) + 1) - 1)/(-2(1(1(1sin(2\u03c0(-1|x - 3| + 1) + 2) + 1) - 1) + 1) - 1))^2 - 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = 1|(-2(5((-2(3|(3x^2 - 4) - 3| + 1) + 2)/(-1(3|(3x^2 - 4) - 3| + 1) + 2)) + 3)^2 + 2(5((-2(3|(3x^2 - 4) - 3| + 1) + 2)/(-1(3|(3x^2 - 4) - 3| + 1) + 2)) + 3) - 1) - 3| - 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -1(-1(2|(1(1|(-5x^2 + 3x + 2) - 2| - 3)^2 - 3(1|(-5x^2 + 3x + 2) - 2| - 3) - 4) + 1| - 3) + 4) - 5 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -1(-2(-2|(-2|(1|(2sin(2\u03c0x - 3) + 2) + 3| - 1) + 1| - 2) - 3|)^2 + 1(-2|(-2|(1|(2sin(2\u03c0x - 3) + 2) + 3| - 1) + 1| - 2) - 3|) - 5) + 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -1|(-1sin(1\u03c0(-1(1|(2|(-3x - 1) - 2| + 2) - 1| - 1) + 4) + 3) - 3) + 3| + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "229", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -1|(1sin(3\u03c0(2(-3|(-3|(-2x + 5) - 1| + 1) + 3| + 2)^2 + 4(-3|(-3|(-2x + 5) - 1| + 1) + 3| + 2) + 5) + 1)) - 2| where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "100", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = -2|(-5(-1(-3(-1|((1x - 1)/(-2x - 2)) - 2| + 2) + 1)^2 - 3(-3(-1|((1x - 1)/(-2x - 2)) - 2| + 2) + 1))^2 + 1(-1(-3(-1|((1x - 1)/(-2x - 2)) - 2| + 2) + 1)^2 - 3(-3(-1|((1x - 1)/(-2x - 2)) - 2| + 2) + 1)) - 1) + 3| in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = 4(-2((-2(1(1(2cos(3\u03c0x))^2 + 2(2cos(3\u03c0x)))^2 + 5(1(2cos(3\u03c0x))^2 + 2(2cos(3\u03c0x))) + 1) + 2)/(1(1(1(2cos(3\u03c0x))^2 + 2(2cos(3\u03c0x)))^2 + 5(1(2cos(3\u03c0x))^2 + 2(2cos(3\u03c0x))) + 1) - 2))^2 - 2((-2(1(1(2cos(3\u03c0x))^2 + 2(2cos(3\u03c0x)))^2 + 5(1(2cos(3\u03c0x))^2 + 2(2cos(3\u03c0x))) + 1) + 2)/(1(1(1(2cos(3\u03c0x))^2 + 2(2cos(3\u03c0x)))^2 + 5(1(2cos(3\u03c0x))^2 + 2(2cos(3\u03c0x))) + 1) - 2)) - 2) - 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -5(-2cos(2\u03c0(-2(5(-1|(-2|x - 1| + 1) - 1| + 1)^2 + 2(-1|(-2|x - 1| + 1) - 1| + 1) - 1)^2 - 4(5(-1|(-2|x - 1| + 1) - 1| + 1)^2 + 2(-1|(-2|x - 1| + 1) - 1| + 1) - 1) + 5) - 3) + 3)^2 - 3(-2cos(2\u03c0(-2(5(-1|(-2|x - 1| + 1) - 1| + 1)^2 + 2(-1|(-2|x - 1| + 1) - 1| + 1) - 1)^2 - 4(5(-1|(-2|x - 1| + 1) - 1| + 1)^2 + 2(-1|(-2|x - 1| + 1) - 1| + 1) - 1) + 5) - 3) + 3) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -1(2sin(1\u03c0(-4(3|(4(-1x - 3) - 2) + 3| + 3) - 5) + 2) + 3)^2 - 3(2sin(1\u03c0(-4(3|(4(-1x - 3) - 2) + 3| + 3) - 5) + 2) + 3) + 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "608", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -1(-5(-1((-2(3(4x + 1)^2 + 5(4x + 1) - 1))/(-1(3(4x + 1)^2 + 5(4x + 1) - 1) + 3)) + 3)^2 + 5(-1((-2(3(4x + 1)^2 + 5(4x + 1) - 1))/(-1(3(4x + 1)^2 + 5(4x + 1) - 1) + 3)) + 3) + 5)^2 - 1(-5(-1((-2(3(4x + 1)^2 + 5(4x + 1) - 1))/(-1(3(4x + 1)^2 + 5(4x + 1) - 1) + 3)) + 3)^2 + 5(-1((-2(3(4x + 1)^2 + 5(4x + 1) - 1))/(-1(3(4x + 1)^2 + 5(4x + 1) - 1) + 3)) + 3) + 5) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = (-1(-1cos(3\u03c0((2(-1(-4(-3|x - 2| + 2)^2 + 4)^2 + 4(-4(-3|x - 2| + 2)^2 + 4) - 1) + 3)/(-1(-1(-4(-3|x - 2| + 2)^2 + 4)^2 + 4(-4(-3|x - 2| + 2)^2 + 4) - 1))) + 3)))/(-1(-1cos(3\u03c0((2(-1(-4(-3|x - 2| + 2)^2 + 4)^2 + 4(-4(-3|x - 2| + 2)^2 + 4) - 1) + 3)/(-1(-1(-4(-3|x - 2| + 2)^2 + 4)^2 + 4(-4(-3|x - 2| + 2)^2 + 4) - 1))) + 3)) + 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = 5(-3(2sin(2\u03c0(2(1((2x)/(-1x + 3))^2 + 2((2x)/(-1x + 3)) + 2)^2 - 3(1((2x)/(-1x + 3))^2 + 2((2x)/(-1x + 3)) + 2) - 3)) - 3)^2 + 1) - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 3(-1|(-5(-1(-3cos(2\u03c0(-2x - 4)) - 2)^2 - 2) + 2) + 1| + 3) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "160", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = (2(-1e^(-2(-1(1(-1(-2x^2 + 3x + 3)^2 - 2(-2x^2 + 3x + 3) + 1)^2 - 5(-1(-2x^2 + 3x + 3)^2 - 2(-2x^2 + 3x + 3) + 1) - 1)^2 - 2(1(-1(-2x^2 + 3x + 3)^2 - 2(-2x^2 + 3x + 3) + 1)^2 - 5(-1(-2x^2 + 3x + 3)^2 - 2(-2x^2 + 3x + 3) + 1) - 1) - 3)) - 3) + 2)/(3(-1e^(-2(-1(1(-1(-2x^2 + 3x + 3)^2 - 2(-2x^2 + 3x + 3) + 1)^2 - 5(-1(-2x^2 + 3x + 3)^2 - 2(-2x^2 + 3x + 3) + 1) - 1)^2 - 2(1(-1(-2x^2 + 3x + 3)^2 - 2(-2x^2 + 3x + 3) + 1)^2 - 5(-1(-2x^2 + 3x + 3)^2 - 2(-2x^2 + 3x + 3) + 1) - 1) - 3)) - 3)) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = (-3(1(-3|(3|((2(-1sin(2\u03c0x + 3) + 2))/(-3(-1sin(2\u03c0x + 3) + 2) + 1)) + 1|) - 2| + 2)^2 + 3(-3|(3|((2(-1sin(2\u03c0x + 3) + 2))/(-3(-1sin(2\u03c0x + 3) + 2) + 1)) + 1|) - 2| + 2) - 4) - 2)/(1(1(-3|(3|((2(-1sin(2\u03c0x + 3) + 2))/(-3(-1sin(2\u03c0x + 3) + 2) + 1)) + 1|) - 2| + 2)^2 + 3(-3|(3|((2(-1sin(2\u03c0x + 3) + 2))/(-3(-1sin(2\u03c0x + 3) + 2) + 1)) + 1|) - 2| + 2) - 4) - 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 3(3(1|(-3|(-2((1x + 3)/(-2x))^2 - 3((1x + 3)/(-2x)) + 3) - 2| + 2) + 1| - 1))^2 + 1(3(1|(-3|(-2((1x + 3)/(-2x))^2 - 3((1x + 3)/(-2x)) + 3) - 2| + 2) + 1| - 1)) - 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -5((3(-2(5(-1e^(1(4x - 1)) - 3) + 5) + 4) - 1)/(-2(-2(5(-1e^(1(4x - 1)) - 3) + 5) + 4) + 1)) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -3|(-3|(-2|(3|((2(2cos(3\u03c0x + 3) - 2) + 1)/(1(2cos(3\u03c0x + 3) - 2))) - 2| + 3) + 3| + 1) + 3| + 3) - 1| - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "57", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -3(-5(-5(-3cos(2\u03c0((-2(-1|x + 2| + 2))/(2(-1|x + 2| + 2) - 1))) + 2) - 1)^2 - 4(-5(-3cos(2\u03c0((-2(-1|x + 2| + 2))/(2(-1|x + 2| + 2) - 1))) + 2) - 1) - 1) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 1(2(-2|(2(1|(1x - 3)| - 1)^2 - 1) - 3| + 2)^2 + 5(-2|(2(1|(1x - 3)| - 1)^2 - 1) - 3| + 2) + 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = 2cos(2\u03c0(2((2(-3(3(4x^2 - 5x - 1) + 5) - 2) + 2)/(3(-3(3(4x^2 - 5x - 1) + 5) - 2) - 1))^2 - 4((2(-3(3(4x^2 - 5x - 1) + 5) - 2) + 2)/(3(-3(3(4x^2 - 5x - 1) + 5) - 2) - 1))) + 1) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 3|(-3(-4(4(2((-1x + 1)/(3x + 2)) - 2) + 1)^2 - 5(4(2((-1x + 1)/(3x + 2)) - 2) + 1) + 5) + 4) - 2| + 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 3(-4(-3(-2|(2cos(1\u03c0(-2x^2 + 5x + 2) - 3) - 2) + 2| + 2)^2 + 3(-2|(2cos(1\u03c0(-2x^2 + 5x + 2) - 3) - 2) + 2| + 2) - 3) + 2)^2 - 4(-4(-3(-2|(2cos(1\u03c0(-2x^2 + 5x + 2) - 3) - 2) + 2| + 2)^2 + 3(-2|(2cos(1\u03c0(-2x^2 + 5x + 2) - 3) - 2) + 2| + 2) - 3) + 2) + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "365", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -1((3(2|((1(3(-2x) + 5) - 1)/(1(3(-2x) + 5))) - 2| - 2) + 1)/(3(2|((1(3(-2x) + 5) - 1)/(1(3(-2x) + 5))) - 2| - 2) - 2))^2 - 2((3(2|((1(3(-2x) + 5) - 1)/(1(3(-2x) + 5))) - 2| - 2) + 1)/(3(2|((1(3(-2x) + 5) - 1)/(1(3(-2x) + 5))) - 2| - 2) - 2)) + 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -1sin(1\u03c0(3(-2(-1((-2(-2x - 2) + 1)/(1(-2x - 2) + 1))^2 + 3((-2(-2x - 2) + 1)/(1(-2x - 2) + 1)))^2 - 3(-1((-2(-2x - 2) + 1)/(1(-2x - 2) + 1))^2 + 3((-2(-2x - 2) + 1)/(1(-2x - 2) + 1))) - 5) + 4) - 2) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "237", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -1sin(2\u03c0(-2(-1(-1|((3(-4x - 2))/(-2(-4x - 2) - 2)) + 2| - 2)^2 - 4(-1|((3(-4x - 2))/(-2(-4x - 2) - 2)) + 2| - 2) - 5) + 5) + 1) + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = -1(-1(-1|(1(5((2x - 3)/(1x + 3))^2 + 1((2x - 3)/(1x + 3)) - 3)^2 - 2(5((2x - 3)/(1x + 3))^2 + 1((2x - 3)/(1x + 3)) - 3) - 2) + 1|) - 2) - 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 3|((2(-2|((3(-3sin(3\u03c0((-2x + 3)/(-3x + 1)) + 2) + 3) + 3)/(3(-3sin(3\u03c0((-2x + 3)/(-3x + 1)) + 2) + 3) + 2)) + 1| + 1) - 2)/(-2(-2|((3(-3sin(3\u03c0((-2x + 3)/(-3x + 1)) + 2) + 3) + 3)/(3(-3sin(3\u03c0((-2x + 3)/(-3x + 1)) + 2) + 3) + 2)) + 1| + 1) - 3)) + 2| + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 3(-5(-2sin(2\u03c0((3(1|(2|x + 2| - 2) + 2| - 2) - 3)/(-1(1|(2|x + 2| - 2) + 2| - 2) + 3)) + 1) + 3) + 3) - 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "44", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 1(3|((-2(-2sin(3\u03c0(2(1|x - 3| - 1)^2 - 2(1|x - 3| - 1) + 2) - 3) + 2) - 2)/(2(-2sin(3\u03c0(2(1|x - 3| - 1)^2 - 2(1|x - 3| - 1) + 2) - 3) + 2) + 1)) + 3| - 3) - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "454", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -3|((3(4((-3((-3(-1x) - 1)/(-1(-1x) + 3)) - 2)/(-1((-3(-1x) - 1)/(-1(-1x) + 3))))^2 - 3((-3((-3(-1x) - 1)/(-1(-1x) + 3)) - 2)/(-1((-3(-1x) - 1)/(-1(-1x) + 3)))) + 5) - 1)/(-1(4((-3((-3(-1x) - 1)/(-1(-1x) + 3)) - 2)/(-1((-3(-1x) - 1)/(-1(-1x) + 3))))^2 - 3((-3((-3(-1x) - 1)/(-1(-1x) + 3)) - 2)/(-1((-3(-1x) - 1)/(-1(-1x) + 3)))) + 5) - 2)) + 2| where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -1|(-2e^(1(-1|(-5(1(1x^2 + 1x - 3) + 2)) + 3| - 1)))| where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = 2((2(-3cos(2\u03c0(-1|(5((-2x - 3)/(1x - 2))^2 + 3((-2x - 3)/(1x - 2)) - 4) - 2| - 1) + 3) - 1) - 2)/(2(-3cos(2\u03c0(-1|(5((-2x - 3)/(1x - 2))^2 + 3((-2x - 3)/(1x - 2)) - 4) - 2| - 1) + 3) - 1)))^2 + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "197", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = (-1((2(-2((2(5(-4x + 5)^2 + 5(-4x + 5) + 3) + 1)/(-1(5(-4x + 5)^2 + 5(-4x + 5) + 3) + 2)) + 2) - 3)/(-1(-2((2(5(-4x + 5)^2 + 5(-4x + 5) + 3) + 1)/(-1(5(-4x + 5)^2 + 5(-4x + 5) + 3) + 2)) + 2) - 2)) - 1)/(-3((2(-2((2(5(-4x + 5)^2 + 5(-4x + 5) + 3) + 1)/(-1(5(-4x + 5)^2 + 5(-4x + 5) + 3) + 2)) + 2) - 3)/(-1(-2((2(5(-4x + 5)^2 + 5(-4x + 5) + 3) + 1)/(-1(5(-4x + 5)^2 + 5(-4x + 5) + 3) + 2)) + 2) - 2)) - 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "405", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = (-1(3|((3(-1|(1(1x - 3) + 5) - 3| + 1) + 2)/(-2(-1|(1(1x - 3) + 5) - 3| + 1) - 3)) - 3| - 2))/(-3(3|((3(-1|(1(1x - 3) + 5) - 3| + 1) + 2)/(-2(-1|(1(1x - 3) + 5) - 3| + 1) - 3)) - 3| - 2)) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "84", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 3(-4(1((2(-3sin(1\u03c0(-3x + 1) + 2) - 1) - 1)/(3(-3sin(1\u03c0(-3x + 1) + 2) - 1) + 1)) - 5) + 2)^2 - 2(-4(1((2(-3sin(1\u03c0(-3x + 1) + 2) - 1) - 1)/(3(-3sin(1\u03c0(-3x + 1) + 2) - 1) + 1)) - 5) + 2) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "83", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = -5(3(-5(1(-2(-3sin(3\u03c0x - 2) - 3)^2 + 2(-3sin(3\u03c0x - 2) - 3) - 2)^2 - 5(-2(-3sin(3\u03c0x - 2) - 3)^2 + 2(-3sin(3\u03c0x - 2) - 3) - 2) + 1)^2 - 4(1(-2(-3sin(3\u03c0x - 2) - 3)^2 + 2(-3sin(3\u03c0x - 2) - 3) - 2)^2 - 5(-2(-3sin(3\u03c0x - 2) - 3)^2 + 2(-3sin(3\u03c0x - 2) - 3) - 2) + 1) - 1)^2 + 3(-5(1(-2(-3sin(3\u03c0x - 2) - 3)^2 + 2(-3sin(3\u03c0x - 2) - 3) - 2)^2 - 5(-2(-3sin(3\u03c0x - 2) - 3)^2 + 2(-3sin(3\u03c0x - 2) - 3) - 2) + 1)^2 - 4(1(-2(-3sin(3\u03c0x - 2) - 3)^2 + 2(-3sin(3\u03c0x - 2) - 3) - 2)^2 - 5(-2(-3sin(3\u03c0x - 2) - 3)^2 + 2(-3sin(3\u03c0x - 2) - 3) - 2) + 1) - 1) + 1)^2 + 3(3(-5(1(-2(-3sin(3\u03c0x - 2) - 3)^2 + 2(-3sin(3\u03c0x - 2) - 3) - 2)^2 - 5(-2(-3sin(3\u03c0x - 2) - 3)^2 + 2(-3sin(3\u03c0x - 2) - 3) - 2) + 1)^2 - 4(1(-2(-3sin(3\u03c0x - 2) - 3)^2 + 2(-3sin(3\u03c0x - 2) - 3) - 2)^2 - 5(-2(-3sin(3\u03c0x - 2) - 3)^2 + 2(-3sin(3\u03c0x - 2) - 3) - 2) + 1) - 1)^2 + 3(-5(1(-2(-3sin(3\u03c0x - 2) - 3)^2 + 2(-3sin(3\u03c0x - 2) - 3) - 2)^2 - 5(-2(-3sin(3\u03c0x - 2) - 3)^2 + 2(-3sin(3\u03c0x - 2) - 3) - 2) + 1)^2 - 4(1(-2(-3sin(3\u03c0x - 2) - 3)^2 + 2(-3sin(3\u03c0x - 2) - 3) - 2)^2 - 5(-2(-3sin(3\u03c0x - 2) - 3)^2 + 2(-3sin(3\u03c0x - 2) - 3) - 2) + 1) - 1) + 1) + 5 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "27", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = (1(3(-2sin(2\u03c0(3|(-4((1x - 3)/(1x + 3))) + 3| - 1) + 3) - 2)^2 - 1(-2sin(2\u03c0(3|(-4((1x - 3)/(1x + 3))) + 3| - 1) + 3) - 2) - 5) + 3)/(3(3(-2sin(2\u03c0(3|(-4((1x - 3)/(1x + 3))) + 3| - 1) + 3) - 2)^2 - 1(-2sin(2\u03c0(3|(-4((1x - 3)/(1x + 3))) + 3| - 1) + 3) - 2) - 5) + 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "213", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = 5(-2(1((-3(3|(-3sin(2\u03c0x + 3)) - 3|) + 3)/(1(3|(-3sin(2\u03c0x + 3)) - 3|) + 3))^2 - 2((-3(3|(-3sin(2\u03c0x + 3)) - 3|) + 3)/(1(3|(-3sin(2\u03c0x + 3)) - 3|) + 3)) - 3) + 4) + 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = 3(3(-2sin(1\u03c0(-2(-1(-4x^2 - 1x)^2 - 3(-4x^2 - 1x) + 4)^2 + 4(-1(-4x^2 - 1x)^2 - 3(-4x^2 - 1x) + 4) - 4) - 1) - 1)^2 + 3(-2sin(1\u03c0(-2(-1(-4x^2 - 1x)^2 - 3(-4x^2 - 1x) + 4)^2 + 4(-1(-4x^2 - 1x)^2 - 3(-4x^2 - 1x) + 4) - 4) - 1) - 1) - 4)^2 + 4(3(-2sin(1\u03c0(-2(-1(-4x^2 - 1x)^2 - 3(-4x^2 - 1x) + 4)^2 + 4(-1(-4x^2 - 1x)^2 - 3(-4x^2 - 1x) + 4) - 4) - 1) - 1)^2 + 3(-2sin(1\u03c0(-2(-1(-4x^2 - 1x)^2 - 3(-4x^2 - 1x) + 4)^2 + 4(-1(-4x^2 - 1x)^2 - 3(-4x^2 - 1x) + 4) - 4) - 1) - 1) - 4) + 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "24", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 1(5(-3(3cos(1\u03c0(-4((-2x - 2)/(2x + 1)) + 5)) - 2) - 3)^2 + 3(-3(3cos(1\u03c0(-4((-2x - 2)/(2x + 1)) + 5)) - 2) - 3) - 2)^2 - 5(5(-3(3cos(1\u03c0(-4((-2x - 2)/(2x + 1)) + 5)) - 2) - 3)^2 + 3(-3(3cos(1\u03c0(-4((-2x - 2)/(2x + 1)) + 5)) - 2) - 3) - 2) + 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = -4(-1(1cos(2\u03c0((-1(-2|(1|x - 2|) - 3| + 1) - 1)/(-2(-2|(1|x - 2|) - 3| + 1))) + 1) - 1)^2 - 2(1cos(2\u03c0((-1(-2|(1|x - 2|) - 3| + 1) - 1)/(-2(-2|(1|x - 2|) - 3| + 1))) + 1) - 1) + 4) + 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "43", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -5(-1(-2(5(1(-1cos(3\u03c0x - 2) - 2)^2 - 2) + 5)^2 + 2(5(1(-1cos(3\u03c0x - 2) - 2)^2 - 2) + 5) + 2) + 1) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = 1sin(2\u03c0((2((1(1((-3((-3x)/(-2x - 2)) + 2)/(-1((-3x)/(-2x - 2)) + 2))^2 - 1((-3((-3x)/(-2x - 2)) + 2)/(-1((-3x)/(-2x - 2)) + 2)) - 1) - 2)/(2(1((-3((-3x)/(-2x - 2)) + 2)/(-1((-3x)/(-2x - 2)) + 2))^2 - 1((-3((-3x)/(-2x - 2)) + 2)/(-1((-3x)/(-2x - 2)) + 2)) - 1))) + 3)/(1((1(1((-3((-3x)/(-2x - 2)) + 2)/(-1((-3x)/(-2x - 2)) + 2))^2 - 1((-3((-3x)/(-2x - 2)) + 2)/(-1((-3x)/(-2x - 2)) + 2)) - 1) - 2)/(2(1((-3((-3x)/(-2x - 2)) + 2)/(-1((-3x)/(-2x - 2)) + 2))^2 - 1((-3((-3x)/(-2x - 2)) + 2)/(-1((-3x)/(-2x - 2)) + 2)) - 1))) + 1)) - 3) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = -5(-2sin(1\u03c0(-4(1(1(3|x + 2| + 1) - 2)^2 + 3(1(3|x + 2| + 1) - 2) - 5)^2 - 4(1(1(3|x + 2| + 1) - 2)^2 + 3(1(3|x + 2| + 1) - 2) - 5) + 4)) + 3)^2 - 2(-2sin(1\u03c0(-4(1(1(3|x + 2| + 1) - 2)^2 + 3(1(3|x + 2| + 1) - 2) - 5)^2 - 4(1(1(3|x + 2| + 1) - 2)^2 + 3(1(3|x + 2| + 1) - 2) - 5) + 4)) + 3) + 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "24", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -3|(1|(-2|(-1(-2sin(2\u03c0(-2|x - 2| - 2) - 3) - 3)^2 - 5(-2sin(2\u03c0(-2|x - 2| - 2) - 3) - 3) + 4) + 1| + 2)| - 2) + 1| - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 1|((-1(2(2cos(3\u03c0(-2|(-1x + 3) - 2| + 3) - 3) + 3)^2 - 2(2cos(3\u03c0(-2|(-1x + 3) - 2| + 3) - 3) + 3) + 1) - 3)/(-3(2(2cos(3\u03c0(-2|(-1x + 3) - 2| + 3) - 3) + 3)^2 - 2(2cos(3\u03c0(-2|(-1x + 3) - 2| + 3) - 3) + 3) + 1) + 1)) + 2| + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "59", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -2(-5(3|(-2((1(-5x^2 - 4x + 5) - 3)/(2(-5x^2 - 4x + 5) - 1)) - 3) + 2| - 2) - 3) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -3(-2|(-4(-4(3|(-4x - 4) + 2| - 2)^2 - 3(3|(-4x - 4) + 2| - 2) + 1) + 1) - 2| + 3) - 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = 3((-1(-3(2sin(3\u03c0((-1(3x + 5) - 3)/(3(3x + 5) + 2)) - 3) + 2)))/(2(-3(2sin(3\u03c0((-1(3x + 5) - 3)/(3(3x + 5) + 2)) - 3) + 2)) - 3)) + 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -1(-2|(1(-3((2(2sin(2\u03c0x - 3) - 1) + 1)/(-1(2sin(2\u03c0x - 3) - 1) + 2)) + 1)^2 + 4(-3((2(2sin(2\u03c0x - 3) - 1) + 1)/(-1(2sin(2\u03c0x - 3) - 1) + 2)) + 1) - 4)| - 2)^2 + 3(-2|(1(-3((2(2sin(2\u03c0x - 3) - 1) + 1)/(-1(2sin(2\u03c0x - 3) - 1) + 2)) + 1)^2 + 4(-3((2(2sin(2\u03c0x - 3) - 1) + 1)/(-1(2sin(2\u03c0x - 3) - 1) + 2)) + 1) - 4)| - 2) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -3(3|(-5((2(-2cos(2\u03c0((1x + 2)/(-3x + 2)) - 2) - 2) + 1)/(-1(-2cos(2\u03c0((1x + 2)/(-3x + 2)) - 2) - 2) + 3))^2 + 4((2(-2cos(2\u03c0((1x + 2)/(-3x + 2)) - 2) - 2) + 1)/(-1(-2cos(2\u03c0((1x + 2)/(-3x + 2)) - 2) - 2) + 3)) + 5) - 1| - 2)^2 - 4(3|(-5((2(-2cos(2\u03c0((1x + 2)/(-3x + 2)) - 2) - 2) + 1)/(-1(-2cos(2\u03c0((1x + 2)/(-3x + 2)) - 2) - 2) + 3))^2 + 4((2(-2cos(2\u03c0((1x + 2)/(-3x + 2)) - 2) - 2) + 1)/(-1(-2cos(2\u03c0((1x + 2)/(-3x + 2)) - 2) - 2) + 3)) + 5) - 1| - 2) - 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 2|(3|(1cos(1\u03c0(2((3((-1x + 2)/(2x - 1)) + 2)/(-2((-1x + 2)/(2x - 1)) + 1))^2 + 2((3((-1x + 2)/(2x - 1)) + 2)/(-2((-1x + 2)/(2x - 1)) + 1)) - 2)) + 2) + 2| + 1) + 3| have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "24", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = (2(3|(3sin(1\u03c0(1(2|(3|x| - 1)| - 2) - 1) - 2)) + 2| + 2) - 1)/(-1(3|(3sin(1\u03c0(1(2|(3|x| - 1)| - 2) - 1) - 2)) + 2| + 2) + 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "241", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 4(-1((-2((-3(-3cos(2\u03c0(2|x - 2| - 1) + 2) + 2) + 3)/(-1(-3cos(2\u03c0(2|x - 2| - 1) + 2) + 2) - 2)) - 2)/(-2((-3(-3cos(2\u03c0(2|x - 2| - 1) + 2) + 2) + 3)/(-1(-3cos(2\u03c0(2|x - 2| - 1) + 2) + 2) - 2)) + 3))^2 + 3((-2((-3(-3cos(2\u03c0(2|x - 2| - 1) + 2) + 2) + 3)/(-1(-3cos(2\u03c0(2|x - 2| - 1) + 2) + 2) - 2)) - 2)/(-2((-3(-3cos(2\u03c0(2|x - 2| - 1) + 2) + 2) + 3)/(-1(-3cos(2\u03c0(2|x - 2| - 1) + 2) + 2) - 2)) + 3)) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "161", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 1((-3((3(-4(-5(-2cos(1\u03c0x) + 3) - 4) + 4) + 1)/(1(-4(-5(-2cos(1\u03c0x) + 3) - 4) + 4))))/(1((3(-4(-5(-2cos(1\u03c0x) + 3) - 4) + 4) + 1)/(1(-4(-5(-2cos(1\u03c0x) + 3) - 4) + 4))) + 3))^2 + 3((-3((3(-4(-5(-2cos(1\u03c0x) + 3) - 4) + 4) + 1)/(1(-4(-5(-2cos(1\u03c0x) + 3) - 4) + 4))))/(1((3(-4(-5(-2cos(1\u03c0x) + 3) - 4) + 4) + 1)/(1(-4(-5(-2cos(1\u03c0x) + 3) - 4) + 4))) + 3)) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 2sin(2\u03c0(2(1(-2(4(-4x^2 + 3x - 3)^2 + 3(-4x^2 + 3x - 3) - 5) + 1) + 5) - 1) + 3) + 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "99", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -4(3|(3(4(-5(4x^2 - 3)^2 - 4(4x^2 - 3) - 1)^2 - 4(-5(4x^2 - 3)^2 - 4(4x^2 - 3) - 1) - 4) + 5) - 1| - 1)^2 + 3(3|(3(4(-5(4x^2 - 3)^2 - 4(4x^2 - 3) - 1)^2 - 4(-5(4x^2 - 3)^2 - 4(4x^2 - 3) - 1) - 4) + 5) - 1| - 1) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 1(1|(-4((1(-3(3|x| - 2)^2 - 3(3|x| - 2) - 2) + 1)/(1(-3(3|x| - 2)^2 - 3(3|x| - 2) - 2) - 2)) - 2) + 1| - 1)^2 - 4(1|(-4((1(-3(3|x| - 2)^2 - 3(3|x| - 2) - 2) + 1)/(1(-3(3|x| - 2)^2 - 3(3|x| - 2) - 2) - 2)) - 2) + 1| - 1) - 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -5(3|(2|(-4((2(-1x^2 - 2))/(-2(-1x^2 - 2) + 1)) - 4) + 2|) - 3| - 3)^2 - 2(3|(2|(-4((2(-1x^2 - 2))/(-2(-1x^2 - 2) + 1)) - 4) + 2|) - 3| - 3) - 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = 3(1|(2((-3(-1cos(3\u03c0((-2x - 2)/(-2x + 3)) + 2) - 3) - 3)/(2(-1cos(3\u03c0((-2x - 2)/(-2x + 3)) + 2) - 3) - 1)) - 5) - 3| - 3)^2 + 4 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = (-2((2(1(2|(1sin(2\u03c0(1x^2 + 4x - 5) - 2)) + 3|) - 5))/(-2(1(2|(1sin(2\u03c0(1x^2 + 4x - 5) - 2)) + 3|) - 5) + 3)) - 1)/(1((2(1(2|(1sin(2\u03c0(1x^2 + 4x - 5) - 2)) + 3|) - 5))/(-2(1(2|(1sin(2\u03c0(1x^2 + 4x - 5) - 2)) + 3|) - 5) + 3)) + 2) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "416", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 4(-4(1(-1(2cos(3\u03c0(3x - 3) + 3) - 3) - 5) + 5)^2 - 3(1(-1(2cos(3\u03c0(3x - 3) + 3) - 3) - 5) + 5) + 4) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "90", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = (-2(2|((2(-2((1(-3cos(3\u03c0x) + 1))/(2(-3cos(3\u03c0x) + 1) - 3))^2 - 5((1(-3cos(3\u03c0x) + 1))/(2(-3cos(3\u03c0x) + 1) - 3)) + 3) - 3)/(2(-2((1(-3cos(3\u03c0x) + 1))/(2(-3cos(3\u03c0x) + 1) - 3))^2 - 5((1(-3cos(3\u03c0x) + 1))/(2(-3cos(3\u03c0x) + 1) - 3)) + 3) + 3)) + 2| + 3) + 3)/(1(2|((2(-2((1(-3cos(3\u03c0x) + 1))/(2(-3cos(3\u03c0x) + 1) - 3))^2 - 5((1(-3cos(3\u03c0x) + 1))/(2(-3cos(3\u03c0x) + 1) - 3)) + 3) - 3)/(2(-2((1(-3cos(3\u03c0x) + 1))/(2(-3cos(3\u03c0x) + 1) - 3))^2 - 5((1(-3cos(3\u03c0x) + 1))/(2(-3cos(3\u03c0x) + 1) - 3)) + 3) + 3)) + 2| + 3)) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "77", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 3(-3|((3(-3|(-1cos(3\u03c0((-2x + 1)/(3x + 3)) - 1) + 2) - 3| - 3) - 2)/(-1(-3|(-1cos(3\u03c0((-2x + 1)/(3x + 3)) - 1) + 2) - 3| - 3) - 3)) - 2| + 3) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -1((2(2cos(3\u03c0(-2|(-3(-3|x|)^2 + 5(-3|x|) + 3) - 3| + 1) - 2) - 3) - 1)/(-2(2cos(3\u03c0(-2|(-3(-3|x|)^2 + 5(-3|x|) + 3) - 3| + 1) - 2) - 3) + 3))^2 - 1((2(2cos(3\u03c0(-2|(-3(-3|x|)^2 + 5(-3|x|) + 3) - 3| + 1) - 2) - 3) - 1)/(-2(2cos(3\u03c0(-2|(-3(-3|x|)^2 + 5(-3|x|) + 3) - 3| + 1) - 2) - 3) + 3)) - 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "276", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -3cos(2\u03c0(-4(-2(1(-2|(-2|x + 2|) + 3| - 2) - 3)^2 + 1)^2 + 2(-2(1(-2|(-2|x + 2|) + 3| - 2) - 3)^2 + 1) + 3) - 3) - 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -2|(-2|(2sin(3\u03c0(5(-2|(-2|x - 3|) - 3| + 1)^2 - 3) + 1) - 1) + 2| - 2) - 2| + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "279", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -2|(5(1|(-1(3(2|x + 2|)^2 - 3(2|x + 2|) - 5) + 1) + 2| - 3) - 3) + 2| + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = 4(1(-2sin(1\u03c0(1|(4((-3x + 2)/(-1x))^2 - 3((-3x + 2)/(-1x)) - 4) - 2| + 3) + 1) - 2) + 2)^2 - 5(1(-2sin(1\u03c0(1|(4((-3x + 2)/(-1x))^2 - 3((-3x + 2)/(-1x)) - 4) - 2| + 3) + 1) - 2) + 2) + 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "76", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = (-1((2(3(4(-5(-3x - 3)^2 - 5)^2 - 2(-5(-3x - 3)^2 - 5) + 5)^2 + 1(4(-5(-3x - 3)^2 - 5)^2 - 2(-5(-3x - 3)^2 - 5) + 5) + 4) + 2)/(-1(3(4(-5(-3x - 3)^2 - 5)^2 - 2(-5(-3x - 3)^2 - 5) + 5)^2 + 1(4(-5(-3x - 3)^2 - 5)^2 - 2(-5(-3x - 3)^2 - 5) + 5) + 4) + 2)) + 2)/(-2((2(3(4(-5(-3x - 3)^2 - 5)^2 - 2(-5(-3x - 3)^2 - 5) + 5)^2 + 1(4(-5(-3x - 3)^2 - 5)^2 - 2(-5(-3x - 3)^2 - 5) + 5) + 4) + 2)/(-1(3(4(-5(-3x - 3)^2 - 5)^2 - 2(-5(-3x - 3)^2 - 5) + 5)^2 + 1(4(-5(-3x - 3)^2 - 5)^2 - 2(-5(-3x - 3)^2 - 5) + 5) + 4) + 2)) - 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 4(-2|((-2((3((2(-1cos(1\u03c0x + 1)) - 2)/(-2(-1cos(1\u03c0x + 1)) - 1)) + 3)/(1((2(-1cos(1\u03c0x + 1)) - 2)/(-2(-1cos(1\u03c0x + 1)) - 1)))) + 2)/(-2((3((2(-1cos(1\u03c0x + 1)) - 2)/(-2(-1cos(1\u03c0x + 1)) - 1)) + 3)/(1((2(-1cos(1\u03c0x + 1)) - 2)/(-2(-1cos(1\u03c0x + 1)) - 1)))) + 3)) - 2| + 1)^2 - 1(-2|((-2((3((2(-1cos(1\u03c0x + 1)) - 2)/(-2(-1cos(1\u03c0x + 1)) - 1)) + 3)/(1((2(-1cos(1\u03c0x + 1)) - 2)/(-2(-1cos(1\u03c0x + 1)) - 1)))) + 2)/(-2((3((2(-1cos(1\u03c0x + 1)) - 2)/(-2(-1cos(1\u03c0x + 1)) - 1)) + 3)/(1((2(-1cos(1\u03c0x + 1)) - 2)/(-2(-1cos(1\u03c0x + 1)) - 1)))) + 3)) - 2| + 1) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = 2|(-2sin(1\u03c0(5(4((1(-3|x - 2|) - 1)/(1(-3|x - 2|) - 3))^2 + 2)^2 - 1(4((1(-3|x - 2|) - 1)/(1(-3|x - 2|) - 3))^2 + 2) - 1) - 2) - 1) - 1| - 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "122", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -4(-1|(-1(-3sin(2\u03c0(-1(-2|x - 1| + 3)^2 - 1(-2|x - 1| + 3) - 5) - 2)) - 4) + 1|)^2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "443", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = (1(-2(-1(-3(-2sin(3\u03c0(2|x - 1| + 1) + 2) + 3)^2 + 2(-2sin(3\u03c0(2|x - 1| + 1) + 2) + 3) - 5)^2 - 3) + 3) + 1)/(3(-2(-1(-3(-2sin(3\u03c0(2|x - 1| + 1) + 2) + 3)^2 + 2(-2sin(3\u03c0(2|x - 1| + 1) + 2) + 3) - 5)^2 - 3) + 3) + 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = 2|(-3(-1|(2(1sin(3\u03c0(-1|x - 3| + 3)) + 3)^2 + 3(1sin(3\u03c0(-1|x - 3| + 3)) + 3) + 2) + 1| + 3)^2 - 3(-1|(2(1sin(3\u03c0(-1|x - 3| + 3)) + 3)^2 + 3(1sin(3\u03c0(-1|x - 3| + 3)) + 3) + 2) + 1| + 3) + 2) + 1| + 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -5(1(-4(3cos(2\u03c0(3|(-3x + 5) - 3| - 3) + 3) - 1)^2 - 2(3cos(2\u03c0(3|(-3x + 5) - 3| - 3) + 3) - 1) - 5) + 2) + 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "713", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = (-2(-2|(-2|(-3((3(-3x) + 1)/(2(-3x) + 2))^2 - 1) + 3| + 1) - 3| + 3) + 2)/(1(-2|(-2|(-3((3(-3x) + 1)/(2(-3x) + 2))^2 - 1) + 3| + 1) - 3| + 3) + 3) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -2sin(3\u03c0(1|((-2(1|(5(5x - 5) - 1) + 3| - 3) - 3)/(1(1|(5(5x - 5) - 1) + 3| - 3) - 2))| - 2) + 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = 5(-1(-5(-5(3(-2|x + 2| + 2)^2 + 1(-2|x + 2| + 2) - 5) - 2) - 1)^2 - 2(-5(-5(3(-2|x + 2| + 2)^2 + 1(-2|x + 2| + 2) - 5) - 2) - 1) + 1) - 4 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = -1|(-1((-2(-3((1(-2|x - 3| + 2) + 3)/(-3(-2|x - 3| + 2) - 3))^2 + 5((1(-2|x - 3| + 2) + 3)/(-3(-2|x - 3| + 2) - 3)) + 4) + 3)/(2(-3((1(-2|x - 3| + 2) + 3)/(-3(-2|x - 3| + 2) - 3))^2 + 5((1(-2|x - 3| + 2) + 3)/(-3(-2|x - 3| + 2) - 3)) + 4) + 1)) - 4) + 2| in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = (-2(-3(-2sin(3\u03c0(1|(4(-2|x + 2| + 2)^2 + 2(-2|x + 2| + 2) - 4) + 3| - 2) - 2) + 2) - 4) - 2)/(-3(-3(-2sin(3\u03c0(1|(4(-2|x + 2| + 2)^2 + 2(-2|x + 2| + 2) - 4) + 3| - 2) - 2) + 2) - 4) + 4) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "353", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 4((-1(-1sin(1\u03c0(-5(-1|(-5x^2 + 3x + 5) + 1| + 3)^2 + 4(-1|(-5x^2 + 3x + 5) + 1| + 3) + 5) - 2) + 1))/(-2(-1sin(1\u03c0(-5(-1|(-5x^2 + 3x + 5) + 1| + 3)^2 + 4(-1|(-5x^2 + 3x + 5) + 1| + 3) + 5) - 2) + 1) - 3)) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "116", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = 3|(2(1sin(3\u03c0(2((2((-3x - 3)/(1x)) + 1)/(3((-3x - 3)/(1x)) + 2))) - 3) - 1)^2 + 4(1sin(3\u03c0(2((2((-3x - 3)/(1x)) + 1)/(3((-3x - 3)/(1x)) + 2))) - 3) - 1) + 5) + 1| - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 2((2(-3sin(1\u03c0(3(3((2x - 3)/(-3x - 3))^2 - 5((2x - 3)/(-3x - 3)) - 4) - 4) - 3) + 3) + 3)/(-1(-3sin(1\u03c0(3(3((2x - 3)/(-3x - 3))^2 - 5((2x - 3)/(-3x - 3)) - 4) - 4) - 3) + 3) - 3)) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "72", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 4(3|((-1(-3|((-1(2sin(3\u03c0x) + 1))/(-3(2sin(3\u03c0x) + 1) - 2)) - 1| - 3) - 2)/(2(-3|((-1(2sin(3\u03c0x) + 1))/(-3(2sin(3\u03c0x) + 1) - 2)) - 1| - 3) + 3)) - 3| - 2) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "117", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 2|((-2(1(1|(-3|(1|x| + 2) - 3|) + 3|)^2 - 4(1|(-3|(1|x| + 2) - 3|) + 3|) - 3))/(-1(1(1|(-3|(1|x| + 2) - 3|) + 3|)^2 - 4(1|(-3|(1|x| + 2) - 3|) + 3|) - 3) - 3)) - 1| - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -3|(1(-1(-3|(2(1cos(3\u03c0x - 3) + 1) - 5) - 2| + 3) - 3)^2 + 5(-1(-3|(2(1cos(3\u03c0x - 3) + 1) - 5) - 2| + 3) - 3) - 3) + 2| in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 3(-2cos(3\u03c0(1|((1(2|(-4x + 5) + 3| - 2))/(2(2|(-4x + 5) + 3| - 2) + 3)) + 1| + 3) + 2)) + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = (-1(1(5(2cos(2\u03c0(5((1x + 3)/(3x + 3)) + 5) - 2) - 1)^2 - 5(2cos(2\u03c0(5((1x + 3)/(3x + 3)) + 5) - 2) - 1) + 4) + 5) + 3)/(1(1(5(2cos(2\u03c0(5((1x + 3)/(3x + 3)) + 5) - 2) - 1)^2 - 5(2cos(2\u03c0(5((1x + 3)/(3x + 3)) + 5) - 2) - 1) + 4) + 5)) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "51", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -2cos(1\u03c0((2(-3|(-1(4((-3x - 2)/(3x - 2)) - 2)^2 - 2(4((-3x - 2)/(3x - 2)) - 2) + 1) + 2| - 2) - 3)/(-1(-3|(-1(4((-3x - 2)/(3x - 2)) - 2)^2 - 2(4((-3x - 2)/(3x - 2)) - 2) + 1) + 2| - 2) - 2)) - 1) - 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 3|(2cos(2\u03c0(5(1((-1(-1x^2 + 2x - 3) - 3)/(1(-1x^2 + 2x - 3) - 3)))^2 - 5(1((-1(-1x^2 + 2x - 3) - 3)/(1(-1x^2 + 2x - 3) - 3))) - 2) - 1) - 3) - 1| have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -3|(1|(1|(-5(-1|(1x^2 + 4x - 1) - 3| + 2)^2 - 4(-1|(1x^2 + 4x - 1) - 3| + 2) - 4) + 2| + 2) - 2| - 2) - 3| + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = 1(-1|(-2sin(2\u03c0(-2|((-1(-2x) + 3)/(2(-2x) + 3)) - 3| + 2) - 1) + 2) + 3| - 3)^2 + 5(-1|(-2sin(2\u03c0(-2|((-1(-2x) + 3)/(2(-2x) + 3)) - 3| + 2) - 1) + 2) + 3| - 3) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = 1cos(2\u03c0(-3|(-5(5(1(-4x - 4)^2 + 3(-4x - 4) + 3)^2 + 1(1(-4x - 4)^2 + 3(-4x - 4) + 3) - 5)^2 + 3(5(1(-4x - 4)^2 + 3(-4x - 4) + 3)^2 + 1(1(-4x - 4)^2 + 3(-4x - 4) + 3) - 5) - 5)| + 1)) + 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -3sin(1\u03c0(-3(3|(3|((2(-1x^2 + 2x - 3))/(3(-1x^2 + 2x - 3) - 1)) + 2| + 2)| - 3)^2 - 4(3|(3|((2(-1x^2 + 2x - 3))/(3(-1x^2 + 2x - 3) - 1)) + 2| + 2)| - 3) - 3) + 1) - 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "252", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -4((2(-1|(4(-1|((3x + 1)/(1x + 1)) - 3| + 2)^2 - 5(-1|((3x + 1)/(1x + 1)) - 3| + 2) - 1)| + 1) - 2)/(3(-1|(4(-1|((3x + 1)/(1x + 1)) - 3| + 2)^2 - 5(-1|((3x + 1)/(1x + 1)) - 3| + 2) - 1)| + 1)))^2 - 1((2(-1|(4(-1|((3x + 1)/(1x + 1)) - 3| + 2)^2 - 5(-1|((3x + 1)/(1x + 1)) - 3| + 2) - 1)| + 1) - 2)/(3(-1|(4(-1|((3x + 1)/(1x + 1)) - 3| + 2)^2 - 5(-1|((3x + 1)/(1x + 1)) - 3| + 2) - 1)| + 1))) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = (-2(3(1|(3((-1(2|x + 1| - 2) - 2)/(-2(2|x + 1| - 2) + 3))^2 + 5((-1(2|x + 1| - 2) - 2)/(-2(2|x + 1| - 2) + 3)) - 2)| - 2) - 2) + 1)/(3(3(1|(3((-1(2|x + 1| - 2) - 2)/(-2(2|x + 1| - 2) + 3))^2 + 5((-1(2|x + 1| - 2) - 2)/(-2(2|x + 1| - 2) + 3)) - 2)| - 2) - 2) - 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -3cos(2\u03c0((2(-4(1(-3|(1x^2 - 1x - 4) + 3| + 2)^2 - 1) - 4) + 3)/(-2(-4(1(-3|(1x^2 - 1x - 4) + 3| + 2)^2 - 1) - 4) - 1)) + 1) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = 2(2|(1|(-1(1(-3x^2 - 4x + 2) + 3)^2 + 2(1(-3x^2 - 4x + 2) + 3) + 2) - 2| - 3) - 2| - 2) - 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -2sin(3\u03c0(1|(1|(-2|(-3(4x^2 + 4x + 1)^2 + 1(4x^2 + 4x + 1) - 1) + 2| - 2)| - 1) - 1| - 3) - 1) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "56", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = (3(-2(2sin(1\u03c0(-3(5((3x)/(3x - 2))^2 - 4((3x)/(3x - 2)))^2 + 1(5((3x)/(3x - 2))^2 - 4((3x)/(3x - 2))) - 4) + 2) - 1)^2 + 2(2sin(1\u03c0(-3(5((3x)/(3x - 2))^2 - 4((3x)/(3x - 2)))^2 + 1(5((3x)/(3x - 2))^2 - 4((3x)/(3x - 2))) - 4) + 2) - 1) - 5) + 1)/(-2(-2(2sin(1\u03c0(-3(5((3x)/(3x - 2))^2 - 4((3x)/(3x - 2)))^2 + 1(5((3x)/(3x - 2))^2 - 4((3x)/(3x - 2))) - 4) + 2) - 1)^2 + 2(2sin(1\u03c0(-3(5((3x)/(3x - 2))^2 - 4((3x)/(3x - 2)))^2 + 1(5((3x)/(3x - 2))^2 - 4((3x)/(3x - 2))) - 4) + 2) - 1) - 5) - 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "125", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -4(-1(2((3(2|(3cos(1\u03c0x) + 3) + 3| + 1) + 2)/(1(2|(3cos(1\u03c0x) + 3) + 3| + 1) - 2)) - 2) + 3)^2 - 2(-1(2((3(2|(3cos(1\u03c0x) + 3) + 3| + 1) + 2)/(1(2|(3cos(1\u03c0x) + 3) + 3| + 1) - 2)) - 2) + 3) - 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -2(-3((1(2cos(2\u03c0(4(2x - 2)^2 + 3(2x - 2) - 2) - 1) + 1) - 2)/(1(2cos(2\u03c0(4(2x - 2)^2 + 3(2x - 2) - 2) - 1) + 1)))) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "281", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = (-1(3|(3(1|((-3((1x - 1)/(2x + 1)) - 2)/(2((1x - 1)/(2x + 1)) - 1)) - 1| - 2)^2) - 3| - 2) + 2)/(1(3|(3(1|((-3((1x - 1)/(2x + 1)) - 2)/(2((1x - 1)/(2x + 1)) - 1)) - 1| - 2)^2) - 3| - 2)) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = (1(5(1sin(1\u03c0(-1(-3((-2x)/(-1x - 1))^2 + 1((-2x)/(-1x - 1)) - 3) - 4) + 1) - 3)^2 - 3(1sin(1\u03c0(-1(-3((-2x)/(-1x - 1))^2 + 1((-2x)/(-1x - 1)) - 3) - 4) + 1) - 3) + 5) + 2)/(3(5(1sin(1\u03c0(-1(-3((-2x)/(-1x - 1))^2 + 1((-2x)/(-1x - 1)) - 3) - 4) + 1) - 3)^2 - 3(1sin(1\u03c0(-1(-3((-2x)/(-1x - 1))^2 + 1((-2x)/(-1x - 1)) - 3) - 4) + 1) - 3) + 5) - 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "83", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 5((-2(-3(4(-3|(-1cos(3\u03c0x + 3) - 2) + 2| + 1)^2 + 1(-3|(-1cos(3\u03c0x + 3) - 2) + 2| + 1) - 1)^2 + 1(4(-3|(-1cos(3\u03c0x + 3) - 2) + 2| + 1)^2 + 1(-3|(-1cos(3\u03c0x + 3) - 2) + 2| + 1) - 1) - 5) + 3)/(-2(-3(4(-3|(-1cos(3\u03c0x + 3) - 2) + 2| + 1)^2 + 1(-3|(-1cos(3\u03c0x + 3) - 2) + 2| + 1) - 1)^2 + 1(4(-3|(-1cos(3\u03c0x + 3) - 2) + 2| + 1)^2 + 1(-3|(-1cos(3\u03c0x + 3) - 2) + 2| + 1) - 1) - 5))) - 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "480", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 1(-4(-4(-3sin(3\u03c0(1|(3x^2 - 4x + 3)| + 2) - 1) + 1) + 1)^2 - 4(-4(-3sin(3\u03c0(1|(3x^2 - 4x + 3)| + 2) - 1) + 1) + 1) + 3) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "157", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 3|(-2|(-5((-3(-2|(4x^2 + 2x + 2) - 2| + 2))/(1(-2|(4x^2 + 2x + 2) - 2| + 2) + 1))^2 - 5((-3(-2|(4x^2 + 2x + 2) - 2| + 2))/(1(-2|(4x^2 + 2x + 2) - 2| + 2) + 1)))| + 1) - 3| + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -3sin(1\u03c0(-1|(2|(-1|(2|(-2x^2 - 3x - 3)|) - 3| - 2) + 3| - 2) - 2| - 2) + 1) - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "267", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -4(3(-4(2cos(2\u03c0(4(-1|x - 2| + 3)^2 - 2(-1|x - 2| + 3) + 2)) + 1) + 4)^2 - 2(-4(2cos(2\u03c0(4(-1|x - 2| + 3)^2 - 2(-1|x - 2| + 3) + 2)) + 1) + 4) - 3) + 5 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "459", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 4(-1|(-3|(3cos(2\u03c0(-1|(1x - 5) - 1| - 1) - 1) + 2)|) - 2| - 1)^2 - 2(-1|(-3|(3cos(2\u03c0(-1|(1x - 5) - 1| - 1) - 1) + 2)|) - 2| - 1) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "59", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 3(3(-4((1(5(-5x^2 + 3x + 5) - 4) - 2)/(-2(5(-5x^2 + 3x + 5) - 4) - 3)))^2 + 2(-4((1(5(-5x^2 + 3x + 5) - 4) - 2)/(-2(5(-5x^2 + 3x + 5) - 4) - 3))) - 4)^2 - 1(3(-4((1(5(-5x^2 + 3x + 5) - 4) - 2)/(-2(5(-5x^2 + 3x + 5) - 4) - 3)))^2 + 2(-4((1(5(-5x^2 + 3x + 5) - 4) - 2)/(-2(5(-5x^2 + 3x + 5) - 4) - 3))) - 4) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = (-1(-2sin(2\u03c0(-5(-3|(3|(-2x^2 + 1x + 3) - 2| + 2)| - 2)^2 - 2(-3|(3|(-2x^2 + 1x + 3) - 2| + 2)| - 2) - 4) + 1) - 1) + 2)/(-2(-2sin(2\u03c0(-5(-3|(3|(-2x^2 + 1x + 3) - 2| + 2)| - 2)^2 - 2(-3|(3|(-2x^2 + 1x + 3) - 2| + 2)| - 2) - 4) + 1) - 1) + 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = (3(-2|(-3(2e^(-1(-1|((-2x + 2)/(-1x + 2)) - 3| + 3)) - 2) - 3) - 2| + 2) + 3)/(-1(-2|(-3(2e^(-1(-1|((-2x + 2)/(-1x + 2)) - 3| + 3)) - 2) - 3) - 2| + 2) + 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = (1((-2(-4(-5(2sin(1\u03c0(-1x^2 - 3x - 2) + 1) - 1)^2 + 2(2sin(1\u03c0(-1x^2 - 3x - 2) + 1) - 1) + 1)^2 - 5(-5(2sin(1\u03c0(-1x^2 - 3x - 2) + 1) - 1)^2 + 2(2sin(1\u03c0(-1x^2 - 3x - 2) + 1) - 1) + 1) + 3) + 1)/(-2(-4(-5(2sin(1\u03c0(-1x^2 - 3x - 2) + 1) - 1)^2 + 2(2sin(1\u03c0(-1x^2 - 3x - 2) + 1) - 1) + 1)^2 - 5(-5(2sin(1\u03c0(-1x^2 - 3x - 2) + 1) - 1)^2 + 2(2sin(1\u03c0(-1x^2 - 3x - 2) + 1) - 1) + 1) + 3))))/(3((-2(-4(-5(2sin(1\u03c0(-1x^2 - 3x - 2) + 1) - 1)^2 + 2(2sin(1\u03c0(-1x^2 - 3x - 2) + 1) - 1) + 1)^2 - 5(-5(2sin(1\u03c0(-1x^2 - 3x - 2) + 1) - 1)^2 + 2(2sin(1\u03c0(-1x^2 - 3x - 2) + 1) - 1) + 1) + 3) + 1)/(-2(-4(-5(2sin(1\u03c0(-1x^2 - 3x - 2) + 1) - 1)^2 + 2(2sin(1\u03c0(-1x^2 - 3x - 2) + 1) - 1) + 1)^2 - 5(-5(2sin(1\u03c0(-1x^2 - 3x - 2) + 1) - 1)^2 + 2(2sin(1\u03c0(-1x^2 - 3x - 2) + 1) - 1) + 1) + 3))) - 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "288", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = 3cos(3\u03c0((3(5(3(5((-2x)/(-3x - 1))^2 + 3((-2x)/(-3x - 1)) - 2)^2 + 5(5((-2x)/(-3x - 1))^2 + 3((-2x)/(-3x - 1)) - 2) + 3)^2 - 3(3(5((-2x)/(-3x - 1))^2 + 3((-2x)/(-3x - 1)) - 2)^2 + 5(5((-2x)/(-3x - 1))^2 + 3((-2x)/(-3x - 1)) - 2) + 3) - 4))/(2(5(3(5((-2x)/(-3x - 1))^2 + 3((-2x)/(-3x - 1)) - 2)^2 + 5(5((-2x)/(-3x - 1))^2 + 3((-2x)/(-3x - 1)) - 2) + 3)^2 - 3(3(5((-2x)/(-3x - 1))^2 + 3((-2x)/(-3x - 1)) - 2)^2 + 5(5((-2x)/(-3x - 1))^2 + 3((-2x)/(-3x - 1)) - 2) + 3) - 4) + 3))) + 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = (-2(-5(-2|(4(-2cos(2\u03c0(-3x) - 2) + 3)) + 1| + 2) + 1) + 3)/(2(-5(-2|(4(-2cos(2\u03c0(-3x) - 2) + 3)) + 1| + 2) + 1) + 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = (-3(3sin(3\u03c0(2|(-5(-1(2|x - 3|)^2 - 4(2|x - 3|) - 2) + 2) + 1| - 2) - 1) + 3) + 2)/(1(3sin(3\u03c0(2|(-5(-1(2|x - 3|)^2 - 4(2|x - 3|) - 2) + 2) + 1| - 2) - 1) + 3)) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "452", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 1(1(1(2(-1sin(3\u03c0(3x^2 - 1x + 5) + 3) + 2) + 5) - 4)^2 + 2(1(2(-1sin(3\u03c0(3x^2 - 1x + 5) + 3) + 2) + 5) - 4) - 5) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "228", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 2(1cos(2\u03c0(1(-5(-2|(-1|x + 1| + 2)| - 2) + 4) - 1) + 1) - 2)^2 + 2(1cos(2\u03c0(1(-5(-2|(-1|x + 1| + 2)| - 2) + 4) - 1) + 1) - 2) - 4 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "403", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 5((1(-1(4(2(-1x^2 - 1x + 4)^2 - 1(-1x^2 - 1x + 4) - 2)^2 - 1(2(-1x^2 - 1x + 4)^2 - 1(-1x^2 - 1x + 4) - 2) + 1) - 5) + 3)/(2(-1(4(2(-1x^2 - 1x + 4)^2 - 1(-1x^2 - 1x + 4) - 2)^2 - 1(2(-1x^2 - 1x + 4)^2 - 1(-1x^2 - 1x + 4) - 2) + 1) - 5) + 3)) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -5(-3(-1(3sin(3\u03c0(3|((2x - 2)/(1x + 2)) - 1| + 2) + 1) + 3)^2 - 4(3sin(3\u03c0(3|((2x - 2)/(1x + 2)) - 1| + 2) + 1) + 3) - 2) - 4)^2 + 4(-3(-1(3sin(3\u03c0(3|((2x - 2)/(1x + 2)) - 1| + 2) + 1) + 3)^2 - 4(3sin(3\u03c0(3|((2x - 2)/(1x + 2)) - 1| + 2) + 1) + 3) - 2) - 4) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "115", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -3(3sin(3\u03c0(-1|(5(-2(3x) - 1) + 1) + 1|) - 2) + 3) - 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "199", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = -1|((-2((-3(-5((-2(-3cos(1\u03c0x + 2) + 1) + 1)/(-3(-3cos(1\u03c0x + 2) + 1) + 4))^2 - 3((-2(-3cos(1\u03c0x + 2) + 1) + 1)/(-3(-3cos(1\u03c0x + 2) + 1) + 4))) - 2)/(3(-5((-2(-3cos(1\u03c0x + 2) + 1) + 1)/(-3(-3cos(1\u03c0x + 2) + 1) + 4))^2 - 3((-2(-3cos(1\u03c0x + 2) + 1) + 1)/(-3(-3cos(1\u03c0x + 2) + 1) + 4))) - 2)) + 2)/(3((-3(-5((-2(-3cos(1\u03c0x + 2) + 1) + 1)/(-3(-3cos(1\u03c0x + 2) + 1) + 4))^2 - 3((-2(-3cos(1\u03c0x + 2) + 1) + 1)/(-3(-3cos(1\u03c0x + 2) + 1) + 4))) - 2)/(3(-5((-2(-3cos(1\u03c0x + 2) + 1) + 1)/(-3(-3cos(1\u03c0x + 2) + 1) + 4))^2 - 3((-2(-3cos(1\u03c0x + 2) + 1) + 1)/(-3(-3cos(1\u03c0x + 2) + 1) + 4))) - 2)))) - 3| in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -2|(1(-3(-1|(1|(3x^2 - 5x - 5) - 3| + 2) - 2| + 2)^2 + 4(-1|(1|(3x^2 - 5x - 5) - 3| + 2) - 2| + 2) - 1)^2 + 4(-3(-1|(1|(3x^2 - 5x - 5) - 3| + 2) - 2| + 2)^2 + 4(-1|(1|(3x^2 - 5x - 5) - 3| + 2) - 2| + 2) - 1) - 5) - 3| + 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = 2|((3(-1(-3(-2(-2|x + 3| - 1)^2 - 5)^2 - 2(-2(-2|x + 3| - 1)^2 - 5) + 3)^2 - 3(-3(-2(-2|x + 3| - 1)^2 - 5)^2 - 2(-2(-2|x + 3| - 1)^2 - 5) + 3) - 3) + 1)/(1(-1(-3(-2(-2|x + 3| - 1)^2 - 5)^2 - 2(-2(-2|x + 3| - 1)^2 - 5) + 3)^2 - 3(-3(-2(-2|x + 3| - 1)^2 - 5)^2 - 2(-2(-2|x + 3| - 1)^2 - 5) + 3) - 3))) + 1| - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "49", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 2|(-1((-2((-3(-2sin(2\u03c0(-3|x + 2| - 3)) + 1) - 2)/(-2(-2sin(2\u03c0(-3|x + 2| - 3)) + 1) - 3)) - 3)/(-2((-3(-2sin(2\u03c0(-3|x + 2| - 3)) + 1) - 2)/(-2(-2sin(2\u03c0(-3|x + 2| - 3)) + 1) - 3)) - 2)) + 1) + 3| + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "119", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = (-3(5((2((3(4(-3x^2 + 2x + 4)) + 3)/(-1(4(-3x^2 + 2x + 4)) - 2)) - 3)/(-2((3(4(-3x^2 + 2x + 4)) + 3)/(-1(4(-3x^2 + 2x + 4)) - 2)) - 1))^2 - 2) - 3)/(-2(5((2((3(4(-3x^2 + 2x + 4)) + 3)/(-1(4(-3x^2 + 2x + 4)) - 2)) - 3)/(-2((3(4(-3x^2 + 2x + 4)) + 3)/(-1(4(-3x^2 + 2x + 4)) - 2)) - 1))^2 - 2) - 2) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "202", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 1cos(3\u03c0(-3(-4((-1(5(-4x + 2)^2 + 5(-4x + 2) + 2) + 3)/(-1(5(-4x + 2)^2 + 5(-4x + 2) + 2)))^2 + 4((-1(5(-4x + 2)^2 + 5(-4x + 2) + 2) + 3)/(-1(5(-4x + 2)^2 + 5(-4x + 2) + 2))) + 4)^2 - 1(-4((-1(5(-4x + 2)^2 + 5(-4x + 2) + 2) + 3)/(-1(5(-4x + 2)^2 + 5(-4x + 2) + 2)))^2 + 4((-1(5(-4x + 2)^2 + 5(-4x + 2) + 2) + 3)/(-1(5(-4x + 2)^2 + 5(-4x + 2) + 2))) + 4) - 5) + 1) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 3(3(1(3|(-1e^(2(-3x - 3)) - 3) - 1| + 3) + 1)^2 - 1(1(3|(-1e^(2(-3x - 3)) - 3) - 1| + 3) + 1) - 1) - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 2(-2|(-4((-2(4(-1x^2 + 4x + 4)^2 - 1(-1x^2 + 4x + 4)) + 1)/(-1(4(-1x^2 + 4x + 4)^2 - 1(-1x^2 + 4x + 4)) + 2))^2 + 2((-2(4(-1x^2 + 4x + 4)^2 - 1(-1x^2 + 4x + 4)) + 1)/(-1(4(-1x^2 + 4x + 4)^2 - 1(-1x^2 + 4x + 4)) + 2)) - 4) + 2| - 2)^2 + 1(-2|(-4((-2(4(-1x^2 + 4x + 4)^2 - 1(-1x^2 + 4x + 4)) + 1)/(-1(4(-1x^2 + 4x + 4)^2 - 1(-1x^2 + 4x + 4)) + 2))^2 + 2((-2(4(-1x^2 + 4x + 4)^2 - 1(-1x^2 + 4x + 4)) + 1)/(-1(4(-1x^2 + 4x + 4)^2 - 1(-1x^2 + 4x + 4)) + 2)) - 4) + 2| - 2) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -1(1|((3(-5(1sin(1\u03c0(-1x^2 + 3x + 3) - 1))^2 - 3(1sin(1\u03c0(-1x^2 + 3x + 3) - 1)) - 5) - 1)/(1(-5(1sin(1\u03c0(-1x^2 + 3x + 3) - 1))^2 - 3(1sin(1\u03c0(-1x^2 + 3x + 3) - 1)) - 5) + 2)) + 3| + 1)^2 + 5(1|((3(-5(1sin(1\u03c0(-1x^2 + 3x + 3) - 1))^2 - 3(1sin(1\u03c0(-1x^2 + 3x + 3) - 1)) - 5) - 1)/(1(-5(1sin(1\u03c0(-1x^2 + 3x + 3) - 1))^2 - 3(1sin(1\u03c0(-1x^2 + 3x + 3) - 1)) - 5) + 2)) + 3| + 1) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "149", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -3(-1|((-2(-3((2(-1cos(2\u03c0x - 2)) - 1)/(3(-1cos(2\u03c0x - 2)) - 2))^2 + 4) - 3)/(-2(-3((2(-1cos(2\u03c0x - 2)) - 1)/(3(-1cos(2\u03c0x - 2)) - 2))^2 + 4))) - 1| - 3) + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "168", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 4(3|(4(-2((-1(-4x - 4) + 3)/(3(-4x - 4)))^2 - 5((-1(-4x - 4) + 3)/(3(-4x - 4))) - 3)^2) - 2| + 2) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -2|((2((1(-3cos(2\u03c0(-3|(5x - 3)|) + 2) - 1) + 1)/(-3(-3cos(2\u03c0(-3|(5x - 3)|) + 2) - 1) + 2)) + 1)/(-1((1(-3cos(2\u03c0(-3|(5x - 3)|) + 2) - 1) + 1)/(-3(-3cos(2\u03c0(-3|(5x - 3)|) + 2) - 1) + 2)) - 3)) + 2| + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "629", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -4(-1(-4((-3(-3sin(1\u03c0(-3|x - 3| + 2) + 3) - 2) + 3)/(-2(-3sin(1\u03c0(-3|x - 3| + 2) + 3) - 2) + 3)))^2 + 3(-4((-3(-3sin(1\u03c0(-3|x - 3| + 2) + 3) - 2) + 3)/(-2(-3sin(1\u03c0(-3|x - 3| + 2) + 3) - 2) + 3))) + 5) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = (-3(1|(-2|(2sin(1\u03c0(-5(-3|x + 2| - 2) - 1) - 3) - 1) - 1| - 1) + 2| + 3) - 1)/(2(1|(-2|(2sin(1\u03c0(-5(-3|x + 2| - 2) - 1) - 3) - 1) - 1| - 1) + 2| + 3)) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "463", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 3(-1(2|(-2(5(3x^2 + 4x + 1) - 2)^2 + 2(5(3x^2 + 4x + 1) - 2) + 1) + 3| + 1) + 5) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -1(-5(-4(2(-5((-1x + 2)/(3x + 2)) + 1)^2 + 2(-5((-1x + 2)/(3x + 2)) + 1) + 1) + 5)^2 + 1(-4(2(-5((-1x + 2)/(3x + 2)) + 1)^2 + 2(-5((-1x + 2)/(3x + 2)) + 1) + 1) + 5) + 5)^2 - 5(-5(-4(2(-5((-1x + 2)/(3x + 2)) + 1)^2 + 2(-5((-1x + 2)/(3x + 2)) + 1) + 1) + 5)^2 + 1(-4(2(-5((-1x + 2)/(3x + 2)) + 1)^2 + 2(-5((-1x + 2)/(3x + 2)) + 1) + 1) + 5) + 5) + 5 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -1|(-2(3e^(2(1|((1((2x)/(-3x)) + 2)/(-3((2x)/(-3x)) - 1))| + 1)) + 2)^2 + 3(3e^(2(1|((1((2x)/(-3x)) + 2)/(-3((2x)/(-3x)) - 1))| + 1)) + 2) - 1) - 2| in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 1|(1(3|((1(1(2e^(1x) + 1) - 3) + 3)/(-1(1(2e^(1x) + 1) - 3) + 2)) + 3| - 2)^2 - 2(3|((1(1(2e^(1x) + 1) - 3) + 3)/(-1(1(2e^(1x) + 1) - 3) + 2)) + 3| - 2) - 1) - 1| + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -1((2(-1|(5(1|((1x - 3)/(1x + 3))| - 1)^2 + 5(1|((1x - 3)/(1x + 3))| - 1) + 2) - 1| - 1) + 1)/(3(-1|(5(1|((1x - 3)/(1x + 3))| - 1)^2 + 5(1|((1x - 3)/(1x + 3))| - 1) + 2) - 1| - 1) + 1)) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = -2|(1(-5(-3(1(2|x - 2| + 1)^2 - 5(2|x - 2| + 1)) - 4) - 3) - 3)| in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = (2(1(-2(3(-2(-1sin(3\u03c0x - 3) + 3)^2 - 5(-1sin(3\u03c0x - 3) + 3) + 3)^2 + 4(-2(-1sin(3\u03c0x - 3) + 3)^2 - 5(-1sin(3\u03c0x - 3) + 3) + 3) + 3)^2 + 5(3(-2(-1sin(3\u03c0x - 3) + 3)^2 - 5(-1sin(3\u03c0x - 3) + 3) + 3)^2 + 4(-2(-1sin(3\u03c0x - 3) + 3)^2 - 5(-1sin(3\u03c0x - 3) + 3) + 3) + 3) - 5) - 1) + 3)/(1(1(-2(3(-2(-1sin(3\u03c0x - 3) + 3)^2 - 5(-1sin(3\u03c0x - 3) + 3) + 3)^2 + 4(-2(-1sin(3\u03c0x - 3) + 3)^2 - 5(-1sin(3\u03c0x - 3) + 3) + 3) + 3)^2 + 5(3(-2(-1sin(3\u03c0x - 3) + 3)^2 - 5(-1sin(3\u03c0x - 3) + 3) + 3)^2 + 4(-2(-1sin(3\u03c0x - 3) + 3)^2 - 5(-1sin(3\u03c0x - 3) + 3) + 3) + 3) - 5) - 1) + 1) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "54", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 1|((-2(1(-2((1(-5x - 3) - 3)/(-3(-5x - 3) - 3))^2 - 5((1(-5x - 3) - 3)/(-3(-5x - 3) - 3)) + 5) + 5) + 1)/(3(1(-2((1(-5x - 3) - 3)/(-3(-5x - 3) - 3))^2 - 5((1(-5x - 3) - 3)/(-3(-5x - 3) - 3)) + 5) + 5) + 3)) + 1| + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = 4(-1(-1(-2((1(2|x - 3| - 2) + 2)/(-3(2|x - 3| - 2) - 3)) - 1) - 1)^2 - 3(-1(-2((1(2|x - 3| - 2) + 2)/(-3(2|x - 3| - 2) - 3)) - 1) - 1) + 4)^2 - 5(-1(-1(-2((1(2|x - 3| - 2) + 2)/(-3(2|x - 3| - 2) - 3)) - 1) - 1)^2 - 3(-1(-2((1(2|x - 3| - 2) + 2)/(-3(2|x - 3| - 2) - 3)) - 1) - 1) + 4) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -1cos(3\u03c0((3((-1(-5(-3(1x^2 - 2x - 4)^2 + 4(1x^2 - 2x - 4) - 5) - 2) + 2)/(-2(-5(-3(1x^2 - 2x - 4)^2 + 4(1x^2 - 2x - 4) - 5) - 2) - 3)) - 3)/(2((-1(-5(-3(1x^2 - 2x - 4)^2 + 4(1x^2 - 2x - 4) - 5) - 2) + 2)/(-2(-5(-3(1x^2 - 2x - 4)^2 + 4(1x^2 - 2x - 4) - 5) - 2) - 3)) + 3)) - 2) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = 1(4(-2((3(-2sin(2\u03c0((-2x - 2)/(-3x + 1)) - 3) + 3) - 3)/(2(-2sin(2\u03c0((-2x - 2)/(-3x + 1)) - 3) + 3) - 1))^2 + 5((3(-2sin(2\u03c0((-2x - 2)/(-3x + 1)) - 3) + 3) - 3)/(2(-2sin(2\u03c0((-2x - 2)/(-3x + 1)) - 3) + 3) - 1)) + 3) - 3)^2 - 5(4(-2((3(-2sin(2\u03c0((-2x - 2)/(-3x + 1)) - 3) + 3) - 3)/(2(-2sin(2\u03c0((-2x - 2)/(-3x + 1)) - 3) + 3) - 1))^2 + 5((3(-2sin(2\u03c0((-2x - 2)/(-3x + 1)) - 3) + 3) - 3)/(2(-2sin(2\u03c0((-2x - 2)/(-3x + 1)) - 3) + 3) - 1)) + 3) - 3) + 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 1e^(-1((-3(-3|(-3((-1(-2x - 5) + 3)/(1(-2x - 5)))^2 + 5) + 1| - 2))/(2(-3|(-3((-1(-2x - 5) + 3)/(1(-2x - 5)))^2 + 5) + 1| - 2) - 1))) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = (-1(3(-4(-5(4(-1sin(2\u03c0x - 3) + 1)^2 + 4(-1sin(2\u03c0x - 3) + 1) + 4) - 5) - 5)^2 + 4(-4(-5(4(-1sin(2\u03c0x - 3) + 1)^2 + 4(-1sin(2\u03c0x - 3) + 1) + 4) - 5) - 5) + 3))/(-2(3(-4(-5(4(-1sin(2\u03c0x - 3) + 1)^2 + 4(-1sin(2\u03c0x - 3) + 1) + 4) - 5) - 5)^2 + 4(-4(-5(4(-1sin(2\u03c0x - 3) + 1)^2 + 4(-1sin(2\u03c0x - 3) + 1) + 4) - 5) - 5) + 3) + 1) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = (2(-3(4(-3(4((3x + 3)/(1x + 2))^2 + 3)^2 + 3(4((3x + 3)/(1x + 2))^2 + 3) - 4)^2 - 5(-3(4((3x + 3)/(1x + 2))^2 + 3)^2 + 3(4((3x + 3)/(1x + 2))^2 + 3) - 4) - 3)^2 - 4(4(-3(4((3x + 3)/(1x + 2))^2 + 3)^2 + 3(4((3x + 3)/(1x + 2))^2 + 3) - 4)^2 - 5(-3(4((3x + 3)/(1x + 2))^2 + 3)^2 + 3(4((3x + 3)/(1x + 2))^2 + 3) - 4) - 3) + 2) + 1)/(-2(-3(4(-3(4((3x + 3)/(1x + 2))^2 + 3)^2 + 3(4((3x + 3)/(1x + 2))^2 + 3) - 4)^2 - 5(-3(4((3x + 3)/(1x + 2))^2 + 3)^2 + 3(4((3x + 3)/(1x + 2))^2 + 3) - 4) - 3)^2 - 4(4(-3(4((3x + 3)/(1x + 2))^2 + 3)^2 + 3(4((3x + 3)/(1x + 2))^2 + 3) - 4)^2 - 5(-3(4((3x + 3)/(1x + 2))^2 + 3)^2 + 3(4((3x + 3)/(1x + 2))^2 + 3) - 4) - 3) + 2) + 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = (2((1(-1e^(2(-2(-1(1x - 1) - 1) + 1))) - 3)/(-3(-1e^(2(-2(-1(1x - 1) - 1) + 1))) - 2)) - 2)/(2((1(-1e^(2(-2(-1(1x - 1) - 1) + 1))) - 3)/(-3(-1e^(2(-2(-1(1x - 1) - 1) + 1))) - 2)) - 3) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -2(3e^(1(1|(-2|(-2(4x^2 - 4x - 5) + 3) - 3| + 1) + 2| + 2)) - 3) + 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -4(1(4(-2(3cos(2\u03c0(-3|x - 2| - 1) + 3))^2 + 4(3cos(2\u03c0(-3|x - 2| - 1) + 3)) + 2) - 3) - 4)^2 + 1(1(4(-2(3cos(2\u03c0(-3|x - 2| - 1) + 3))^2 + 4(3cos(2\u03c0(-3|x - 2| - 1) + 3)) + 2) - 3) - 4) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "429", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = (1(-2|(2sin(2\u03c0(3(-2|(2x + 1)| - 2)^2 - 4(-2|(2x + 1)| - 2) - 1) + 2) - 1) - 1| + 3) - 2)/(1(-2|(2sin(2\u03c0(3(-2|(2x + 1)| - 2)^2 - 4(-2|(2x + 1)| - 2) - 1) + 2) - 1) - 1| + 3)) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "425", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 1(3|(3(-3|((-3(1x^2 - 3x + 2))/(-1(1x^2 - 3x + 2) - 2)) - 2|)^2 + 3(-3|((-3(1x^2 - 3x + 2))/(-1(1x^2 - 3x + 2) - 2)) - 2|) - 4) + 3| + 3)^2 - 1(3|(3(-3|((-3(1x^2 - 3x + 2))/(-1(1x^2 - 3x + 2) - 2)) - 2|)^2 + 3(-3|((-3(1x^2 - 3x + 2))/(-1(1x^2 - 3x + 2) - 2)) - 2|) - 4) + 3| + 3) - 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -2((-3(1e^(1(-1(2(-2|x - 1|) + 5)^2 - 2(2(-2|x - 1|) + 5) - 2))) + 3)/(-1(1e^(1(-1(2(-2|x - 1|) + 5)^2 - 2(2(-2|x - 1|) + 5) - 2))) - 3))^2 - 5((-3(1e^(1(-1(2(-2|x - 1|) + 5)^2 - 2(2(-2|x - 1|) + 5) - 2))) + 3)/(-1(1e^(1(-1(2(-2|x - 1|) + 5)^2 - 2(2(-2|x - 1|) + 5) - 2))) - 3)) + 4 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -4(-3(-3|(-1cos(1\u03c0(-3(3x^2 - 3x + 1)) - 3) - 1) - 2| + 3) - 2) + 4 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "527", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -3cos(3\u03c0(3(-1(-3|(1|(-4x - 4) - 3| + 1) + 3| - 2) + 1) + 1)) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "161", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = 1|(-1((2(-2(-3sin(3\u03c0(-5x^2 - 3x - 5) - 1) + 3)^2 + 1(-3sin(3\u03c0(-5x^2 - 3x - 5) - 1) + 3) + 1) - 2)/(-3(-2(-3sin(3\u03c0(-5x^2 - 3x - 5) - 1) + 3)^2 + 1(-3sin(3\u03c0(-5x^2 - 3x - 5) - 1) + 3) + 1) + 1))^2 + 1((2(-2(-3sin(3\u03c0(-5x^2 - 3x - 5) - 1) + 3)^2 + 1(-3sin(3\u03c0(-5x^2 - 3x - 5) - 1) + 3) + 1) - 2)/(-3(-2(-3sin(3\u03c0(-5x^2 - 3x - 5) - 1) + 3)^2 + 1(-3sin(3\u03c0(-5x^2 - 3x - 5) - 1) + 3) + 1) + 1)) + 3) + 3| - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "75", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -1(3|(-3|(-3(-3sin(3\u03c0(2|x - 1|))) - 3) + 3| + 3) + 1| - 1)^2 + 1(3|(-3|(-3(-3sin(3\u03c0(2|x - 1|))) - 3) + 3| + 3) + 1| - 1) - 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "123", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 2e^(1(-1(-3(-2(-2|(-1x - 2) + 2| + 3)^2 - 1(-2|(-1x - 2) + 2| + 3) - 1) - 3) - 4)) - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 1(1(-2sin(1\u03c0(2((-1(4x - 1) + 2)/(3(4x - 1))) - 3) + 2) - 2)^2 + 5(-2sin(1\u03c0(2((-1(4x - 1) + 2)/(3(4x - 1))) - 3) + 2) - 2) + 5)^2 - 4(1(-2sin(1\u03c0(2((-1(4x - 1) + 2)/(3(4x - 1))) - 3) + 2) - 2)^2 + 5(-2sin(1\u03c0(2((-1(4x - 1) + 2)/(3(4x - 1))) - 3) + 2) - 2) + 5) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = 2|(-3|(-5(1(-1|(5x^2 - 3x - 1) - 3| + 2)^2 - 4(-1|(5x^2 - 3x - 1) - 3| + 2) + 1) - 3) + 3| + 1) + 3| - 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = 1|(2|((2((1(1(2sin(3\u03c0x + 3) + 1)^2 - 1(2sin(3\u03c0x + 3) + 1) + 2))/(3(1(2sin(3\u03c0x + 3) + 1)^2 - 1(2sin(3\u03c0x + 3) + 1) + 2) + 1)))/(-2((1(1(2sin(3\u03c0x + 3) + 1)^2 - 1(2sin(3\u03c0x + 3) + 1) + 2))/(3(1(2sin(3\u03c0x + 3) + 1)^2 - 1(2sin(3\u03c0x + 3) + 1) + 2) + 1)) - 2)) + 3| - 3) - 1| - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = 4((-1((1(-1|(1|(4x - 4) + 3|) - 1| + 3) - 2)/(-3(-1|(1|(4x - 4) + 3|) - 1| + 3))) - 3)/(-3((1(-1|(1|(4x - 4) + 3|) - 1| + 3) - 2)/(-3(-1|(1|(4x - 4) + 3|) - 1| + 3)))))^2 + 3((-1((1(-1|(1|(4x - 4) + 3|) - 1| + 3) - 2)/(-3(-1|(1|(4x - 4) + 3|) - 1| + 3))) - 3)/(-3((1(-1|(1|(4x - 4) + 3|) - 1| + 3) - 2)/(-3(-1|(1|(4x - 4) + 3|) - 1| + 3))))) - 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -3(1((1(-3|(-5(1sin(2\u03c0x - 1))^2 + 3(1sin(2\u03c0x - 1)) - 3) + 2| + 1))/(-1(-3|(-5(1sin(2\u03c0x - 1))^2 + 3(1sin(2\u03c0x - 1)) - 3) + 2| + 1) - 1)) - 3) - 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "82", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -4(2(-2(-3sin(3\u03c0((-2((-1x - 3)/(-2x + 3)) - 3)/(-3((-1x - 3)/(-2x + 3)) - 3)) + 1))^2 - 1(-3sin(3\u03c0((-2((-1x - 3)/(-2x + 3)) - 3)/(-3((-1x - 3)/(-2x + 3)) - 3)) + 1)) + 1)^2 - 2(-2(-3sin(3\u03c0((-2((-1x - 3)/(-2x + 3)) - 3)/(-3((-1x - 3)/(-2x + 3)) - 3)) + 1))^2 - 1(-3sin(3\u03c0((-2((-1x - 3)/(-2x + 3)) - 3)/(-3((-1x - 3)/(-2x + 3)) - 3)) + 1)) + 1) + 4)^2 + 4(2(-2(-3sin(3\u03c0((-2((-1x - 3)/(-2x + 3)) - 3)/(-3((-1x - 3)/(-2x + 3)) - 3)) + 1))^2 - 1(-3sin(3\u03c0((-2((-1x - 3)/(-2x + 3)) - 3)/(-3((-1x - 3)/(-2x + 3)) - 3)) + 1)) + 1)^2 - 2(-2(-3sin(3\u03c0((-2((-1x - 3)/(-2x + 3)) - 3)/(-3((-1x - 3)/(-2x + 3)) - 3)) + 1))^2 - 1(-3sin(3\u03c0((-2((-1x - 3)/(-2x + 3)) - 3)/(-3((-1x - 3)/(-2x + 3)) - 3)) + 1)) + 1) + 4) - 5 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "24", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = 1|(-1sin(2\u03c0(-2((3(-3|(1|x - 3| + 3)| + 1) + 2)/(2(-3|(1|x - 3| + 3)| + 1) - 1))^2 - 3((3(-3|(1|x - 3| + 3)| + 1) + 2)/(2(-3|(1|x - 3| + 3)| + 1) - 1)) + 5) + 2) + 3) - 2| + 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 4((2(3(-3(-1((-3x - 3)/(1x - 2))^2 + 5((-3x - 3)/(1x - 2)) - 5)^2 + 3(-1((-3x - 3)/(1x - 2))^2 + 5((-3x - 3)/(1x - 2)) - 5) - 4)^2 - 3(-3(-1((-3x - 3)/(1x - 2))^2 + 5((-3x - 3)/(1x - 2)) - 5)^2 + 3(-1((-3x - 3)/(1x - 2))^2 + 5((-3x - 3)/(1x - 2)) - 5) - 4) - 3) - 2)/(1(3(-3(-1((-3x - 3)/(1x - 2))^2 + 5((-3x - 3)/(1x - 2)) - 5)^2 + 3(-1((-3x - 3)/(1x - 2))^2 + 5((-3x - 3)/(1x - 2)) - 5) - 4)^2 - 3(-3(-1((-3x - 3)/(1x - 2))^2 + 5((-3x - 3)/(1x - 2)) - 5)^2 + 3(-1((-3x - 3)/(1x - 2))^2 + 5((-3x - 3)/(1x - 2)) - 5) - 4) - 3)))^2 - 1((2(3(-3(-1((-3x - 3)/(1x - 2))^2 + 5((-3x - 3)/(1x - 2)) - 5)^2 + 3(-1((-3x - 3)/(1x - 2))^2 + 5((-3x - 3)/(1x - 2)) - 5) - 4)^2 - 3(-3(-1((-3x - 3)/(1x - 2))^2 + 5((-3x - 3)/(1x - 2)) - 5)^2 + 3(-1((-3x - 3)/(1x - 2))^2 + 5((-3x - 3)/(1x - 2)) - 5) - 4) - 3) - 2)/(1(3(-3(-1((-3x - 3)/(1x - 2))^2 + 5((-3x - 3)/(1x - 2)) - 5)^2 + 3(-1((-3x - 3)/(1x - 2))^2 + 5((-3x - 3)/(1x - 2)) - 5) - 4)^2 - 3(-3(-1((-3x - 3)/(1x - 2))^2 + 5((-3x - 3)/(1x - 2)) - 5)^2 + 3(-1((-3x - 3)/(1x - 2))^2 + 5((-3x - 3)/(1x - 2)) - 5) - 4) - 3))) - 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -5(2(-1sin(1\u03c0(5(-2|(-1x + 2) - 3| - 1)^2 - 2(-2|(-1x + 2) - 3| - 1) + 1) - 2) - 1) - 5)^2 - 1(2(-1sin(1\u03c0(5(-2|(-1x + 2) - 3| - 1)^2 - 2(-2|(-1x + 2) - 3| - 1) + 1) - 2) - 1) - 5) - 4 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "485", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = 3(-1|(-1(2((-1(-2sin(1\u03c0x + 1) - 3) - 2)/(-3(-2sin(1\u03c0x + 1) - 3) - 1))^2 + 5((-1(-2sin(1\u03c0x + 1) - 3) - 2)/(-3(-2sin(1\u03c0x + 1) - 3) - 1)) - 2)^2 + 2(2((-1(-2sin(1\u03c0x + 1) - 3) - 2)/(-3(-2sin(1\u03c0x + 1) - 3) - 1))^2 + 5((-1(-2sin(1\u03c0x + 1) - 3) - 2)/(-3(-2sin(1\u03c0x + 1) - 3) - 1)) - 2) - 3) + 2| - 1)^2 + 1(-1|(-1(2((-1(-2sin(1\u03c0x + 1) - 3) - 2)/(-3(-2sin(1\u03c0x + 1) - 3) - 1))^2 + 5((-1(-2sin(1\u03c0x + 1) - 3) - 2)/(-3(-2sin(1\u03c0x + 1) - 3) - 1)) - 2)^2 + 2(2((-1(-2sin(1\u03c0x + 1) - 3) - 2)/(-3(-2sin(1\u03c0x + 1) - 3) - 1))^2 + 5((-1(-2sin(1\u03c0x + 1) - 3) - 2)/(-3(-2sin(1\u03c0x + 1) - 3) - 1)) - 2) - 3) + 2| - 1) - 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = (1(-2sin(1\u03c0(1(3|(-5(1x + 2)^2 + 3(1x + 2) + 1)| + 2)^2 + 1) - 1) - 3))/(2(-2sin(1\u03c0(1(3|(-5(1x + 2)^2 + 3(1x + 2) + 1)| + 2)^2 + 1) - 1) - 3) + 1) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "119", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -2(-3(1|(-2(2cos(3\u03c0(3|x + 3| - 3) + 1)) + 3) + 3| + 1) + 2)^2 - 5(-3(1|(-2(2cos(3\u03c0(3|x + 3| - 3) + 1)) + 3) + 3| + 1) + 2) + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "89", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -2|((3(3((-3(-2cos(2\u03c0((-1x + 3)/(-2x + 3)) - 3)))/(-3(-2cos(2\u03c0((-1x + 3)/(-2x + 3)) - 3)) + 1)) - 4) + 1)/(-1(3((-3(-2cos(2\u03c0((-1x + 3)/(-2x + 3)) - 3)))/(-3(-2cos(2\u03c0((-1x + 3)/(-2x + 3)) - 3)) + 1)) - 4) - 2)) - 2| + 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 2((2(2(2e^(2((3(1x^2 - 3x - 3) - 3)/(-2(1x^2 - 3x - 3) + 3))) - 1)^2 - 1(2e^(2((3(1x^2 - 3x - 3) - 3)/(-2(1x^2 - 3x - 3) + 3))) - 1) + 1))/(-3(2(2e^(2((3(1x^2 - 3x - 3) - 3)/(-2(1x^2 - 3x - 3) + 3))) - 1)^2 - 1(2e^(2((3(1x^2 - 3x - 3) - 3)/(-2(1x^2 - 3x - 3) + 3))) - 1) + 1)))^2 + 5((2(2(2e^(2((3(1x^2 - 3x - 3) - 3)/(-2(1x^2 - 3x - 3) + 3))) - 1)^2 - 1(2e^(2((3(1x^2 - 3x - 3) - 3)/(-2(1x^2 - 3x - 3) + 3))) - 1) + 1))/(-3(2(2e^(2((3(1x^2 - 3x - 3) - 3)/(-2(1x^2 - 3x - 3) + 3))) - 1)^2 - 1(2e^(2((3(1x^2 - 3x - 3) - 3)/(-2(1x^2 - 3x - 3) + 3))) - 1) + 1))) + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "92", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -4(3|(1sin(1\u03c0(3(-2(3|x + 2| - 1)^2 - 4(3|x + 2| - 1) + 4) - 2) - 1) + 1) + 1| + 1) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "444", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 1|((-1(3((-3(-3(-2x - 5)^2 - 4(-2x - 5)))/(1(-3(-2x - 5)^2 - 4(-2x - 5)) + 3))^2 + 1((-3(-3(-2x - 5)^2 - 4(-2x - 5)))/(1(-3(-2x - 5)^2 - 4(-2x - 5)) + 3)) - 1) - 2)/(2(3((-3(-3(-2x - 5)^2 - 4(-2x - 5)))/(1(-3(-2x - 5)^2 - 4(-2x - 5)) + 3))^2 + 1((-3(-3(-2x - 5)^2 - 4(-2x - 5)))/(1(-3(-2x - 5)^2 - 4(-2x - 5)) + 3)) - 1) + 3)) - 3| - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -1sin(2\u03c0(2(1(2(-1|(2x + 1) - 3| - 2)^2 + 3(-1|(2x + 1) - 3| - 2) + 4)^2 - 4(2(-1|(2x + 1) - 3| - 2)^2 + 3(-1|(2x + 1) - 3| - 2) + 4))^2 - 2(1(2(-1|(2x + 1) - 3| - 2)^2 + 3(-1|(2x + 1) - 3| - 2) + 4)^2 - 4(2(-1|(2x + 1) - 3| - 2)^2 + 3(-1|(2x + 1) - 3| - 2) + 4)) + 3) + 2) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 1|((-2(-1cos(2\u03c0(3(3|(4x) - 1|) - 4) - 1) - 2) + 3)/(2(-1cos(2\u03c0(3(3|(4x) - 1|) - 4) - 1) - 2) + 3))| - 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "667", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = 3(-1|(3|((-2(5(2x^2 + 5x + 1) - 2))/(-3(5(2x^2 + 5x + 1) - 2) + 4)) - 2| - 2) + 2| + 2)^2 + 1(-1|(3|((-2(5(2x^2 + 5x + 1) - 2))/(-3(5(2x^2 + 5x + 1) - 2) + 4)) - 2| - 2) + 2| + 2) + 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = (-1(2|(-1|(-1|((1(2cos(3\u03c0x + 3)) - 3)/(-2(2cos(3\u03c0x + 3)) + 3)) - 1| + 1) + 2| - 3) + 1| + 3) + 3)/(-2(2|(-1|(-1|((1(2cos(3\u03c0x + 3)) - 3)/(-2(2cos(3\u03c0x + 3)) + 3)) - 1| + 1) + 2| - 3) + 1| + 3) - 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "203", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -2sin(2\u03c0(1(5(2(3|(2x^2 - 4x - 4) + 3| + 3)) + 2)^2 + 4(5(2(3|(2x^2 - 4x - 4) + 3| + 3)) + 2) - 4) - 2) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -5(1(-5(-3|(1|(3sin(1\u03c0x - 3)) + 3| + 3)|)^2 - 2(-3|(1|(3sin(1\u03c0x - 3)) + 3| + 3)|) - 4)^2 - 2(-5(-3|(1|(3sin(1\u03c0x - 3)) + 3| + 3)|)^2 - 2(-3|(1|(3sin(1\u03c0x - 3)) + 3| + 3)|) - 4) + 2)^2 + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -1|(3(-2cos(2\u03c0(2|(2|(-3|x + 2| + 3)|) + 1| + 3) + 3) - 2)^2 + 5(-2cos(2\u03c0(2|(2|(-3|x + 2| + 3)|) + 1| + 3) + 3) - 2) - 1) + 2| + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "647", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = (-2(-2sin(1\u03c0(-1|((1(3((1x - 3)/(-1x - 1))^2 + 4((1x - 3)/(-1x - 1)) - 5) - 2)/(-2(3((1x - 3)/(-1x - 1))^2 + 4((1x - 3)/(-1x - 1)) - 5) - 2)) + 2| - 2) - 3) - 2) - 1)/(-3(-2sin(1\u03c0(-1|((1(3((1x - 3)/(-1x - 1))^2 + 4((1x - 3)/(-1x - 1)) - 5) - 2)/(-2(3((1x - 3)/(-1x - 1))^2 + 4((1x - 3)/(-1x - 1)) - 5) - 2)) + 2| - 2) - 3) - 2) - 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -1((3(-2|(4(-3sin(3\u03c0(1|x| - 2) - 3) - 1)^2 + 3(-3sin(3\u03c0(1|x| - 2) - 3) - 1) + 5) + 3| - 2) + 3)/(-1(-2|(4(-3sin(3\u03c0(1|x| - 2) - 3) - 1)^2 + 3(-3sin(3\u03c0(1|x| - 2) - 3) - 1) + 5) + 3| - 2) + 3))^2 - 4((3(-2|(4(-3sin(3\u03c0(1|x| - 2) - 3) - 1)^2 + 3(-3sin(3\u03c0(1|x| - 2) - 3) - 1) + 5) + 3| - 2) + 3)/(-1(-2|(4(-3sin(3\u03c0(1|x| - 2) - 3) - 1)^2 + 3(-3sin(3\u03c0(1|x| - 2) - 3) - 1) + 5) + 3| - 2) + 3)) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "58", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 3(-3(4(-2((1(-4x^2 - 3x - 5))/(-3(-4x^2 - 3x - 5)))^2 - 5((1(-4x^2 - 3x - 5))/(-3(-4x^2 - 3x - 5))) - 5) + 4) + 5) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "81", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 2|(-1|(-4((3((1(-3cos(3\u03c0x) - 2) - 2)/(-2(-3cos(3\u03c0x) - 2) - 2)) - 1)/(-3((1(-3cos(3\u03c0x) - 2) - 2)/(-2(-3cos(3\u03c0x) - 2) - 2)) + 4))^2 + 3((3((1(-3cos(3\u03c0x) - 2) - 2)/(-2(-3cos(3\u03c0x) - 2) - 2)) - 1)/(-3((1(-3cos(3\u03c0x) - 2) - 2)/(-2(-3cos(3\u03c0x) - 2) - 2)) + 4)) - 3) - 2| + 3) - 2| where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "180", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 2|(2(-5((-3(3sin(1\u03c0((3x + 3)/(-3x + 1))) + 1) - 1)/(2(3sin(1\u03c0((3x + 3)/(-3x + 1))) + 1))) - 1) + 5)| + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = 1((3(1(2(2cos(2\u03c0(2x^2 - 5x + 1) - 3) + 1) + 5)^2 - 1(2(2cos(2\u03c0(2x^2 - 5x + 1) - 3) + 1) + 5) + 1))/(-2(1(2(2cos(2\u03c0(2x^2 - 5x + 1) - 3) + 1) + 5)^2 - 1(2(2cos(2\u03c0(2x^2 - 5x + 1) - 3) + 1) + 5) + 1) + 3)) - 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "105", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -1(3(1cos(1\u03c0(2|(-3|(3x^2 + 4x + 4) + 3| - 2) - 2| - 2) - 3) + 3) - 1)^2 + 2(3(1cos(1\u03c0(2|(-3|(3x^2 + 4x + 4) + 3| - 2) - 2| - 2) - 3) + 3) - 1) + 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "247", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -1|((-2(3(1(2cos(1\u03c0(-1x - 2)) - 1) + 4) - 2) - 3)/(2(3(1(2cos(1\u03c0(-1x - 2)) - 1) + 4) - 2) + 2)) + 3| + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = (2((2(1(3cos(3\u03c0(3((2x + 3)/(-2x + 3)) + 4) + 3)) - 5) + 3)/(-1(1(3cos(3\u03c0(3((2x + 3)/(-2x + 3)) + 4) + 3)) - 5) + 3)) - 1)/(3((2(1(3cos(3\u03c0(3((2x + 3)/(-2x + 3)) + 4) + 3)) - 5) + 3)/(-1(1(3cos(3\u03c0(3((2x + 3)/(-2x + 3)) + 4) + 3)) - 5) + 3)) - 2) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "67", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 3|(1e^(-1(-4(-3((2(3x^2 + 4x - 4) + 1)/(3(3x^2 + 4x - 4) + 1)) + 2)^2 + 3(-3((2(3x^2 + 4x - 4) + 1)/(3(3x^2 + 4x - 4) + 1)) + 2) - 3)) + 3) + 2| where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -1|(3|((2(1|(1(-2|x - 2| + 3) - 1) - 3| - 3) + 1)/(3(1|(1(-2|x - 2| + 3) - 1) - 3| - 3))) + 1| + 3) - 2| - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = 2|(5(4(-2sin(2\u03c0(1(4x + 4) - 3)) + 1) + 4)^2 - 3(4(-2sin(2\u03c0(1(4x + 4) - 3)) + 1) + 4) + 4) - 1| + 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "87", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -5(3(-4(1(-3(2sin(2\u03c0x) + 1))^2 - 5(-3(2sin(2\u03c0x) + 1)) - 1)^2 - 2(1(-3(2sin(2\u03c0x) + 1))^2 - 5(-3(2sin(2\u03c0x) + 1)) - 1) - 1) - 3)^2 + 3(3(-4(1(-3(2sin(2\u03c0x) + 1))^2 - 5(-3(2sin(2\u03c0x) + 1)) - 1)^2 - 2(1(-3(2sin(2\u03c0x) + 1))^2 - 5(-3(2sin(2\u03c0x) + 1)) - 1) - 1) - 3) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -4((-2(2((-3(-3cos(1\u03c0((-2x - 2)/(-2x - 3)) - 1) - 1) + 2)/(2(-3cos(1\u03c0((-2x - 2)/(-2x - 3)) - 1) - 1) + 2)) + 1) + 3)/(1(2((-3(-3cos(1\u03c0((-2x - 2)/(-2x - 3)) - 1) - 1) + 2)/(2(-3cos(1\u03c0((-2x - 2)/(-2x - 3)) - 1) - 1) + 2)) + 1) + 2)) - 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = (1(1|(1sin(2\u03c0((1((-2(-4x - 5) + 1)/(3(-4x - 5) + 1)) - 2)/(2((-2(-4x - 5) + 1)/(3(-4x - 5) + 1)) + 3)) - 2) - 3) - 1| + 1) + 3)/(2(1|(1sin(2\u03c0((1((-2(-4x - 5) + 1)/(3(-4x - 5) + 1)) - 2)/(2((-2(-4x - 5) + 1)/(3(-4x - 5) + 1)) + 3)) - 2) - 3) - 1| + 1)) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -1cos(3\u03c0(-1(-4((1(-2(-2x) - 5))/(2(-2(-2x) - 5) + 1)) + 4)^2 + 3(-4((1(-2(-2x) - 5))/(2(-2(-2x) - 5) + 1)) + 4) + 4) + 3) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -2(-2cos(1\u03c0(3(-1((-2((3x + 1)/(3x + 2)) - 3)/(-2((3x + 1)/(3x + 2)) + 3))^2 + 4((-2((3x + 1)/(3x + 2)) - 3)/(-2((3x + 1)/(3x + 2)) + 3)) - 2) + 2)) - 3)^2 - 1(-2cos(1\u03c0(3(-1((-2((3x + 1)/(3x + 2)) - 3)/(-2((3x + 1)/(3x + 2)) + 3))^2 + 4((-2((3x + 1)/(3x + 2)) - 3)/(-2((3x + 1)/(3x + 2)) + 3)) - 2) + 2)) - 3) - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "108", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -3|((2(-3cos(2\u03c0((1((-1(1x - 1) + 2)/(3(1x - 1) + 1)) - 2)/(1((-1(1x - 1) + 2)/(3(1x - 1) + 1)) + 2)) - 3) + 2) - 3)/(-3(-3cos(2\u03c0((1((-1(1x - 1) + 2)/(3(1x - 1) + 1)) - 2)/(1((-1(1x - 1) + 2)/(3(1x - 1) + 1)) + 2)) - 3) + 2) - 1)) - 1| - 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "48", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = 2|((-3(3((-1(4(-2sin(1\u03c0x - 3) - 2) + 2) - 1)/(3(4(-2sin(1\u03c0x - 3) - 2) + 2) - 2)) + 3) + 3)/(3(3((-1(4(-2sin(1\u03c0x - 3) - 2) + 2) - 1)/(3(4(-2sin(1\u03c0x - 3) - 2) + 2) - 2)) + 3) + 3)) + 3| + 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "26", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = 1((3(-3|((-1(3(4x^2 + 4x - 4) + 5) + 3)/(-2(3(4x^2 + 4x - 4) + 5) - 3)) + 2| + 2) - 2)/(3(-3|((-1(3(4x^2 + 4x - 4) + 5) + 3)/(-2(3(4x^2 + 4x - 4) + 5) - 3)) + 2| + 2)))^2 - 4((3(-3|((-1(3(4x^2 + 4x - 4) + 5) + 3)/(-2(3(4x^2 + 4x - 4) + 5) - 3)) + 2| + 2) - 2)/(3(-3|((-1(3(4x^2 + 4x - 4) + 5) + 3)/(-2(3(4x^2 + 4x - 4) + 5) - 3)) + 2| + 2))) - 4 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -1(-4(-2|((1(3|(-1cos(2\u03c0x + 2) + 2) + 3| + 3) + 2)/(2(3|(-1cos(2\u03c0x + 2) + 2) + 3| + 3) + 3)) - 2| - 2)^2 + 2(-2|((1(3|(-1cos(2\u03c0x + 2) + 2) + 3| + 3) + 2)/(2(3|(-1cos(2\u03c0x + 2) + 2) + 3| + 3) + 3)) - 2| - 2) - 4)^2 + 1(-4(-2|((1(3|(-1cos(2\u03c0x + 2) + 2) + 3| + 3) + 2)/(2(3|(-1cos(2\u03c0x + 2) + 2) + 3| + 3) + 3)) - 2| - 2)^2 + 2(-2|((1(3|(-1cos(2\u03c0x + 2) + 2) + 3| + 3) + 2)/(2(3|(-1cos(2\u03c0x + 2) + 2) + 3| + 3) + 3)) - 2| - 2) - 4) - 4 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 5(-5(1(1(1((-3x - 1)/(3x - 2))^2 - 2((-3x - 1)/(3x - 2)) - 5)^2 + 1(1((-3x - 1)/(3x - 2))^2 - 2((-3x - 1)/(3x - 2)) - 5) - 2)^2 - 5(1(1((-3x - 1)/(3x - 2))^2 - 2((-3x - 1)/(3x - 2)) - 5)^2 + 1(1((-3x - 1)/(3x - 2))^2 - 2((-3x - 1)/(3x - 2)) - 5) - 2))^2 - 3(1(1(1((-3x - 1)/(3x - 2))^2 - 2((-3x - 1)/(3x - 2)) - 5)^2 + 1(1((-3x - 1)/(3x - 2))^2 - 2((-3x - 1)/(3x - 2)) - 5) - 2)^2 - 5(1(1((-3x - 1)/(3x - 2))^2 - 2((-3x - 1)/(3x - 2)) - 5)^2 + 1(1((-3x - 1)/(3x - 2))^2 - 2((-3x - 1)/(3x - 2)) - 5) - 2)) + 3)^2 - 4(-5(1(1(1((-3x - 1)/(3x - 2))^2 - 2((-3x - 1)/(3x - 2)) - 5)^2 + 1(1((-3x - 1)/(3x - 2))^2 - 2((-3x - 1)/(3x - 2)) - 5) - 2)^2 - 5(1(1((-3x - 1)/(3x - 2))^2 - 2((-3x - 1)/(3x - 2)) - 5)^2 + 1(1((-3x - 1)/(3x - 2))^2 - 2((-3x - 1)/(3x - 2)) - 5) - 2))^2 - 3(1(1(1((-3x - 1)/(3x - 2))^2 - 2((-3x - 1)/(3x - 2)) - 5)^2 + 1(1((-3x - 1)/(3x - 2))^2 - 2((-3x - 1)/(3x - 2)) - 5) - 2)^2 - 5(1(1((-3x - 1)/(3x - 2))^2 - 2((-3x - 1)/(3x - 2)) - 5)^2 + 1(1((-3x - 1)/(3x - 2))^2 - 2((-3x - 1)/(3x - 2)) - 5) - 2)) + 3) + 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 1((1(-4(5((3(1x^2 + 1x - 3) - 2)/(1(1x^2 + 1x - 3) + 3))^2 - 3) + 2))/(-3(-4(5((3(1x^2 + 1x - 3) - 2)/(1(1x^2 + 1x - 3) + 3))^2 - 3) + 2) - 1))^2 + 1((1(-4(5((3(1x^2 + 1x - 3) - 2)/(1(1x^2 + 1x - 3) + 3))^2 - 3) + 2))/(-3(-4(5((3(1x^2 + 1x - 3) - 2)/(1(1x^2 + 1x - 3) + 3))^2 - 3) + 2) - 1)) - 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -1(-1(-3(3cos(2\u03c0(5(-5x^2 - 1x + 2) - 3)) - 3) - 2)^2 + 3)^2 - 4(-1(-3(3cos(2\u03c0(5(-5x^2 - 1x + 2) - 3)) - 3) - 2)^2 + 3) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "135", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -2|(-1|(-1sin(1\u03c0(2(-3|((3x - 3)/(-1x)) + 1| + 1)^2 + 4(-3|((3x - 3)/(-1x)) + 1| + 1) - 5) - 2) - 1) + 3| - 2) - 1| - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "99", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 2((-3(-3(-4(-2sin(1\u03c0(3x - 1) + 3) + 2) + 4) - 3) + 1)/(-1(-3(-4(-2sin(1\u03c0(3x - 1) + 3) + 2) + 4) - 3)))^2 - 2((-3(-3(-4(-2sin(1\u03c0(3x - 1) + 3) + 2) + 4) - 3) + 1)/(-1(-3(-4(-2sin(1\u03c0(3x - 1) + 3) + 2) + 4) - 3))) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "72", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 1(1(5(1sin(1\u03c0(-4(-1|x| + 2)^2 + 4(-1|x| + 2) + 4) + 1) - 3) + 2) - 4)^2 - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "284", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = (-1(1cos(2\u03c0((2((3(1(3|x + 3| - 2) - 2) + 1)/(2(1(3|x + 3| - 2) - 2) - 1)) + 3)/(3((3(1(3|x + 3| - 2) - 2) + 1)/(2(1(3|x + 3| - 2) - 2) - 1)) + 3)) + 2) - 3) + 1)/(1(1cos(2\u03c0((2((3(1(3|x + 3| - 2) - 2) + 1)/(2(1(3|x + 3| - 2) - 2) - 1)) + 3)/(3((3(1(3|x + 3| - 2) - 2) + 1)/(2(1(3|x + 3| - 2) - 2) - 1)) + 3)) + 2) - 3)) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 4(1(-5(2|(-1(3sin(3\u03c0x + 3) - 3) + 4) - 1|)^2 + 4(2|(-1(3sin(3\u03c0x + 3) - 3) + 4) - 1|) + 4)^2 - 5(-5(2|(-1(3sin(3\u03c0x + 3) - 3) + 4) - 1|)^2 + 4(2|(-1(3sin(3\u03c0x + 3) - 3) + 4) - 1|) + 4) - 1)^2 + 5(1(-5(2|(-1(3sin(3\u03c0x + 3) - 3) + 4) - 1|)^2 + 4(2|(-1(3sin(3\u03c0x + 3) - 3) + 4) - 1|) + 4)^2 - 5(-5(2|(-1(3sin(3\u03c0x + 3) - 3) + 4) - 1|)^2 + 4(2|(-1(3sin(3\u03c0x + 3) - 3) + 4) - 1|) + 4) - 1) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "56", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 3|((3(3(-3|(1(4x - 1)^2 - 4(4x - 1) - 3) + 2| + 2)^2 + 4(-3|(1(4x - 1)^2 - 4(4x - 1) - 3) + 2| + 2) + 3) + 2)/(-3(3(-3|(1(4x - 1)^2 - 4(4x - 1) - 3) + 2| + 2)^2 + 4(-3|(1(4x - 1)^2 - 4(4x - 1) - 3) + 2| + 2) + 3) + 2)) + 3| - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -4(3sin(2\u03c0((2((2((1((2x - 2)/(-3x - 3)) - 1)/(-1((2x - 2)/(-3x - 3)) + 2)) - 1)/(-1((1((2x - 2)/(-3x - 3)) - 1)/(-1((2x - 2)/(-3x - 3)) + 2)))) + 1)/(1((2((1((2x - 2)/(-3x - 3)) - 1)/(-1((2x - 2)/(-3x - 3)) + 2)) - 1)/(-1((1((2x - 2)/(-3x - 3)) - 1)/(-1((2x - 2)/(-3x - 3)) + 2))))))) - 1)^2 - 3(3sin(2\u03c0((2((2((1((2x - 2)/(-3x - 3)) - 1)/(-1((2x - 2)/(-3x - 3)) + 2)) - 1)/(-1((1((2x - 2)/(-3x - 3)) - 1)/(-1((2x - 2)/(-3x - 3)) + 2)))) + 1)/(1((2((1((2x - 2)/(-3x - 3)) - 1)/(-1((2x - 2)/(-3x - 3)) + 2)) - 1)/(-1((1((2x - 2)/(-3x - 3)) - 1)/(-1((2x - 2)/(-3x - 3)) + 2))))))) - 1) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -2|((1(-1|(-1|(1((-1x + 1)/(3x + 3))^2 + 3((-1x + 1)/(3x + 3)) - 3) - 2| - 3) + 3|) - 1)/(-1(-1|(-1|(1((-1x + 1)/(3x + 3))^2 + 3((-1x + 1)/(3x + 3)) - 3) - 2| - 3) + 3|) - 3)) + 2| - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 1|((-3(-3sin(3\u03c0((2(-2(-1x - 3) + 3))/(-3(-2(-1x - 3) + 3) - 2)) - 1) + 2) + 1)/(1(-3sin(3\u03c0((2(-2(-1x - 3) + 3))/(-3(-2(-1x - 3) + 3) - 2)) - 1) + 2) + 2)) + 2| - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 4(-1cos(3\u03c0(-2(2((1(1x^2 + 2x - 1) - 3)/(1(1x^2 + 2x - 1)))^2 + 5((1(1x^2 + 2x - 1) - 3)/(1(1x^2 + 2x - 1))) + 5) + 4) - 3) - 1) + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "95", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -3|(2|(4(1(-2cos(3\u03c0(-3|x - 3|) - 3)) - 3) - 2) - 2| + 2) + 1| - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "90", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -4(4(1|(3|(-1|((3x)/(1x + 2)) + 3| + 2)|) + 1| - 2) + 3)^2 + 3(4(1|(3|(-1|((3x)/(1x + 2)) + 3| + 2)|) + 1| - 2) + 3) + 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = (-1((3((2((-1(-2cos(3\u03c0((-1x + 1)/(-3x - 1)) + 1) - 1) + 1)/(1(-2cos(3\u03c0((-1x + 1)/(-3x - 1)) + 1) - 1) + 3)) + 2)/(-1((-1(-2cos(3\u03c0((-1x + 1)/(-3x - 1)) + 1) - 1) + 1)/(1(-2cos(3\u03c0((-1x + 1)/(-3x - 1)) + 1) - 1) + 3)))) + 1)/(-2((2((-1(-2cos(3\u03c0((-1x + 1)/(-3x - 1)) + 1) - 1) + 1)/(1(-2cos(3\u03c0((-1x + 1)/(-3x - 1)) + 1) - 1) + 3)) + 2)/(-1((-1(-2cos(3\u03c0((-1x + 1)/(-3x - 1)) + 1) - 1) + 1)/(1(-2cos(3\u03c0((-1x + 1)/(-3x - 1)) + 1) - 1) + 3)))) + 1)) + 1)/(1((3((2((-1(-2cos(3\u03c0((-1x + 1)/(-3x - 1)) + 1) - 1) + 1)/(1(-2cos(3\u03c0((-1x + 1)/(-3x - 1)) + 1) - 1) + 3)) + 2)/(-1((-1(-2cos(3\u03c0((-1x + 1)/(-3x - 1)) + 1) - 1) + 1)/(1(-2cos(3\u03c0((-1x + 1)/(-3x - 1)) + 1) - 1) + 3)))) + 1)/(-2((2((-1(-2cos(3\u03c0((-1x + 1)/(-3x - 1)) + 1) - 1) + 1)/(1(-2cos(3\u03c0((-1x + 1)/(-3x - 1)) + 1) - 1) + 3)) + 2)/(-1((-1(-2cos(3\u03c0((-1x + 1)/(-3x - 1)) + 1) - 1) + 1)/(1(-2cos(3\u03c0((-1x + 1)/(-3x - 1)) + 1) - 1) + 3)))) + 1))) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = 1e^(-1(3(-1(2(-5(1x + 5)^2 + 5(1x + 5))^2 + 5(-5(1x + 5)^2 + 5(1x + 5)) - 5)^2 + 5(2(-5(1x + 5)^2 + 5(1x + 5))^2 + 5(-5(1x + 5)^2 + 5(1x + 5)) - 5) - 4)^2 + 2(-1(2(-5(1x + 5)^2 + 5(1x + 5))^2 + 5(-5(1x + 5)^2 + 5(1x + 5)) - 5)^2 + 5(2(-5(1x + 5)^2 + 5(1x + 5))^2 + 5(-5(1x + 5)^2 + 5(1x + 5)) - 5) - 4) + 4)) + 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = 2|((-1(-2|(3sin(2\u03c0(-1|(-1|x + 2| + 1)| - 2) + 1) + 2) - 3| - 3) + 1)/(1(-2|(3sin(2\u03c0(-1|(-1|x + 2| + 1)| - 2) + 1) + 2) - 3| - 3))) + 2| + 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "83", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 1|(1|((2(-4(-3(-1x^2 + 4x - 2))^2 - 4(-3(-1x^2 + 4x - 2)) - 1) + 3)/(1(-4(-3(-1x^2 + 4x - 2))^2 - 4(-3(-1x^2 + 4x - 2)) - 1))) - 1|) - 3| - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -4((-3(2|(3(-2|((-1x - 3)/(-3x - 1))|)^2 + 1(-2|((-1x - 3)/(-3x - 1))|) - 3) + 3| + 3))/(3(2|(3(-2|((-1x - 3)/(-3x - 1))|)^2 + 1(-2|((-1x - 3)/(-3x - 1))|) - 3) + 3| + 3) + 1))^2 + 3((-3(2|(3(-2|((-1x - 3)/(-3x - 1))|)^2 + 1(-2|((-1x - 3)/(-3x - 1))|) - 3) + 3| + 3))/(3(2|(3(-2|((-1x - 3)/(-3x - 1))|)^2 + 1(-2|((-1x - 3)/(-3x - 1))|) - 3) + 3| + 3) + 1)) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 3(-1cos(1\u03c0(-5((2(-1((-3x - 3)/(-1x - 3))) + 1)/(1(-1((-3x - 3)/(-1x - 3))) - 2))^2 - 4((2(-1((-3x - 3)/(-1x - 3))) + 1)/(1(-1((-3x - 3)/(-1x - 3))) - 2)) + 1) + 3) + 2)^2 - 3(-1cos(1\u03c0(-5((2(-1((-3x - 3)/(-1x - 3))) + 1)/(1(-1((-3x - 3)/(-1x - 3))) - 2))^2 - 4((2(-1((-3x - 3)/(-1x - 3))) + 1)/(1(-1((-3x - 3)/(-1x - 3))) - 2)) + 1) + 3) + 2) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "66", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = (-1(4((3(-2cos(3\u03c0(2|(-2x - 2) + 2| - 1)) - 3) - 2)/(-2(-2cos(3\u03c0(2|(-2x - 2) + 2| - 1)) - 3) - 2)) - 1) + 3)/(3(4((3(-2cos(3\u03c0(2|(-2x - 2) + 2| - 1)) - 3) - 2)/(-2(-2cos(3\u03c0(2|(-2x - 2) + 2| - 1)) - 3) - 2)) - 1)) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "119", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 1(-1(1(-3((-1(-3x + 4) - 1)/(-2(-3x + 4) - 1))^2 + 1((-1(-3x + 4) - 1)/(-2(-3x + 4) - 1)) + 1)^2 + 4(-3((-1(-3x + 4) - 1)/(-2(-3x + 4) - 1))^2 + 1((-1(-3x + 4) - 1)/(-2(-3x + 4) - 1)) + 1) - 4) + 2)^2 - 3(-1(1(-3((-1(-3x + 4) - 1)/(-2(-3x + 4) - 1))^2 + 1((-1(-3x + 4) - 1)/(-2(-3x + 4) - 1)) + 1)^2 + 4(-3((-1(-3x + 4) - 1)/(-2(-3x + 4) - 1))^2 + 1((-1(-3x + 4) - 1)/(-2(-3x + 4) - 1)) + 1) - 4) + 2) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 3((-1(-2|((-2(2|(1cos(3\u03c0x) - 2) - 1| - 3))/(2(2|(1cos(3\u03c0x) - 2) - 1| - 3) + 1)) + 1| + 1) + 1)/(1(-2|((-2(2|(1cos(3\u03c0x) - 2) - 1| - 3))/(2(2|(1cos(3\u03c0x) - 2) - 1| - 3) + 1)) + 1| + 1) + 3)) + 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = -3(-3|(-1cos(2\u03c0(-2(2((3x + 1)/(2x - 1))^2 - 4((3x + 1)/(2x - 1)) - 5) - 5) - 2))| + 2)^2 - 5(-3|(-1cos(2\u03c0(-2(2((3x + 1)/(2x - 1))^2 - 4((3x + 1)/(2x - 1)) - 5) - 5) - 2))| + 2) - 4 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "27", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = 2(-1|(-1|(-3(1|(1x - 1) + 2| - 3)^2 - 4(1|(1x - 1) + 2| - 3) - 1) - 1| + 3) - 3| + 3)^2 + 1(-1|(-1|(-3(1|(1x - 1) + 2| - 3)^2 - 4(1|(1x - 1) + 2| - 3) - 1) - 1| + 3) - 3| + 3) - 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = (1(-2cos(1\u03c0(-1(3|((1((-1x + 1)/(2x + 2)) + 2)/(2((-1x + 1)/(2x + 2)) - 3)) + 3| - 3) + 5) - 2) + 1) + 3)/(2(-2cos(1\u03c0(-1(3|((1((-1x + 1)/(2x + 2)) + 2)/(2((-1x + 1)/(2x + 2)) - 3)) + 3| - 3) + 5) - 2) + 1) - 3) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -2(2((3(1(1(-2x + 3)^2 - 5(-2x + 3) - 4) - 4) + 2)/(-3(1(1(-2x + 3)^2 - 5(-2x + 3) - 4) - 4) + 4)) - 4)^2 - 3(2((3(1(1(-2x + 3)^2 - 5(-2x + 3) - 4) - 4) + 2)/(-3(1(1(-2x + 3)^2 - 5(-2x + 3) - 4) - 4) + 4)) - 4) - 4 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -3(-1((-1(2|(1(-1x^2 + 4x + 5)^2 + 2(-1x^2 + 4x + 5))| - 2) - 1)/(3(2|(1(-1x^2 + 4x + 5)^2 + 2(-1x^2 + 4x + 5))| - 2) + 1)) - 3)^2 + 2(-1((-1(2|(1(-1x^2 + 4x + 5)^2 + 2(-1x^2 + 4x + 5))| - 2) - 1)/(3(2|(1(-1x^2 + 4x + 5)^2 + 2(-1x^2 + 4x + 5))| - 2) + 1)) - 3) + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -2((-1(1|(1cos(1\u03c0(-3(3x - 3) - 3) - 1) - 3) + 1|) + 3)/(-2(1|(1cos(1\u03c0(-3(3x - 3) - 3) - 1) - 3) + 1|) + 1)) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "90", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 1(-1(-4(-2(1|(3x^2 - 1x + 2) - 3| - 3)^2 - 4) - 2)^2 - 2) - 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = -1(-4(-3sin(1\u03c0(3(4(2x^2 + 3x - 5) + 2) - 2) + 1) - 3) - 5)^2 - 4(-4(-3sin(1\u03c0(3(4(2x^2 + 3x - 5) + 2) - 2) + 1) - 3) - 5) + 4 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "258", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = 4(-2cos(2\u03c0(-5(-2(-5(-1|x - 1| + 1)^2 - 3(-1|x - 1| + 1)) + 5)^2 + 3(-2(-5(-1|x - 1| + 1)^2 - 3(-1|x - 1| + 1)) + 5) - 1) + 2))^2 + 4(-2cos(2\u03c0(-5(-2(-5(-1|x - 1| + 1)^2 - 3(-1|x - 1| + 1)) + 5)^2 + 3(-2(-5(-1|x - 1| + 1)^2 - 3(-1|x - 1| + 1)) + 5) - 1) + 2)) - 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "49", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = (2(3|(-3(1(2sin(1\u03c0((-2x + 3)/(-2x - 2)) + 1) + 3)) - 2) + 3| - 1) + 1)/(3(3|(-3(1(2sin(1\u03c0((-2x + 3)/(-2x - 2)) + 1) + 3)) - 2) + 3| - 1) - 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = -4(3sin(1\u03c0((-1(-2|(1|(-1|x - 2| + 1) + 3|) + 3|) - 2)/(1(-2|(1|(-1|x - 2| + 1) + 3|) + 3|) - 2)) - 3) - 1) + 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 1|((3(-3|(3|((3(1sin(1\u03c0x) + 3) - 3)/(-1(1sin(1\u03c0x) + 3) - 2)) + 1| + 3) + 2| - 3) - 2)/(1(-3|(3|((3(1sin(1\u03c0x) + 3) - 3)/(-1(1sin(1\u03c0x) + 3) - 2)) + 1| + 3) + 2| - 3) - 2)) + 3| - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = (-3(-2sin(3\u03c0(2(4((2(-3|x - 1| - 2) - 2)/(-2(-3|x - 1| - 2) - 1)) - 2) + 4) - 3) - 3) + 2)/(-3(-2sin(3\u03c0(2(4((2(-3|x - 1| - 2) - 2)/(-2(-3|x - 1| - 2) - 1)) - 2) + 4) - 3) - 3) - 2) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 4(-5(-1|(1|(2|(1x^2 + 5x - 1)| - 3) - 2| - 1) - 1| - 1) + 2) + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -1(1|(-3|(3|(2cos(3\u03c0(-4x + 1))) - 1| + 3) + 1| - 1)| + 2)^2 - 2(1|(-3|(3|(2cos(3\u03c0(-4x + 1))) - 1| + 3) + 1| - 1)| + 2) + 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "478", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -2|(1((-3((3(-3e^(-2(-1x^2 + 3x - 3)) - 3) - 1)/(2(-3e^(-2(-1x^2 + 3x - 3)) - 3) + 3)) + 3)/(1((3(-3e^(-2(-1x^2 + 3x - 3)) - 3) - 1)/(2(-3e^(-2(-1x^2 + 3x - 3)) - 3) + 3)) - 2))^2 + 1((-3((3(-3e^(-2(-1x^2 + 3x - 3)) - 3) - 1)/(2(-3e^(-2(-1x^2 + 3x - 3)) - 3) + 3)) + 3)/(1((3(-3e^(-2(-1x^2 + 3x - 3)) - 3) - 1)/(2(-3e^(-2(-1x^2 + 3x - 3)) - 3) + 3)) - 2)) - 1)| where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "88", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 3(-1(2(1(-1|(-2sin(1\u03c0x) + 3) - 2|) + 4) + 1)^2 + 3(2(1(-1|(-2sin(1\u03c0x) + 3) - 2|) + 4) + 1) + 2)^2 - 1(-1(2(1(-1|(-2sin(1\u03c0x) + 3) - 2|) + 4) + 1)^2 + 3(2(1(-1|(-2sin(1\u03c0x) + 3) - 2|) + 4) + 1) + 2) + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "50", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = (3(3|(3|(1cos(2\u03c0((-1((-1x)/(2x - 1)) - 3)/(-1((-1x)/(2x - 1)) + 2)) + 1) - 1) + 3| - 2) - 2| - 3))/(3(3|(3|(1cos(2\u03c0((-1((-1x)/(2x - 1)) - 3)/(-1((-1x)/(2x - 1)) + 2)) + 1) - 1) + 3| - 2) - 2| - 3) - 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -1|(-3(-3(-1(1|((2x - 3)/(1x)) - 3| - 2)^2 + 5(1|((2x - 3)/(1x)) - 3| - 2) - 1) - 4)^2 + 4(-3(-1(1|((2x - 3)/(1x)) - 3| - 2)^2 + 5(1|((2x - 3)/(1x)) - 3| - 2) - 1) - 4) - 4)| + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 1|(-1|(2(1(5(1sin(3\u03c0x + 3) + 2)^2 - 5(1sin(3\u03c0x + 3) + 2) - 1) + 4) - 3) + 3| + 3) + 1| + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 2|(-5((2((3(3(-3|x + 1|)^2 + 5(-3|x + 1|) - 3) - 2)/(-2(3(-3|x + 1|)^2 + 5(-3|x + 1|) - 3))) + 2)/(-2((3(3(-3|x + 1|)^2 + 5(-3|x + 1|) - 3) - 2)/(-2(3(-3|x + 1|)^2 + 5(-3|x + 1|) - 3))) + 3)) + 4) - 2| - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -5((-2(-5(3(-2(-2|x| + 2)^2 + 5(-2|x| + 2) - 3)^2 + 1(-2(-2|x| + 2)^2 + 5(-2|x| + 2) - 3) - 2)^2 - 4(3(-2(-2|x| + 2)^2 + 5(-2|x| + 2) - 3)^2 + 1(-2(-2|x| + 2)^2 + 5(-2|x| + 2) - 3) - 2) - 4) + 3)/(3(-5(3(-2(-2|x| + 2)^2 + 5(-2|x| + 2) - 3)^2 + 1(-2(-2|x| + 2)^2 + 5(-2|x| + 2) - 3) - 2)^2 - 4(3(-2(-2|x| + 2)^2 + 5(-2|x| + 2) - 3)^2 + 1(-2(-2|x| + 2)^2 + 5(-2|x| + 2) - 3) - 2) - 4) - 2))^2 - 5((-2(-5(3(-2(-2|x| + 2)^2 + 5(-2|x| + 2) - 3)^2 + 1(-2(-2|x| + 2)^2 + 5(-2|x| + 2) - 3) - 2)^2 - 4(3(-2(-2|x| + 2)^2 + 5(-2|x| + 2) - 3)^2 + 1(-2(-2|x| + 2)^2 + 5(-2|x| + 2) - 3) - 2) - 4) + 3)/(3(-5(3(-2(-2|x| + 2)^2 + 5(-2|x| + 2) - 3)^2 + 1(-2(-2|x| + 2)^2 + 5(-2|x| + 2) - 3) - 2)^2 - 4(3(-2(-2|x| + 2)^2 + 5(-2|x| + 2) - 3)^2 + 1(-2(-2|x| + 2)^2 + 5(-2|x| + 2) - 3) - 2) - 4) - 2)) + 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "53", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = (-2(2cos(1\u03c0(1|(1(-4(-1x - 2)) + 1) + 1| - 3) + 3) - 1) + 1)/(2(2cos(1\u03c0(1|(1(-4(-1x - 2)) + 1) + 1| - 3) + 3) - 1) + 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "79", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 4(3sin(2\u03c0((-3(3(1((-2x)/(-3x - 3)) + 1)^2 + 1(1((-2x)/(-3x - 3)) + 1) - 4) + 1)/(1(3(1((-2x)/(-3x - 3)) + 1)^2 + 1(1((-2x)/(-3x - 3)) + 1) - 4)))) - 1)^2 + 3(3sin(2\u03c0((-3(3(1((-2x)/(-3x - 3)) + 1)^2 + 1(1((-2x)/(-3x - 3)) + 1) - 4) + 1)/(1(3(1((-2x)/(-3x - 3)) + 1)^2 + 1(1((-2x)/(-3x - 3)) + 1) - 4)))) - 1) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 1cos(2\u03c0(4(5(-2|(1|(-5x) + 2| - 1) + 1| - 1)^2 + 3(-2|(1|(-5x) + 2| - 1) + 1| - 1) - 4)) + 2) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "64", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -5((2((1(-4(2cos(2\u03c0((2x + 2)/(-2x - 3)) + 1) - 3)^2 + 5(2cos(2\u03c0((2x + 2)/(-2x - 3)) + 1) - 3)) + 3)/(-1(-4(2cos(2\u03c0((2x + 2)/(-2x - 3)) + 1) - 3)^2 + 5(2cos(2\u03c0((2x + 2)/(-2x - 3)) + 1) - 3)))) + 1)/(3((1(-4(2cos(2\u03c0((2x + 2)/(-2x - 3)) + 1) - 3)^2 + 5(2cos(2\u03c0((2x + 2)/(-2x - 3)) + 1) - 3)) + 3)/(-1(-4(2cos(2\u03c0((2x + 2)/(-2x - 3)) + 1) - 3)^2 + 5(2cos(2\u03c0((2x + 2)/(-2x - 3)) + 1) - 3)))) - 2))^2 - 2((2((1(-4(2cos(2\u03c0((2x + 2)/(-2x - 3)) + 1) - 3)^2 + 5(2cos(2\u03c0((2x + 2)/(-2x - 3)) + 1) - 3)) + 3)/(-1(-4(2cos(2\u03c0((2x + 2)/(-2x - 3)) + 1) - 3)^2 + 5(2cos(2\u03c0((2x + 2)/(-2x - 3)) + 1) - 3)))) + 1)/(3((1(-4(2cos(2\u03c0((2x + 2)/(-2x - 3)) + 1) - 3)^2 + 5(2cos(2\u03c0((2x + 2)/(-2x - 3)) + 1) - 3)) + 3)/(-1(-4(2cos(2\u03c0((2x + 2)/(-2x - 3)) + 1) - 3)^2 + 5(2cos(2\u03c0((2x + 2)/(-2x - 3)) + 1) - 3)))) - 2)) - 5 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 2(2(-2((3((1(3|x + 2| - 3) + 1)/(-1(3|x + 2| - 3) + 2)) - 3)/(2((1(3|x + 2| - 3) + 1)/(-1(3|x + 2| - 3) + 2))))^2 + 3((3((1(3|x + 2| - 3) + 1)/(-1(3|x + 2| - 3) + 2)) - 3)/(2((1(3|x + 2| - 3) + 1)/(-1(3|x + 2| - 3) + 2)))) - 3) + 2) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -3|((-2(1(2cos(1\u03c0(-2((1x - 3)/(3x - 1)) + 4)) - 3)^2 + 2(2cos(1\u03c0(-2((1x - 3)/(3x - 1)) + 4)) - 3) + 5))/(-3(1(2cos(1\u03c0(-2((1x - 3)/(3x - 1)) + 4)) - 3)^2 + 2(2cos(1\u03c0(-2((1x - 3)/(3x - 1)) + 4)) - 3) + 5) + 4)) + 1| in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 2(-2sin(3\u03c0((-1((1(-5(1x^2 - 3x + 1) - 5) - 3)/(-2(-5(1x^2 - 3x + 1) - 5))) + 1)/(1((1(-5(1x^2 - 3x + 1) - 5) - 3)/(-2(-5(1x^2 - 3x + 1) - 5))) + 2)) - 1) + 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 1(1(-2|((-2(-1(-3sin(3\u03c0x - 2) - 3)^2 + 4(-3sin(3\u03c0x - 2) - 3) + 1) + 3)/(-1(-1(-3sin(3\u03c0x - 2) - 3)^2 + 4(-3sin(3\u03c0x - 2) - 3) + 1))) - 2| + 1) + 5) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -1|(3sin(3\u03c0(3(-3(-1(5x^2 + 1x + 1) + 3)^2 - 1(-1(5x^2 + 1x + 1) + 3) + 1)^2 - 1) - 2) + 2) + 1| - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "46", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -2(1(-2sin(1\u03c0(3((-1(5x^2 + 1x - 5) - 3)/(1(5x^2 + 1x - 5) - 3))^2 - 1)) - 3) + 5)^2 - 5(1(-2sin(1\u03c0(3((-1(5x^2 + 1x - 5) - 3)/(1(5x^2 + 1x - 5) - 3))^2 - 1)) - 3) + 5) + 5 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 2(-2|(4(-5(-3sin(3\u03c0((3x - 3)/(-3x - 3)) - 3) + 1) + 3) + 4) + 3| + 1)^2 + 3(-2|(4(-5(-3sin(3\u03c0((3x - 3)/(-3x - 3)) - 3) + 1) + 3) + 4) + 3| + 1) - 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 2|(2(1(3(-2sin(3\u03c0(3x^2 - 4x - 3) + 2)) - 4)^2 + 2(3(-2sin(3\u03c0(3x^2 - 4x - 3) + 2)) - 4) - 1)^2 - 5(1(3(-2sin(3\u03c0(3x^2 - 4x - 3) + 2)) - 4)^2 + 2(3(-2sin(3\u03c0(3x^2 - 4x - 3) + 2)) - 4) - 1)) + 2| - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "241", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = (2(4(3(1(-2|(2|x + 2| + 1) + 2|)^2 + 1(-2|(2|x + 2| + 1) + 2|) + 2)^2 + 3(1(-2|(2|x + 2| + 1) + 2|)^2 + 1(-2|(2|x + 2| + 1) + 2|) + 2) - 5)^2 - 2(3(1(-2|(2|x + 2| + 1) + 2|)^2 + 1(-2|(2|x + 2| + 1) + 2|) + 2)^2 + 3(1(-2|(2|x + 2| + 1) + 2|)^2 + 1(-2|(2|x + 2| + 1) + 2|) + 2) - 5) + 2))/(-3(4(3(1(-2|(2|x + 2| + 1) + 2|)^2 + 1(-2|(2|x + 2| + 1) + 2|) + 2)^2 + 3(1(-2|(2|x + 2| + 1) + 2|)^2 + 1(-2|(2|x + 2| + 1) + 2|) + 2) - 5)^2 - 2(3(1(-2|(2|x + 2| + 1) + 2|)^2 + 1(-2|(2|x + 2| + 1) + 2|) + 2)^2 + 3(1(-2|(2|x + 2| + 1) + 2|)^2 + 1(-2|(2|x + 2| + 1) + 2|) + 2) - 5) + 2)) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "95", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = 5((3(1(1|((1(-2sin(2\u03c0x + 2) + 3))/(-1(-2sin(2\u03c0x + 2) + 3) - 2)) + 3| + 2)^2 - 4(1|((1(-2sin(2\u03c0x + 2) + 3))/(-1(-2sin(2\u03c0x + 2) + 3) - 2)) + 3| + 2) + 5) - 1)/(-1(1(1|((1(-2sin(2\u03c0x + 2) + 3))/(-1(-2sin(2\u03c0x + 2) + 3) - 2)) + 3| + 2)^2 - 4(1|((1(-2sin(2\u03c0x + 2) + 3))/(-1(-2sin(2\u03c0x + 2) + 3) - 2)) + 3| + 2) + 5)))^2 + 4((3(1(1|((1(-2sin(2\u03c0x + 2) + 3))/(-1(-2sin(2\u03c0x + 2) + 3) - 2)) + 3| + 2)^2 - 4(1|((1(-2sin(2\u03c0x + 2) + 3))/(-1(-2sin(2\u03c0x + 2) + 3) - 2)) + 3| + 2) + 5) - 1)/(-1(1(1|((1(-2sin(2\u03c0x + 2) + 3))/(-1(-2sin(2\u03c0x + 2) + 3) - 2)) + 3| + 2)^2 - 4(1|((1(-2sin(2\u03c0x + 2) + 3))/(-1(-2sin(2\u03c0x + 2) + 3) - 2)) + 3| + 2) + 5))) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = (2((2(-4((-2(-3e^(-2(-2x + 3))) - 1)/(1(-3e^(-2(-2x + 3)))))^2 - 5) - 2)/(2(-4((-2(-3e^(-2(-2x + 3))) - 1)/(1(-3e^(-2(-2x + 3)))))^2 - 5) + 2)) - 3)/(-1((2(-4((-2(-3e^(-2(-2x + 3))) - 1)/(1(-3e^(-2(-2x + 3)))))^2 - 5) - 2)/(2(-4((-2(-3e^(-2(-2x + 3))) - 1)/(1(-3e^(-2(-2x + 3)))))^2 - 5) + 2)) - 1) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = (-3(-1|((2(-1(1sin(1\u03c0(-1x - 3)) + 3)^2 - 3(1sin(1\u03c0(-1x - 3)) + 3) + 3) - 2)/(3(-1(1sin(1\u03c0(-1x - 3)) + 3)^2 - 3(1sin(1\u03c0(-1x - 3)) + 3) + 3) + 2)) + 3| + 2) + 1)/(-1(-1|((2(-1(1sin(1\u03c0(-1x - 3)) + 3)^2 - 3(1sin(1\u03c0(-1x - 3)) + 3) + 3) - 2)/(3(-1(1sin(1\u03c0(-1x - 3)) + 3)^2 - 3(1sin(1\u03c0(-1x - 3)) + 3) + 3) + 2)) + 3| + 2)) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 2|(-1(-3cos(2\u03c0(-1(4(-2x^2 - 5x - 2) + 4)^2 + 1(4(-2x^2 - 5x - 2) + 4) + 2) - 1) - 3)^2 - 3(-3cos(2\u03c0(-1(4(-2x^2 - 5x - 2) + 4)^2 + 1(4(-2x^2 - 5x - 2) + 4) + 2) - 1) - 3) + 5) - 2| have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "26", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -3|(2(-2|(-3sin(3\u03c0(-2|(4x) - 3| - 3) + 2) + 3) - 2| + 1) + 2) - 2| + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "769", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 3(4(-3cos(2\u03c0((-2(-1(1|x + 2|) + 2) + 3)/(-2(-1(1|x + 2|) + 2) + 1)) - 2) + 2)^2 - 4(-3cos(2\u03c0((-2(-1(1|x + 2|) + 2) + 3)/(-2(-1(1|x + 2|) + 2) + 1)) - 2) + 2) - 5)^2 + 2(4(-3cos(2\u03c0((-2(-1(1|x + 2|) + 2) + 3)/(-2(-1(1|x + 2|) + 2) + 1)) - 2) + 2)^2 - 4(-3cos(2\u03c0((-2(-1(1|x + 2|) + 2) + 3)/(-2(-1(1|x + 2|) + 2) + 1)) - 2) + 2) - 5) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "48", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -5(2(1|(-3|(2sin(2\u03c0((3x - 1)/(-1x + 2)) - 3) + 3) + 1| - 2) - 1| + 2) + 2) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = (-3(5(-4(-3(3sin(2\u03c0(1x^2 - 2x - 4) + 1) - 2) + 4) + 5)^2 - 3(-4(-3(3sin(2\u03c0(1x^2 - 2x - 4) + 1) - 2) + 4) + 5) + 2))/(-1(5(-4(-3(3sin(2\u03c0(1x^2 - 2x - 4) + 1) - 2) + 4) + 5)^2 - 3(-4(-3(3sin(2\u03c0(1x^2 - 2x - 4) + 1) - 2) + 4) + 5) + 2) + 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "397", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = (2(-3sin(1\u03c0(-4(-1((-1((1x - 3)/(-3x + 1)) - 2)/(1((1x - 3)/(-3x + 1)) - 2)) + 2)^2 + 3(-1((-1((1x - 3)/(-3x + 1)) - 2)/(1((1x - 3)/(-3x + 1)) - 2)) + 2) - 2) + 1) - 3) + 2)/(-3(-3sin(1\u03c0(-4(-1((-1((1x - 3)/(-3x + 1)) - 2)/(1((1x - 3)/(-3x + 1)) - 2)) + 2)^2 + 3(-1((-1((1x - 3)/(-3x + 1)) - 2)/(1((1x - 3)/(-3x + 1)) - 2)) + 2) - 2) + 1) - 3) + 4) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = (2(3(-1|(5(-3cos(1\u03c0(1x^2 - 1) + 1) - 3)^2 - 1(-3cos(1\u03c0(1x^2 - 1) + 1) - 3) - 1) + 2| - 1)^2 - 1(-1|(5(-3cos(1\u03c0(1x^2 - 1) + 1) - 3)^2 - 1(-3cos(1\u03c0(1x^2 - 1) + 1) - 3) - 1) + 2| - 1) - 3) + 2)/(-3(3(-1|(5(-3cos(1\u03c0(1x^2 - 1) + 1) - 3)^2 - 1(-3cos(1\u03c0(1x^2 - 1) + 1) - 3) - 1) + 2| - 1)^2 - 1(-1|(5(-3cos(1\u03c0(1x^2 - 1) + 1) - 3)^2 - 1(-3cos(1\u03c0(1x^2 - 1) + 1) - 3) - 1) + 2| - 1) - 3) - 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "115", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -3cos(2\u03c0((1(1(5(3(-1x^2 - 4x + 5) + 1) - 4)^2 - 1(5(3(-1x^2 - 4x + 5) + 1) - 4) - 5) + 3)/(1(1(5(3(-1x^2 - 4x + 5) + 1) - 4)^2 - 1(5(3(-1x^2 - 4x + 5) + 1) - 4) - 5)))) - 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 4(1|(-1(-3((2(2sin(2\u03c0x) + 1))/(1(2sin(2\u03c0x) + 1) - 2)) + 4) - 2)| - 3) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = (-1(-2(-1(3(1sin(2\u03c0(3x^2 + 1x + 1) + 2) - 3)^2 + 1(1sin(2\u03c0(3x^2 + 1x + 1) + 2) - 3))^2 - 3(3(1sin(2\u03c0(3x^2 + 1x + 1) + 2) - 3)^2 + 1(1sin(2\u03c0(3x^2 + 1x + 1) + 2) - 3)) - 1)^2 + 3(-1(3(1sin(2\u03c0(3x^2 + 1x + 1) + 2) - 3)^2 + 1(1sin(2\u03c0(3x^2 + 1x + 1) + 2) - 3))^2 - 3(3(1sin(2\u03c0(3x^2 + 1x + 1) + 2) - 3)^2 + 1(1sin(2\u03c0(3x^2 + 1x + 1) + 2) - 3)) - 1) - 3) + 1)/(-1(-2(-1(3(1sin(2\u03c0(3x^2 + 1x + 1) + 2) - 3)^2 + 1(1sin(2\u03c0(3x^2 + 1x + 1) + 2) - 3))^2 - 3(3(1sin(2\u03c0(3x^2 + 1x + 1) + 2) - 3)^2 + 1(1sin(2\u03c0(3x^2 + 1x + 1) + 2) - 3)) - 1)^2 + 3(-1(3(1sin(2\u03c0(3x^2 + 1x + 1) + 2) - 3)^2 + 1(1sin(2\u03c0(3x^2 + 1x + 1) + 2) - 3))^2 - 3(3(1sin(2\u03c0(3x^2 + 1x + 1) + 2) - 3)^2 + 1(1sin(2\u03c0(3x^2 + 1x + 1) + 2) - 3)) - 1) - 3) - 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "453", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -1|(-2|(3cos(3\u03c0(-5(3(-4x + 3) - 2)^2 - 5(3(-4x + 3) - 2) + 4) - 1) - 1) - 1| + 1) + 1| - 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "49", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = (1(-1|(-2(4(2|(1x + 2) + 1| - 1)^2 + 5(2|(1x + 2) + 1| - 1) - 3)^2 - 1(4(2|(1x + 2) + 1| - 1)^2 + 5(2|(1x + 2) + 1| - 1) - 3) - 2) - 1| + 2) - 3)/(-1(-1|(-2(4(2|(1x + 2) + 1| - 1)^2 + 5(2|(1x + 2) + 1| - 1) - 3)^2 - 1(4(2|(1x + 2) + 1| - 1)^2 + 5(2|(1x + 2) + 1| - 1) - 3) - 2) - 1| + 2) - 1) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 3|(-4((-1(3(-1(-1|x + 3| - 2) - 3)^2 + 1(-1(-1|x + 3| - 2) - 3) - 4) - 1)/(3(3(-1(-1|x + 3| - 2) - 3)^2 + 1(-1(-1|x + 3| - 2) - 3) - 4)))^2 - 1((-1(3(-1(-1|x + 3| - 2) - 3)^2 + 1(-1(-1|x + 3| - 2) - 3) - 4) - 1)/(3(3(-1(-1|x + 3| - 2) - 3)^2 + 1(-1(-1|x + 3| - 2) - 3) - 4))) - 5) + 2| - 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -1(5((-1(1cos(3\u03c0((3(-5x - 4) + 3)/(-2(-5x - 4)))) + 1) - 3)/(3(1cos(3\u03c0((3(-5x - 4) + 3)/(-2(-5x - 4)))) + 1) + 1))^2 - 2((-1(1cos(3\u03c0((3(-5x - 4) + 3)/(-2(-5x - 4)))) + 1) - 3)/(3(1cos(3\u03c0((3(-5x - 4) + 3)/(-2(-5x - 4)))) + 1) + 1)) - 5)^2 + 5(5((-1(1cos(3\u03c0((3(-5x - 4) + 3)/(-2(-5x - 4)))) + 1) - 3)/(3(1cos(3\u03c0((3(-5x - 4) + 3)/(-2(-5x - 4)))) + 1) + 1))^2 - 2((-1(1cos(3\u03c0((3(-5x - 4) + 3)/(-2(-5x - 4)))) + 1) - 3)/(3(1cos(3\u03c0((3(-5x - 4) + 3)/(-2(-5x - 4)))) + 1) + 1)) - 5) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -2|(1(5(-2(2|(-1x^2 - 2x - 1) + 1| - 1)^2 + 3(2|(-1x^2 - 2x - 1) + 1| - 1)) + 5)) + 1| - 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -2|(1cos(3\u03c0(-2((-3(3|(2x - 5) - 1| + 2) - 3)/(-3(3|(2x - 5) - 1| + 2) + 2)) - 1) - 1) + 3) + 3| + 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 3|((2(-1(1(-2(5x^2 + 3)^2 + 2(5x^2 + 3) - 1)^2 + 1(-2(5x^2 + 3)^2 + 2(5x^2 + 3) - 1) - 4)^2 - 1(1(-2(5x^2 + 3)^2 + 2(5x^2 + 3) - 1)^2 + 1(-2(5x^2 + 3)^2 + 2(5x^2 + 3) - 1) - 4) + 2) - 3)/(1(-1(1(-2(5x^2 + 3)^2 + 2(5x^2 + 3) - 1)^2 + 1(-2(5x^2 + 3)^2 + 2(5x^2 + 3) - 1) - 4)^2 - 1(1(-2(5x^2 + 3)^2 + 2(5x^2 + 3) - 1)^2 + 1(-2(5x^2 + 3)^2 + 2(5x^2 + 3) - 1) - 4) + 2) + 2)) - 2| where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = (1(-3|(4(-1|(-5(1cos(1\u03c0x + 2) + 1)^2 - 3)| - 1)^2 + 4(-1|(-5(1cos(1\u03c0x + 2) + 1)^2 - 3)| - 1)) - 1| + 2) - 3)/(-1(-3|(4(-1|(-5(1cos(1\u03c0x + 2) + 1)^2 - 3)| - 1)^2 + 4(-1|(-5(1cos(1\u03c0x + 2) + 1)^2 - 3)| - 1)) - 1| + 2) + 2) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = (2((-3(-2|(3(2sin(1\u03c0(-3|x - 2| + 3) + 2) - 2)^2 + 2(2sin(1\u03c0(-3|x - 2| + 3) + 2) - 2) + 5) - 3| - 1) + 1)/(2(-2|(3(2sin(1\u03c0(-3|x - 2| + 3) + 2) - 2)^2 + 2(2sin(1\u03c0(-3|x - 2| + 3) + 2) - 2) + 5) - 3| - 1) + 2)) + 3)/(3((-3(-2|(3(2sin(1\u03c0(-3|x - 2| + 3) + 2) - 2)^2 + 2(2sin(1\u03c0(-3|x - 2| + 3) + 2) - 2) + 5) - 3| - 1) + 1)/(2(-2|(3(2sin(1\u03c0(-3|x - 2| + 3) + 2) - 2)^2 + 2(2sin(1\u03c0(-3|x - 2| + 3) + 2) - 2) + 5) - 3| - 1) + 2))) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "61", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -1(-2cos(2\u03c0((1(-3(4(-2x - 5) - 4) - 4) - 1)/(-2(-3(4(-2x - 5) - 4) - 4))) - 3) - 3) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = (-3(-2|(-1(-2sin(1\u03c0(-2(-4x) - 5) + 3) - 1)^2 - 5(-2sin(1\u03c0(-2(-4x) - 5) + 3) - 1) + 2) - 2| + 2) - 3)/(1(-2|(-1(-2sin(1\u03c0(-2(-4x) - 5) + 3) - 1)^2 - 5(-2sin(1\u03c0(-2(-4x) - 5) + 3) - 1) + 2) - 2| + 2) + 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "230", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = 1|(-3((-3(-1|(-2|((2x + 3)/(2x)) - 2| + 3) + 1| - 1) + 3)/(1(-1|(-2|((2x + 3)/(2x)) - 2| + 3) + 1| - 1) + 2)) + 4) + 3| - 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 4(-3(-1|((-3(1sin(1\u03c0(-1|x| + 3) - 2) + 2) + 2)/(3(1sin(1\u03c0(-1|x| + 3) - 2) + 2))) - 2|)^2 + 5(-1|((-3(1sin(1\u03c0(-1|x| + 3) - 2) + 2) + 2)/(3(1sin(1\u03c0(-1|x| + 3) - 2) + 2))) - 2|) + 1) + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = -2sin(3\u03c0(-1(-4((3(-3(1|x| + 2) - 1) - 2)/(1(-3(1|x| + 2) - 1)))^2 - 3((3(-3(1|x| + 2) - 1) - 2)/(1(-3(1|x| + 2) - 1))) + 4)^2 - 1(-4((3(-3(1|x| + 2) - 1) - 2)/(1(-3(1|x| + 2) - 1)))^2 - 3((3(-3(1|x| + 2) - 1) - 2)/(1(-3(1|x| + 2) - 1))) + 4)) + 3) - 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "299", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = 2(-1|(3|(-1e^(-2(-5(-5x^2 - 1x + 3)^2 - 3(-5x^2 - 1x + 3) - 3))) + 1| + 3)| - 1) + 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -1|((-1(-3|(1(3(5x^2 + 3x + 4)^2 + 1)^2 - 1(3(5x^2 + 3x + 4)^2 + 1) - 2) + 3|) + 2)/(3(-3|(1(3(5x^2 + 3x + 4)^2 + 1)^2 - 1(3(5x^2 + 3x + 4)^2 + 1) - 2) + 3|) - 1)) + 2| + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = 1((2(1sin(3\u03c0(3(-2|(-2|x + 2| - 1) + 3|)^2 + 3(-2|(-2|x + 2| - 1) + 3|)) + 3)) + 2)/(-2(1sin(3\u03c0(3(-2|(-2|x + 2| - 1) + 3|)^2 + 3(-2|(-2|x + 2| - 1) + 3|)) + 3)) + 1)) - 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "246", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 3(2(-1((-1(-1(-1cos(1\u03c0x - 3) - 2)^2 - 4(-1cos(1\u03c0x - 3) - 2) + 2) - 1)/(2(-1(-1cos(1\u03c0x - 3) - 2)^2 - 4(-1cos(1\u03c0x - 3) - 2) + 2) + 3))^2 + 3((-1(-1(-1cos(1\u03c0x - 3) - 2)^2 - 4(-1cos(1\u03c0x - 3) - 2) + 2) - 1)/(2(-1(-1cos(1\u03c0x - 3) - 2)^2 - 4(-1cos(1\u03c0x - 3) - 2) + 2) + 3)) + 4) - 1)^2 + 2(2(-1((-1(-1(-1cos(1\u03c0x - 3) - 2)^2 - 4(-1cos(1\u03c0x - 3) - 2) + 2) - 1)/(2(-1(-1cos(1\u03c0x - 3) - 2)^2 - 4(-1cos(1\u03c0x - 3) - 2) + 2) + 3))^2 + 3((-1(-1(-1cos(1\u03c0x - 3) - 2)^2 - 4(-1cos(1\u03c0x - 3) - 2) + 2) - 1)/(2(-1(-1cos(1\u03c0x - 3) - 2)^2 - 4(-1cos(1\u03c0x - 3) - 2) + 2) + 3)) + 4) - 1) - 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 3(-2|(-5(4(2((-1x - 3)/(1x)) + 3)^2 + 1(2((-1x - 3)/(1x)) + 3) - 2)^2 - 5(4(2((-1x - 3)/(1x)) + 3)^2 + 1(2((-1x - 3)/(1x)) + 3) - 2) + 4) + 1| + 2)^2 - 3(-2|(-5(4(2((-1x - 3)/(1x)) + 3)^2 + 1(2((-1x - 3)/(1x)) + 3) - 2)^2 - 5(4(2((-1x - 3)/(1x)) + 3)^2 + 1(2((-1x - 3)/(1x)) + 3) - 2) + 4) + 1| + 2) - 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -2sin(3\u03c0(-2|((-1(3|(3((-2x - 1)/(-2x - 2))^2 - 1((-2x - 1)/(-2x - 2)) + 3) - 2| - 2) + 3)/(2(3|(3((-2x - 1)/(-2x - 2))^2 - 1((-2x - 1)/(-2x - 2)) + 3) - 2| - 2) + 1))|) + 2) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 1((2(-1sin(3\u03c0(-1(1|((3x - 2)/(-2x - 1)) + 3| - 3)^2 + 2(1|((3x - 2)/(-2x - 1)) + 3| - 3) - 2))))/(-3(-1sin(3\u03c0(-1(1|((3x - 2)/(-2x - 1)) + 3| - 3)^2 + 2(1|((3x - 2)/(-2x - 1)) + 3| - 3) - 2))) - 1)) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "52", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -1(-1(-5(-3(-1(1|x|)^2 + 1(1|x|) + 5)^2 + 2(-1(1|x|)^2 + 1(1|x|) + 5) - 3) + 5) + 1)^2 + 4(-1(-5(-3(-1(1|x|)^2 + 1(1|x|) + 5)^2 + 2(-1(1|x|)^2 + 1(1|x|) + 5) - 3) + 5) + 1) + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = 5((1(5((-3(2e^(-2(3x)) - 2) - 1)/(-1(2e^(-2(3x)) - 2) + 2))^2 + 5((-3(2e^(-2(3x)) - 2) - 1)/(-1(2e^(-2(3x)) - 2) + 2)) - 2) - 2)/(3(5((-3(2e^(-2(3x)) - 2) - 1)/(-1(2e^(-2(3x)) - 2) + 2))^2 + 5((-3(2e^(-2(3x)) - 2) - 1)/(-1(2e^(-2(3x)) - 2) + 2)) - 2) - 2))^2 + 2((1(5((-3(2e^(-2(3x)) - 2) - 1)/(-1(2e^(-2(3x)) - 2) + 2))^2 + 5((-3(2e^(-2(3x)) - 2) - 1)/(-1(2e^(-2(3x)) - 2) + 2)) - 2) - 2)/(3(5((-3(2e^(-2(3x)) - 2) - 1)/(-1(2e^(-2(3x)) - 2) + 2))^2 + 5((-3(2e^(-2(3x)) - 2) - 1)/(-1(2e^(-2(3x)) - 2) + 2)) - 2) - 2)) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = 2|((-2(1((1(2(-2sin(3\u03c0x - 1)) + 5) - 1)/(-1(2(-2sin(3\u03c0x - 1)) + 5) + 2)) - 5) + 3)/(1(1((1(2(-2sin(3\u03c0x - 1)) + 5) - 1)/(-1(2(-2sin(3\u03c0x - 1)) + 5) + 2)) - 5) - 3)) - 3| + 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = (-3(-1e^(-1(4(-3|(5((-1x - 3)/(-2x + 1))^2 - 1((-1x - 3)/(-2x + 1)) - 1) - 3| - 1) - 3)) + 2))/(-1(-1e^(-1(4(-3|(5((-1x - 3)/(-2x + 1))^2 - 1((-1x - 3)/(-2x + 1)) - 1) - 3| - 1) - 3)) + 2) + 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "116", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 1((-1(-2(-5(2cos(2\u03c0((-1x - 3)/(1x)) + 1) - 1) + 3) + 2) - 1)/(2(-2(-5(2cos(2\u03c0((-1x - 3)/(1x)) + 1) - 1) + 3) + 2) + 3))^2 - 5((-1(-2(-5(2cos(2\u03c0((-1x - 3)/(1x)) + 1) - 1) + 3) + 2) - 1)/(2(-2(-5(2cos(2\u03c0((-1x - 3)/(1x)) + 1) - 1) + 3) + 2) + 3)) - 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = (2(1((1(-2(-1|(-3|x - 2| + 3) - 1| + 3) + 5) + 3)/(3(-2(-1|(-3|x - 2| + 3) - 1| + 3) + 5) + 1))^2 + 2((1(-2(-1|(-3|x - 2| + 3) - 1| + 3) + 5) + 3)/(3(-2(-1|(-3|x - 2| + 3) - 1| + 3) + 5) + 1)) + 1) - 2)/(-1(1((1(-2(-1|(-3|x - 2| + 3) - 1| + 3) + 5) + 3)/(3(-2(-1|(-3|x - 2| + 3) - 1| + 3) + 5) + 1))^2 + 2((1(-2(-1|(-3|x - 2| + 3) - 1| + 3) + 5) + 3)/(3(-2(-1|(-3|x - 2| + 3) - 1| + 3) + 5) + 1)) + 1) - 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = (1(2sin(2\u03c0((-2(1(3(1x) - 3)^2 - 5(3(1x) - 3) + 3) + 3)/(-1(1(3(1x) - 3)^2 - 5(3(1x) - 3) + 3) - 2)) - 2) + 2) + 2)/(3(2sin(2\u03c0((-2(1(3(1x) - 3)^2 - 5(3(1x) - 3) + 3) + 3)/(-1(1(3(1x) - 3)^2 - 5(3(1x) - 3) + 3) - 2)) - 2) + 2) + 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = 1|(-4(1(-3(1(-1cos(3\u03c0x + 2) - 1)^2 - 2)^2 + 5) - 1) - 4) + 3| + 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "237", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -2|(2|(1((-3(2sin(2\u03c0((-2x - 2)/(-3x + 1)))) + 2)/(1(2sin(2\u03c0((-2x - 2)/(-3x + 1)))) - 3))^2 + 5((-3(2sin(2\u03c0((-2x - 2)/(-3x + 1)))) + 2)/(1(2sin(2\u03c0((-2x - 2)/(-3x + 1)))) - 3)) + 5) + 3| + 1) - 3| have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = (2(-3e^(2(-1|(-2(2((1x + 2)/(2x + 3))^2 + 5((1x + 2)/(2x + 3)) - 5)^2 - 1(2((1x + 2)/(2x + 3))^2 + 5((1x + 2)/(2x + 3)) - 5) - 3) - 3| + 2))) - 3)/(-3(-3e^(2(-1|(-2(2((1x + 2)/(2x + 3))^2 + 5((1x + 2)/(2x + 3)) - 5)^2 - 1(2((1x + 2)/(2x + 3))^2 + 5((1x + 2)/(2x + 3)) - 5) - 3) - 3| + 2))) + 1) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 2|((-2(-3(-5(1(3x^2 - 3x + 4) + 2)^2 + 2(1(3x^2 - 3x + 4) + 2) - 1)^2 - 4(-5(1(3x^2 - 3x + 4) + 2)^2 + 2(1(3x^2 - 3x + 4) + 2) - 1)) - 3)/(1(-3(-5(1(3x^2 - 3x + 4) + 2)^2 + 2(1(3x^2 - 3x + 4) + 2) - 1)^2 - 4(-5(1(3x^2 - 3x + 4) + 2)^2 + 2(1(3x^2 - 3x + 4) + 2) - 1)) - 2))| + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -2cos(2\u03c0(4(-5((1(-5(1|x - 2| + 3)^2 + 3(1|x - 2| + 3) + 3) + 3)/(-1(-5(1|x - 2| + 3)^2 + 3(1|x - 2| + 3) + 3) + 2)) - 3) - 2) + 1) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = 1sin(2\u03c0(1|(-3|((-2(1((1x + 1)/(-3x - 2))^2 - 4((1x + 1)/(-3x - 2)) + 2) + 3)/(-2(1((1x + 1)/(-3x - 2))^2 - 4((1x + 1)/(-3x - 2)) + 2) - 2)) + 1|)| - 3) - 3) - 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = 3(1|(-1(3(5(1|x - 3| - 2) + 5) + 4)^2 - 2(3(5(1|x - 3| - 2) + 5) + 4) + 2) + 3| + 3)^2 + 2(1|(-1(3(5(1|x - 3| - 2) + 5) + 4)^2 - 2(3(5(1|x - 3| - 2) + 5) + 4) + 2) + 3| + 3) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = (2(4(3(-1|(-1(-1sin(2\u03c0x - 1) + 3) - 5) - 1| - 1) - 5)^2 - 1(3(-1|(-1(-1sin(2\u03c0x - 1) + 3) - 5) - 1| - 1) - 5) + 2) + 3)/(-2(4(3(-1|(-1(-1sin(2\u03c0x - 1) + 3) - 5) - 1| - 1) - 5)^2 - 1(3(-1|(-1(-1sin(2\u03c0x - 1) + 3) - 5) - 1| - 1) - 5) + 2) + 3) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -5(3cos(1\u03c0(2((3((3(-2|x| + 1) + 3)/(1(-2|x| + 1))) + 1)/(2((3(-2|x| + 1) + 3)/(1(-2|x| + 1))) - 1)) + 1) - 3) - 3)^2 + 2(3cos(1\u03c0(2((3((3(-2|x| + 1) + 3)/(1(-2|x| + 1))) + 1)/(2((3(-2|x| + 1) + 3)/(1(-2|x| + 1))) - 1)) + 1) - 3) - 3) + 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = (3(-1|((-1(2(-1|(1x) - 1| + 1)^2 - 3(-1|(1x) - 1| + 1) - 3) - 1)/(1(2(-1|(1x) - 1| + 1)^2 - 3(-1|(1x) - 1| + 1) - 3))) - 2| - 3) - 2)/(1(-1|((-1(2(-1|(1x) - 1| + 1)^2 - 3(-1|(1x) - 1| + 1) - 3) - 1)/(1(2(-1|(1x) - 1| + 1)^2 - 3(-1|(1x) - 1| + 1) - 3))) - 2| - 3) - 3) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = 2(1(-2(5(4(-5x^2 + 1x + 1)^2 + 4(-5x^2 + 1x + 1) - 3)^2 + 1(4(-5x^2 + 1x + 1)^2 + 4(-5x^2 + 1x + 1) - 3) - 4)^2 + 3(5(4(-5x^2 + 1x + 1)^2 + 4(-5x^2 + 1x + 1) - 3)^2 + 1(4(-5x^2 + 1x + 1)^2 + 4(-5x^2 + 1x + 1) - 3) - 4) - 3) + 3)^2 - 5(1(-2(5(4(-5x^2 + 1x + 1)^2 + 4(-5x^2 + 1x + 1) - 3)^2 + 1(4(-5x^2 + 1x + 1)^2 + 4(-5x^2 + 1x + 1) - 3) - 4)^2 + 3(5(4(-5x^2 + 1x + 1)^2 + 4(-5x^2 + 1x + 1) - 3)^2 + 1(4(-5x^2 + 1x + 1)^2 + 4(-5x^2 + 1x + 1) - 3) - 4) - 3) + 3) + 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = (-2((-2(2(1(4((3x + 2)/(-2x + 1))^2 + 1((3x + 2)/(-2x + 1)) - 3)^2 - 2(4((3x + 2)/(-2x + 1))^2 + 1((3x + 2)/(-2x + 1)) - 3) + 2) + 4) + 2)/(3(2(1(4((3x + 2)/(-2x + 1))^2 + 1((3x + 2)/(-2x + 1)) - 3)^2 - 2(4((3x + 2)/(-2x + 1))^2 + 1((3x + 2)/(-2x + 1)) - 3) + 2) + 4) + 3)) + 2)/(3((-2(2(1(4((3x + 2)/(-2x + 1))^2 + 1((3x + 2)/(-2x + 1)) - 3)^2 - 2(4((3x + 2)/(-2x + 1))^2 + 1((3x + 2)/(-2x + 1)) - 3) + 2) + 4) + 2)/(3(2(1(4((3x + 2)/(-2x + 1))^2 + 1((3x + 2)/(-2x + 1)) - 3)^2 - 2(4((3x + 2)/(-2x + 1))^2 + 1((3x + 2)/(-2x + 1)) - 3) + 2) + 4) + 3)) - 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = (-1((-1(3(4(-1(-1sin(3\u03c0x) + 3)^2 - 4(-1sin(3\u03c0x) + 3) - 4) + 5) - 5) - 2)/(-1(3(4(-1(-1sin(3\u03c0x) + 3)^2 - 4(-1sin(3\u03c0x) + 3) - 4) + 5) - 5) - 1)) - 2)/(1((-1(3(4(-1(-1sin(3\u03c0x) + 3)^2 - 4(-1sin(3\u03c0x) + 3) - 4) + 5) - 5) - 2)/(-1(3(4(-1(-1sin(3\u03c0x) + 3)^2 - 4(-1sin(3\u03c0x) + 3) - 4) + 5) - 5) - 1)) + 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -1sin(3\u03c0((1(2(2|((-1(3x + 1) + 1)/(3(3x + 1) + 1)) + 2| + 1) + 4) + 3)/(-1(2(2|((-1(3x + 1) + 1)/(3(3x + 1) + 1)) + 2| + 1) + 4) + 2)) - 3) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = (1(-1((2(3|(-5((-3x - 1)/(1x - 2))^2 + 2((-3x - 1)/(1x - 2)))| - 1) + 3)/(-3(3|(-5((-3x - 1)/(1x - 2))^2 + 2((-3x - 1)/(1x - 2)))| - 1) + 4))^2 - 3((2(3|(-5((-3x - 1)/(1x - 2))^2 + 2((-3x - 1)/(1x - 2)))| - 1) + 3)/(-3(3|(-5((-3x - 1)/(1x - 2))^2 + 2((-3x - 1)/(1x - 2)))| - 1) + 4)) - 1) + 3)/(-1(-1((2(3|(-5((-3x - 1)/(1x - 2))^2 + 2((-3x - 1)/(1x - 2)))| - 1) + 3)/(-3(3|(-5((-3x - 1)/(1x - 2))^2 + 2((-3x - 1)/(1x - 2)))| - 1) + 4))^2 - 3((2(3|(-5((-3x - 1)/(1x - 2))^2 + 2((-3x - 1)/(1x - 2)))| - 1) + 3)/(-3(3|(-5((-3x - 1)/(1x - 2))^2 + 2((-3x - 1)/(1x - 2)))| - 1) + 4)) - 1) + 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 2(1(-2|((3(-1(-4x - 3)^2 + 5(-4x - 3) + 4))/(2(-1(-4x - 3)^2 + 5(-4x - 3) + 4))) - 3| + 2) + 2)^2 - 3(1(-2|((3(-1(-4x - 3)^2 + 5(-4x - 3) + 4))/(2(-1(-4x - 3)^2 + 5(-4x - 3) + 4))) - 3| + 2) + 2) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "70", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = (-3(-5(-2sin(3\u03c0((-1(2|(1|x - 2| - 3) + 1| - 2))/(1(2|(1|x - 2| - 3) + 1| - 2) + 3)) - 3) + 2)^2 + 4(-2sin(3\u03c0((-1(2|(1|x - 2| - 3) + 1| - 2))/(1(2|(1|x - 2| - 3) + 1| - 2) + 3)) - 3) + 2) - 1) + 1)/(-3(-5(-2sin(3\u03c0((-1(2|(1|x - 2| - 3) + 1| - 2))/(1(2|(1|x - 2| - 3) + 1| - 2) + 3)) - 3) + 2)^2 + 4(-2sin(3\u03c0((-1(2|(1|x - 2| - 3) + 1| - 2))/(1(2|(1|x - 2| - 3) + 1| - 2) + 3)) - 3) + 2) - 1)) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 5(-1sin(2\u03c0(-3((-2(5(-1|x + 2| + 2)^2 - 2(-1|x + 2| + 2) - 5) - 2)/(1(5(-1|x + 2| + 2)^2 - 2(-1|x + 2| + 2) - 5) - 3)) - 3) - 1) - 3)^2 + 4(-1sin(2\u03c0(-3((-2(5(-1|x + 2| + 2)^2 - 2(-1|x + 2| + 2) - 5) - 2)/(1(5(-1|x + 2| + 2)^2 - 2(-1|x + 2| + 2) - 5) - 3)) - 3) - 1) - 3) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "72", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -1(1e^(-1(-4(1(5(5x + 5)^2 - 1(5x + 5))^2 - 1(5(5x + 5)^2 - 1(5x + 5)) - 4) + 4)) - 1)^2 - 3(1e^(-1(-4(1(5(5x + 5)^2 - 1(5x + 5))^2 - 1(5(5x + 5)^2 - 1(5x + 5)) - 4) + 4)) - 1) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 1(-2cos(2\u03c0(1|(-1(-2(-3|x + 1| + 2)^2 - 1(-3|x + 1| + 2) + 4) - 4) - 2| + 3) + 2)) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "487", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = (-1(3(1sin(3\u03c0(1|(-4(3x + 3) + 1)| + 2) - 1) - 3) + 5))/(1(3(1sin(3\u03c0(1|(-4(3x + 3) + 1)| + 2) - 1) - 3) + 5) - 3) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "509", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = (2(1|(-3|((-1(1e^(-2(1x^2 + 2x - 3)) - 3) + 2)/(-1(1e^(-2(1x^2 + 2x - 3)) - 3) + 3)) - 2| + 2) + 3| + 2) + 3)/(-1(1|(-3|((-1(1e^(-2(1x^2 + 2x - 3)) - 3) + 2)/(-1(1e^(-2(1x^2 + 2x - 3)) - 3) + 3)) - 2| + 2) + 3| + 2)) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = (1(2(-5(-5(-2cos(3\u03c0(2x + 3) + 2) + 2)^2 + 3(-2cos(3\u03c0(2x + 3) + 2) + 2) - 2)^2 + 1(-5(-2cos(3\u03c0(2x + 3) + 2) + 2)^2 + 3(-2cos(3\u03c0(2x + 3) + 2) + 2) - 2) + 4)^2 + 3(-5(-5(-2cos(3\u03c0(2x + 3) + 2) + 2)^2 + 3(-2cos(3\u03c0(2x + 3) + 2) + 2) - 2)^2 + 1(-5(-2cos(3\u03c0(2x + 3) + 2) + 2)^2 + 3(-2cos(3\u03c0(2x + 3) + 2) + 2) - 2) + 4) + 4) + 2)/(1(2(-5(-5(-2cos(3\u03c0(2x + 3) + 2) + 2)^2 + 3(-2cos(3\u03c0(2x + 3) + 2) + 2) - 2)^2 + 1(-5(-2cos(3\u03c0(2x + 3) + 2) + 2)^2 + 3(-2cos(3\u03c0(2x + 3) + 2) + 2) - 2) + 4)^2 + 3(-5(-5(-2cos(3\u03c0(2x + 3) + 2) + 2)^2 + 3(-2cos(3\u03c0(2x + 3) + 2) + 2) - 2)^2 + 1(-5(-2cos(3\u03c0(2x + 3) + 2) + 2)^2 + 3(-2cos(3\u03c0(2x + 3) + 2) + 2) - 2) + 4) + 4)) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "235", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = (-3(-2|((2(-2cos(1\u03c0((3(5x^2 + 4x))/(-2(5x^2 + 4x) - 1)) + 1) - 3) + 2)/(-1(-2cos(1\u03c0((3(5x^2 + 4x))/(-2(5x^2 + 4x) - 1)) + 1) - 3) + 2)) + 3| + 2) - 2)/(-1(-2|((2(-2cos(1\u03c0((3(5x^2 + 4x))/(-2(5x^2 + 4x) - 1)) + 1) - 3) + 2)/(-1(-2cos(1\u03c0((3(5x^2 + 4x))/(-2(5x^2 + 4x) - 1)) + 1) - 3) + 2)) + 3| + 2) + 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = (-1(5(4(-4(2|(1cos(1\u03c0x - 3)) - 2| - 1) + 2) + 4)^2 + 1(4(-4(2|(1cos(1\u03c0x - 3)) - 2| - 1) + 2) + 4)))/(3(5(4(-4(2|(1cos(1\u03c0x - 3)) - 2| - 1) + 2) + 4)^2 + 1(4(-4(2|(1cos(1\u03c0x - 3)) - 2| - 1) + 2) + 4))) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "305", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = -3(-4(-2(1|(4(3sin(2\u03c0x) + 2)^2 - 5(3sin(2\u03c0x) + 2) + 4)| + 3) + 1)) + 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -3|(1cos(2\u03c0(4((-2(1(3x^2 - 5x - 3) + 5) - 1)/(3(1(3x^2 - 5x - 3) + 5) - 2))^2 - 2((-2(1(3x^2 - 5x - 3) + 5) - 1)/(3(1(3x^2 - 5x - 3) + 5) - 2)) + 5) - 3)) + 3| - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -2(-3|((-3((2(1|(3sin(2\u03c0x + 2) + 2) + 2| - 1))/(-1(1|(3sin(2\u03c0x + 2) + 2) + 2| - 1) - 1)) - 3)/(-2((2(1|(3sin(2\u03c0x + 2) + 2) + 2| - 1))/(-1(1|(3sin(2\u03c0x + 2) + 2) + 2| - 1) - 1)) - 1)) + 1| - 3) - 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "78", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = 1sin(3\u03c0(-1((-3(-2|(-2|((-1x)/(3x - 2)) + 1| - 2)| - 1) - 3)/(-1(-2|(-2|((-1x)/(3x - 2)) + 1| - 2)| - 1)))^2 + 3((-3(-2|(-2|((-1x)/(3x - 2)) + 1| - 2)| - 1) - 3)/(-1(-2|(-2|((-1x)/(3x - 2)) + 1| - 2)| - 1))) + 1)) + 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -4(-3cos(2\u03c0(-5(-5(1((-3x + 1)/(2x + 3)) - 5)^2 - 1(1((-3x + 1)/(2x + 3)) - 5) + 4) - 3) - 1) - 1)^2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "178", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = (2(-3|(-4(-3(1(5x + 4)^2)^2 - 2(1(5x + 4)^2) + 4)^2 + 2(-3(1(5x + 4)^2)^2 - 2(1(5x + 4)^2) + 4) + 5) - 3| - 2) - 2)/(-1(-3|(-4(-3(1(5x + 4)^2)^2 - 2(1(5x + 4)^2) + 4)^2 + 2(-3(1(5x + 4)^2)^2 - 2(1(5x + 4)^2) + 4) + 5) - 3| - 2) - 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "23", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 1|(-2(-4((2(4(3sin(2\u03c0x + 2) - 2)^2 - 3(3sin(2\u03c0x + 2) - 2) + 2) + 3)/(2(4(3sin(2\u03c0x + 2) - 2)^2 - 3(3sin(2\u03c0x + 2) - 2) + 2) + 2))^2 - 1((2(4(3sin(2\u03c0x + 2) - 2)^2 - 3(3sin(2\u03c0x + 2) - 2) + 2) + 3)/(2(4(3sin(2\u03c0x + 2) - 2)^2 - 3(3sin(2\u03c0x + 2) - 2) + 2) + 2)) - 4) - 1) + 2| + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 3|(2cos(1\u03c0(-2|(-1(4(1x - 3)^2 + 5(1x - 3) - 5)^2 + 4(4(1x - 3)^2 + 5(1x - 3) - 5) - 3) + 3| - 3) + 3) + 3) + 3| + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "107", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 5(-3cos(1\u03c0(-4(5(-1(-2x^2 + 3x - 1) + 4) + 3) - 3) - 3) - 3) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "230", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 2|(2(1(-2((-2(3x + 3) - 2)/(-3(3x + 3)))^2 - 4((-2(3x + 3) - 2)/(-3(3x + 3))) + 3)^2 - 1(-2((-2(3x + 3) - 2)/(-3(3x + 3)))^2 - 4((-2(3x + 3) - 2)/(-3(3x + 3))) + 3) - 4)^2 + 1(1(-2((-2(3x + 3) - 2)/(-3(3x + 3)))^2 - 4((-2(3x + 3) - 2)/(-3(3x + 3))) + 3)^2 - 1(-2((-2(3x + 3) - 2)/(-3(3x + 3)))^2 - 4((-2(3x + 3) - 2)/(-3(3x + 3))) + 3) - 4) - 4) - 2| + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -1|(-4(3(5(3|(-1cos(3\u03c0x + 1) - 1) + 2| + 3) + 1)^2 + 1(5(3|(-1cos(3\u03c0x + 1) - 1) + 2| + 3) + 1) + 3)^2 - 4(3(5(3|(-1cos(3\u03c0x + 1) - 1) + 2| + 3) + 1)^2 + 1(5(3|(-1cos(3\u03c0x + 1) - 1) + 2| + 3) + 1) + 3) - 4) - 3| - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "53", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 2(2((3(5(1(-2|x - 3| - 1) + 4)^2 + 5(1(-2|x - 3| - 1) + 4) - 5) + 2)/(-1(5(1(-2|x - 3| - 1) + 4)^2 + 5(1(-2|x - 3| - 1) + 4) - 5) + 3)) + 3)^2 + 4(2((3(5(1(-2|x - 3| - 1) + 4)^2 + 5(1(-2|x - 3| - 1) + 4) - 5) + 2)/(-1(5(1(-2|x - 3| - 1) + 4)^2 + 5(1(-2|x - 3| - 1) + 4) - 5) + 3)) + 3) - 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -5(-2(1((2(-1cos(2\u03c0(-2|x - 2| + 1)) + 2) - 3)/(-3(-1cos(2\u03c0(-2|x - 2| + 1)) + 2) - 2)) - 3)^2 - 2(1((2(-1cos(2\u03c0(-2|x - 2| + 1)) + 2) - 3)/(-3(-1cos(2\u03c0(-2|x - 2| + 1)) + 2) - 2)) - 3) - 5)^2 + 3(-2(1((2(-1cos(2\u03c0(-2|x - 2| + 1)) + 2) - 3)/(-3(-1cos(2\u03c0(-2|x - 2| + 1)) + 2) - 2)) - 3)^2 - 2(1((2(-1cos(2\u03c0(-2|x - 2| + 1)) + 2) - 3)/(-3(-1cos(2\u03c0(-2|x - 2| + 1)) + 2) - 2)) - 3) - 5) - 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 2|(2(3|((-1(2sin(3\u03c0(5x - 1) - 2) + 1) + 3)/(3(2sin(3\u03c0(5x - 1) - 2) + 1) - 2)) + 3| - 3) + 5) - 1| + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "402", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -4(4(5(-2cos(2\u03c0(-1(-1|x - 2| - 3)^2 + 2(-1|x - 2| - 3) + 1) + 2) + 3) - 2)^2 - 5) - 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "672", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = (-1((-3(-1|(-2cos(1\u03c0(3(2x + 3)^2 + 3(2x + 3) - 3) - 3)) - 1| + 1) - 2)/(-3(-1|(-2cos(1\u03c0(3(2x + 3)^2 + 3(2x + 3) - 3) - 3)) - 1| + 1) - 1)) + 3)/(1((-3(-1|(-2cos(1\u03c0(3(2x + 3)^2 + 3(2x + 3) - 3) - 3)) - 1| + 1) - 2)/(-3(-1|(-2cos(1\u03c0(3(2x + 3)^2 + 3(2x + 3) - 3) - 3)) - 1| + 1) - 1)) + 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "176", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 3|(-2|(2|((-1(2sin(1\u03c0(-5x^2 - 1x)) + 3) - 1)/(3(2sin(1\u03c0(-5x^2 - 1x)) + 3) + 3)) + 3| - 3) - 1| + 1) + 1| + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "68", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -3|(5(2(4(1sin(3\u03c0(-4x^2 - 2x + 4)) + 1) - 3) - 4)^2 + 1) - 3| + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "327", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = (-1(-2(-4(1(3|(5x + 3) - 1| + 1)^2 + 3(3|(5x + 3) - 1| + 1) + 5)^2 + 3(1(3|(5x + 3) - 1| + 1)^2 + 3(3|(5x + 3) - 1| + 1) + 5) - 1)^2 + 4(-4(1(3|(5x + 3) - 1| + 1)^2 + 3(3|(5x + 3) - 1| + 1) + 5)^2 + 3(1(3|(5x + 3) - 1| + 1)^2 + 3(3|(5x + 3) - 1| + 1) + 5) - 1) + 2) - 3)/(2(-2(-4(1(3|(5x + 3) - 1| + 1)^2 + 3(3|(5x + 3) - 1| + 1) + 5)^2 + 3(1(3|(5x + 3) - 1| + 1)^2 + 3(3|(5x + 3) - 1| + 1) + 5) - 1)^2 + 4(-4(1(3|(5x + 3) - 1| + 1)^2 + 3(3|(5x + 3) - 1| + 1) + 5)^2 + 3(1(3|(5x + 3) - 1| + 1)^2 + 3(3|(5x + 3) - 1| + 1) + 5) - 1) + 2) + 1) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 4(-5(-1((2(5(3cos(2\u03c0x - 1)) + 5) - 1)/(3(5(3cos(2\u03c0x - 1)) + 5) + 3))^2 - 1((2(5(3cos(2\u03c0x - 1)) + 5) - 1)/(3(5(3cos(2\u03c0x - 1)) + 5) + 3)) - 4)^2 + 2(-1((2(5(3cos(2\u03c0x - 1)) + 5) - 1)/(3(5(3cos(2\u03c0x - 1)) + 5) + 3))^2 - 1((2(5(3cos(2\u03c0x - 1)) + 5) - 1)/(3(5(3cos(2\u03c0x - 1)) + 5) + 3)) - 4) + 1) - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "45", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = (-3((-3(-5(-2((-2(-1cos(3\u03c0x) - 1))/(1(-1cos(3\u03c0x) - 1) + 3))^2 - 1((-2(-1cos(3\u03c0x) - 1))/(1(-1cos(3\u03c0x) - 1) + 3)) + 5)^2 + 2(-2((-2(-1cos(3\u03c0x) - 1))/(1(-1cos(3\u03c0x) - 1) + 3))^2 - 1((-2(-1cos(3\u03c0x) - 1))/(1(-1cos(3\u03c0x) - 1) + 3)) + 5) - 2))/(2(-5(-2((-2(-1cos(3\u03c0x) - 1))/(1(-1cos(3\u03c0x) - 1) + 3))^2 - 1((-2(-1cos(3\u03c0x) - 1))/(1(-1cos(3\u03c0x) - 1) + 3)) + 5)^2 + 2(-2((-2(-1cos(3\u03c0x) - 1))/(1(-1cos(3\u03c0x) - 1) + 3))^2 - 1((-2(-1cos(3\u03c0x) - 1))/(1(-1cos(3\u03c0x) - 1) + 3)) + 5) - 2) + 2)) + 3)/(2((-3(-5(-2((-2(-1cos(3\u03c0x) - 1))/(1(-1cos(3\u03c0x) - 1) + 3))^2 - 1((-2(-1cos(3\u03c0x) - 1))/(1(-1cos(3\u03c0x) - 1) + 3)) + 5)^2 + 2(-2((-2(-1cos(3\u03c0x) - 1))/(1(-1cos(3\u03c0x) - 1) + 3))^2 - 1((-2(-1cos(3\u03c0x) - 1))/(1(-1cos(3\u03c0x) - 1) + 3)) + 5) - 2))/(2(-5(-2((-2(-1cos(3\u03c0x) - 1))/(1(-1cos(3\u03c0x) - 1) + 3))^2 - 1((-2(-1cos(3\u03c0x) - 1))/(1(-1cos(3\u03c0x) - 1) + 3)) + 5)^2 + 2(-2((-2(-1cos(3\u03c0x) - 1))/(1(-1cos(3\u03c0x) - 1) + 3))^2 - 1((-2(-1cos(3\u03c0x) - 1))/(1(-1cos(3\u03c0x) - 1) + 3)) + 5) - 2) + 2)) + 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "56", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 1(-1cos(2\u03c0(5(-2(-3((-3x - 2)/(-2x + 3))^2 + 3((-3x - 2)/(-2x + 3)) + 5) + 5) - 5) - 1) - 1) + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "135", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 2e^(-1((3(2((-1((-2(1x - 5))/(-2(1x - 5) + 3)))/(-3((-2(1x - 5))/(-2(1x - 5) + 3)))) + 2) + 1)/(1(2((-1((-2(1x - 5))/(-2(1x - 5) + 3)))/(-3((-2(1x - 5))/(-2(1x - 5) + 3)))) + 2) + 3))) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "204", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -3(1(3|(2|(-3(-5x^2 - 5x + 3) - 2) - 2| + 2) - 3| - 2)^2 + 4(3|(2|(-3(-5x^2 - 5x + 3) - 2) - 2| + 2) - 3| - 2) - 5)^2 + 5(1(3|(2|(-3(-5x^2 - 5x + 3) - 2) - 2| + 2) - 3| - 2)^2 + 4(3|(2|(-3(-5x^2 - 5x + 3) - 2) - 2| + 2) - 3| - 2) - 5) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -4(1|(2|(-2cos(3\u03c0(-4(1x - 3)^2 + 3(1x - 3) + 5) - 2) + 3) - 3| - 2) - 2| + 2)^2 + 4(1|(2|(-2cos(3\u03c0(-4(1x - 3)^2 + 3(1x - 3) + 5) - 2) + 3) - 3| - 2) - 2| + 2) - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "474", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = (1(2|(-2|(1|(2(-1x + 2) + 3) + 1| - 3) - 3| + 2) - 1| - 1))/(2(2|(-2|(1|(2(-1x + 2) + 3) + 1| - 3) - 3| + 2) - 1| - 1) + 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -4(1((2(1sin(1\u03c0((-3(-2|x| + 1) + 3)/(1(-2|x| + 1) - 2))) + 2) - 3)/(2(1sin(1\u03c0((-3(-2|x| + 1) + 3)/(1(-2|x| + 1) - 2))) + 2) + 2)) - 1) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -1(4(4(3|((-1(-2sin(2\u03c0x + 2) + 2) - 3)/(3(-2sin(2\u03c0x + 2) + 2))) + 3| - 3)^2 + 4(3|((-1(-2sin(2\u03c0x + 2) + 2) - 3)/(3(-2sin(2\u03c0x + 2) + 2))) + 3| - 3) - 4)^2 + 3(4(3|((-1(-2sin(2\u03c0x + 2) + 2) - 3)/(3(-2sin(2\u03c0x + 2) + 2))) + 3| - 3)^2 + 4(3|((-1(-2sin(2\u03c0x + 2) + 2) - 3)/(3(-2sin(2\u03c0x + 2) + 2))) + 3| - 3) - 4) + 5)^2 + 3(4(4(3|((-1(-2sin(2\u03c0x + 2) + 2) - 3)/(3(-2sin(2\u03c0x + 2) + 2))) + 3| - 3)^2 + 4(3|((-1(-2sin(2\u03c0x + 2) + 2) - 3)/(3(-2sin(2\u03c0x + 2) + 2))) + 3| - 3) - 4)^2 + 3(4(3|((-1(-2sin(2\u03c0x + 2) + 2) - 3)/(3(-2sin(2\u03c0x + 2) + 2))) + 3| - 3)^2 + 4(3|((-1(-2sin(2\u03c0x + 2) + 2) - 3)/(3(-2sin(2\u03c0x + 2) + 2))) + 3| - 3) - 4) + 5) - 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -1|(3|(2(-3sin(3\u03c0(-3(5x + 4)^2 - 5(5x + 4) - 4) - 2) + 1)^2 + 4) - 1|) - 2| in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "44", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = (2(4(2(1|(-2cos(1\u03c0(5x^2 - 4)) + 3) - 3| - 2)^2 + 1(1|(-2cos(1\u03c0(5x^2 - 4)) + 3) - 3| - 2) + 1)^2 + 5(2(1|(-2cos(1\u03c0(5x^2 - 4)) + 3) - 3| - 2)^2 + 1(1|(-2cos(1\u03c0(5x^2 - 4)) + 3) - 3| - 2) + 1) + 4) + 1)/(-3(4(2(1|(-2cos(1\u03c0(5x^2 - 4)) + 3) - 3| - 2)^2 + 1(1|(-2cos(1\u03c0(5x^2 - 4)) + 3) - 3| - 2) + 1)^2 + 5(2(1|(-2cos(1\u03c0(5x^2 - 4)) + 3) - 3| - 2)^2 + 1(1|(-2cos(1\u03c0(5x^2 - 4)) + 3) - 3| - 2) + 1) + 4) + 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "315", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = (3(-2|(3(2sin(2\u03c0(2|((-3x + 3)/(2x)) - 2| - 2) + 2) + 3)^2 - 5(2sin(2\u03c0(2|((-3x + 3)/(2x)) - 2| - 2) + 2) + 3) - 5) + 2| + 2))/(-1(-2|(3(2sin(2\u03c0(2|((-3x + 3)/(2x)) - 2| - 2) + 2) + 3)^2 - 5(2sin(2\u03c0(2|((-3x + 3)/(2x)) - 2| - 2) + 2) + 3) - 5) + 2| + 2) - 2) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 3(-2|((-1((1(-2|(-3x + 4)| - 3) + 2)/(-1(-2|(-3x + 4)| - 3) - 3)))/(-3((1(-2|(-3x + 4)| - 3) + 2)/(-1(-2|(-3x + 4)| - 3) - 3))))| - 1)^2 - 5(-2|((-1((1(-2|(-3x + 4)| - 3) + 2)/(-1(-2|(-3x + 4)| - 3) - 3)))/(-3((1(-2|(-3x + 4)| - 3) + 2)/(-1(-2|(-3x + 4)| - 3) - 3))))| - 1) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "103", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 2|(-3|((-3(2(3(1cos(2\u03c0x - 1) - 1) - 1) - 1) - 2)/(-1(2(3(1cos(2\u03c0x - 1) - 1) - 1) - 1) - 3)) - 1| - 2) - 1| + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -1((-1((-3(-2e^(2(-2(-1x + 4)^2 - 1(-1x + 4) + 1)) + 1) - 3)/(-2(-2e^(2(-2(-1x + 4)^2 - 1(-1x + 4) + 1)) + 1) + 3)) + 3)/(1((-3(-2e^(2(-2(-1x + 4)^2 - 1(-1x + 4) + 1)) + 1) - 3)/(-2(-2e^(2(-2(-1x + 4)^2 - 1(-1x + 4) + 1)) + 1) + 3))))^2 + 2((-1((-3(-2e^(2(-2(-1x + 4)^2 - 1(-1x + 4) + 1)) + 1) - 3)/(-2(-2e^(2(-2(-1x + 4)^2 - 1(-1x + 4) + 1)) + 1) + 3)) + 3)/(1((-3(-2e^(2(-2(-1x + 4)^2 - 1(-1x + 4) + 1)) + 1) - 3)/(-2(-2e^(2(-2(-1x + 4)^2 - 1(-1x + 4) + 1)) + 1) + 3)))) + 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = (-2(3(-5((-3(3cos(1\u03c0(3|x + 3| + 3) - 2) + 2) - 2)/(1(3cos(1\u03c0(3|x + 3| + 3) - 2) + 2) + 2)) + 2)^2 - 3(-5((-3(3cos(1\u03c0(3|x + 3| + 3) - 2) + 2) - 2)/(1(3cos(1\u03c0(3|x + 3| + 3) - 2) + 2) + 2)) + 2) + 3))/(-2(3(-5((-3(3cos(1\u03c0(3|x + 3| + 3) - 2) + 2) - 2)/(1(3cos(1\u03c0(3|x + 3| + 3) - 2) + 2) + 2)) + 2)^2 - 3(-5((-3(3cos(1\u03c0(3|x + 3| + 3) - 2) + 2) - 2)/(1(3cos(1\u03c0(3|x + 3| + 3) - 2) + 2) + 2)) + 2) + 3) - 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "104", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = -2sin(2\u03c0(1|(1((2(-3(-3|x - 3| + 2) - 2) - 2)/(-3(-3(-3|x - 3| + 2) - 2) - 2)) + 1)| - 1) + 3) + 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -3|((-1(-3|(-2(2|(-2|x - 1|)| - 3) - 3) - 1|) + 3)/(-1(-3|(-2(2|(-2|x - 1|)| - 3) - 3) - 1|))) - 2| - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -3|(2|(2(3|(-2sin(3\u03c0(1x - 3) - 2) + 3) - 3| + 3)^2 + 2(3|(-2sin(3\u03c0(1x - 3) - 2) + 3) - 3| + 3) + 5) - 3| - 3) + 1| - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "112", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = (-3((2(2(-3(5(-3x^2 + 2x - 2)^2 + 5(-3x^2 + 2x - 2) - 3)^2 + 3(5(-3x^2 + 2x - 2)^2 + 5(-3x^2 + 2x - 2) - 3))^2 - 5(-3(5(-3x^2 + 2x - 2)^2 + 5(-3x^2 + 2x - 2) - 3)^2 + 3(5(-3x^2 + 2x - 2)^2 + 5(-3x^2 + 2x - 2) - 3)) - 1) - 2)/(3(2(-3(5(-3x^2 + 2x - 2)^2 + 5(-3x^2 + 2x - 2) - 3)^2 + 3(5(-3x^2 + 2x - 2)^2 + 5(-3x^2 + 2x - 2) - 3))^2 - 5(-3(5(-3x^2 + 2x - 2)^2 + 5(-3x^2 + 2x - 2) - 3)^2 + 3(5(-3x^2 + 2x - 2)^2 + 5(-3x^2 + 2x - 2) - 3)) - 1) - 1)) + 3)/(2((2(2(-3(5(-3x^2 + 2x - 2)^2 + 5(-3x^2 + 2x - 2) - 3)^2 + 3(5(-3x^2 + 2x - 2)^2 + 5(-3x^2 + 2x - 2) - 3))^2 - 5(-3(5(-3x^2 + 2x - 2)^2 + 5(-3x^2 + 2x - 2) - 3)^2 + 3(5(-3x^2 + 2x - 2)^2 + 5(-3x^2 + 2x - 2) - 3)) - 1) - 2)/(3(2(-3(5(-3x^2 + 2x - 2)^2 + 5(-3x^2 + 2x - 2) - 3)^2 + 3(5(-3x^2 + 2x - 2)^2 + 5(-3x^2 + 2x - 2) - 3))^2 - 5(-3(5(-3x^2 + 2x - 2)^2 + 5(-3x^2 + 2x - 2) - 3)^2 + 3(5(-3x^2 + 2x - 2)^2 + 5(-3x^2 + 2x - 2) - 3)) - 1) - 1)) - 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "83", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = 1(1(2(-1|(-2cos(3\u03c0(1x^2 + 2x - 5) + 2)) - 1| + 3)^2 - 4(-1|(-2cos(3\u03c0(1x^2 + 2x - 5) + 2)) - 1| + 3))^2 + 4)^2 + 5(1(2(-1|(-2cos(3\u03c0(1x^2 + 2x - 5) + 2)) - 1| + 3)^2 - 4(-1|(-2cos(3\u03c0(1x^2 + 2x - 5) + 2)) - 1| + 3))^2 + 4) + 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "367", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 4(5((3(2sin(1\u03c0(-1|((3x - 2)/(2x - 1)) + 3| + 2) + 1) - 2))/(-2(2sin(1\u03c0(-1|((3x - 2)/(2x - 1)) + 3| + 2) + 1) - 2) - 1)) - 5)^2 - 1(5((3(2sin(1\u03c0(-1|((3x - 2)/(2x - 1)) + 3| + 2) + 1) - 2))/(-2(2sin(1\u03c0(-1|((3x - 2)/(2x - 1)) + 3| + 2) + 1) - 2) - 1)) - 5) - 4 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = (-3(2|((-2(-3cos(1\u03c0((3(2x^2 - 2x - 1) - 2)/(-3(2x^2 - 2x - 1) + 4)) - 3) + 3) + 1)/(-3(-3cos(1\u03c0((3(2x^2 - 2x - 1) - 2)/(-3(2x^2 - 2x - 1) + 4)) - 3) + 3) + 2)) + 2| + 1) - 2)/(-3(2|((-2(-3cos(1\u03c0((3(2x^2 - 2x - 1) - 2)/(-3(2x^2 - 2x - 1) + 4)) - 3) + 3) + 1)/(-3(-3cos(1\u03c0((3(2x^2 - 2x - 1) - 2)/(-3(2x^2 - 2x - 1) + 4)) - 3) + 3) + 2)) + 2| + 1) - 3) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -3|(-2(-3|(1((1((-3x + 3)/(2x)) + 3)/(2((-3x + 3)/(2x)) - 1))^2 - 3((1((-3x + 3)/(2x)) + 3)/(2((-3x + 3)/(2x)) - 1)) - 2) - 3|)^2 - 4(-3|(1((1((-3x + 3)/(2x)) + 3)/(2((-3x + 3)/(2x)) - 1))^2 - 3((1((-3x + 3)/(2x)) + 3)/(2((-3x + 3)/(2x)) - 1)) - 2) - 3|) + 1) - 3| - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 1(3sin(2\u03c0(-3|(1(4(-5x - 2) + 4) - 2)|) - 3) - 3) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "203", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 4(-5(-1|(2(2(3|x + 2| - 2)^2 - 5(3|x + 2| - 2) - 5)^2 - 4(2(3|x + 2| - 2)^2 - 5(3|x + 2| - 2) - 5) + 5) - 1| + 3) - 5) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 3(2|((1(3e^(1(3|(-1x - 2) + 3| + 3)) - 1) + 3)/(1(3e^(1(3|(-1x - 2) + 3| + 3)) - 1))) - 1| + 2) + 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = (3(-4(-1sin(2\u03c0(1|(-1(-2|x + 2| + 1)^2 + 5(-2|x + 2| + 1)) + 1| + 2) - 1) + 3)^2 - 2(-1sin(2\u03c0(1|(-1(-2|x + 2| + 1)^2 + 5(-2|x + 2| + 1)) + 1| + 2) - 1) + 3) + 4) - 3)/(1(-4(-1sin(2\u03c0(1|(-1(-2|x + 2| + 1)^2 + 5(-2|x + 2| + 1)) + 1| + 2) - 1) + 3)^2 - 2(-1sin(2\u03c0(1|(-1(-2|x + 2| + 1)^2 + 5(-2|x + 2| + 1)) + 1| + 2) - 1) + 3) + 4)) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "513", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -3|(-4(-1|(2(1|(-1cos(3\u03c0x - 1)) - 1|)^2 - 1(1|(-1cos(3\u03c0x - 1)) - 1|) - 4)| + 3) - 3)| - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "239", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 1(-1|(2|(1|((-1(-5x^2 - 4x - 1) + 1)/(-1(-5x^2 - 4x - 1) - 3)) + 3| - 3) - 3| - 1) - 3| - 3) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -4(3((3(-2((2(1cos(1\u03c0x - 2) - 1) - 3)/(3(1cos(1\u03c0x - 2) - 1)))^2 + 3((2(1cos(1\u03c0x - 2) - 1) - 3)/(3(1cos(1\u03c0x - 2) - 1))) - 2) - 2)/(1(-2((2(1cos(1\u03c0x - 2) - 1) - 3)/(3(1cos(1\u03c0x - 2) - 1)))^2 + 3((2(1cos(1\u03c0x - 2) - 1) - 3)/(3(1cos(1\u03c0x - 2) - 1))) - 2) + 2))^2 + 4((3(-2((2(1cos(1\u03c0x - 2) - 1) - 3)/(3(1cos(1\u03c0x - 2) - 1)))^2 + 3((2(1cos(1\u03c0x - 2) - 1) - 3)/(3(1cos(1\u03c0x - 2) - 1))) - 2) - 2)/(1(-2((2(1cos(1\u03c0x - 2) - 1) - 3)/(3(1cos(1\u03c0x - 2) - 1)))^2 + 3((2(1cos(1\u03c0x - 2) - 1) - 3)/(3(1cos(1\u03c0x - 2) - 1))) - 2) + 2)) + 2) + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 4(-3sin(2\u03c0(1(5(-1(-3x^2 + 5x + 4) + 5)^2 + 2)^2 - 4(5(-1(-3x^2 + 5x + 4) + 5)^2 + 2) - 2) + 3) + 3) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "23", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = (3((-3(3sin(3\u03c0(3(-2|(-2|x - 3| - 2) - 1| + 2)^2 + 1(-2|(-2|x - 3| - 2) - 1| + 2) + 1) - 2) - 2))/(3(3sin(3\u03c0(3(-2|(-2|x - 3| - 2) - 1| + 2)^2 + 1(-2|(-2|x - 3| - 2) - 1| + 2) + 1) - 2) - 2) + 3)) + 3)/(2((-3(3sin(3\u03c0(3(-2|(-2|x - 3| - 2) - 1| + 2)^2 + 1(-2|(-2|x - 3| - 2) - 1| + 2) + 1) - 2) - 2))/(3(3sin(3\u03c0(3(-2|(-2|x - 3| - 2) - 1| + 2)^2 + 1(-2|(-2|x - 3| - 2) - 1| + 2) + 1) - 2) - 2) + 3)) - 3) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "168", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -1(-1((-1(4(1(1cos(3\u03c0x) + 3)^2 + 5(1cos(3\u03c0x) + 3) - 3) + 1) - 3)/(3(4(1(1cos(3\u03c0x) + 3)^2 + 5(1cos(3\u03c0x) + 3) - 3) + 1))) + 5)^2 + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -2(-1(2(4(1|(-3cos(3\u03c0x + 1) - 2) + 3|) - 1)^2 + 2(4(1|(-3cos(3\u03c0x + 1) - 2) + 3|) - 1) + 4) - 5) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 1|(-2(1(-1(3sin(3\u03c0(-3|x + 2| - 2)) + 2)^2 - 3) - 2) - 5) - 2| + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "361", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -2|((1(2(3|(-2cos(1\u03c0(-3x^2 + 4) - 3) - 2) + 2| + 2)^2 - 5(3|(-2cos(1\u03c0(-3x^2 + 4) - 3) - 2) + 2| + 2) - 5) + 2)/(1(2(3|(-2cos(1\u03c0(-3x^2 + 4) - 3) - 2) + 2| + 2)^2 - 5(3|(-2cos(1\u03c0(-3x^2 + 4) - 3) - 2) + 2| + 2) - 5))) - 2| - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "326", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -4(-1e^(1(-2(3(-3|(-2x^2 - 2x + 5) - 2| + 2) + 3)^2 + 3(3(-3|(-2x^2 - 2x + 5) - 2| + 2) + 3) - 1)) + 2)^2 - 3(-1e^(1(-2(3(-3|(-2x^2 - 2x + 5) - 2| + 2) + 3)^2 + 3(3(-3|(-2x^2 - 2x + 5) - 2| + 2) + 3) - 1)) + 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = 1(1(-5(1cos(3\u03c0(2((3x + 2)/(2x - 3)) + 1)) + 1)^2 + 5(1cos(3\u03c0(2((3x + 2)/(2x - 3)) + 1)) + 1) + 5) - 1) - 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "57", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -1(4(1|((-1(2sin(1\u03c0((1x - 3)/(-1x - 2)) + 2) + 3) + 2)/(1(2sin(1\u03c0((1x - 3)/(-1x - 2)) + 2) + 3))) - 1| - 1) - 2) - 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = (-1(-3((2(-2sin(2\u03c0(-2|(5x + 1) - 2| + 2) + 2)) + 3)/(-1(-2sin(2\u03c0(-2|(5x + 1) - 2| + 2) + 2)) + 2))^2 - 3((2(-2sin(2\u03c0(-2|(5x + 1) - 2| + 2) + 2)) + 3)/(-1(-2sin(2\u03c0(-2|(5x + 1) - 2| + 2) + 2)) + 2)) - 2) + 1)/(1(-3((2(-2sin(2\u03c0(-2|(5x + 1) - 2| + 2) + 2)) + 3)/(-1(-2sin(2\u03c0(-2|(5x + 1) - 2| + 2) + 2)) + 2))^2 - 3((2(-2sin(2\u03c0(-2|(5x + 1) - 2| + 2) + 2)) + 3)/(-1(-2sin(2\u03c0(-2|(5x + 1) - 2| + 2) + 2)) + 2)) - 2) + 1) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "399", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = (3(2(2cos(3\u03c0(3(-3|(-5x + 4) + 1| + 1)^2 + 1(-3|(-5x + 4) + 1| + 1) + 1) - 3) + 2) - 2) + 2)/(-2(2(2cos(3\u03c0(3(-3|(-5x + 4) + 1| + 1)^2 + 1(-3|(-5x + 4) + 1| + 1) + 1) - 3) + 2) - 2)) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "26", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = (3(-1|((-1(3(4((1x + 2)/(2x - 3))^2 + 3((1x + 2)/(2x - 3)) + 3)^2 - 2(4((1x + 2)/(2x - 3))^2 + 3((1x + 2)/(2x - 3)) + 3) + 2) - 2)/(3(3(4((1x + 2)/(2x - 3))^2 + 3((1x + 2)/(2x - 3)) + 3)^2 - 2(4((1x + 2)/(2x - 3))^2 + 3((1x + 2)/(2x - 3)) + 3) + 2) - 1)) + 3| + 1))/(1(-1|((-1(3(4((1x + 2)/(2x - 3))^2 + 3((1x + 2)/(2x - 3)) + 3)^2 - 2(4((1x + 2)/(2x - 3))^2 + 3((1x + 2)/(2x - 3)) + 3) + 2) - 2)/(3(3(4((1x + 2)/(2x - 3))^2 + 3((1x + 2)/(2x - 3)) + 3)^2 - 2(4((1x + 2)/(2x - 3))^2 + 3((1x + 2)/(2x - 3)) + 3) + 2) - 1)) + 3| + 1)) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "239", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -2((-2(1cos(3\u03c0(1|((2(-5x^2 + 3x + 4) + 1)/(3(-5x^2 + 3x + 4) + 2))| + 3) - 2) - 1) - 1)/(3(1cos(3\u03c0(1|((2(-5x^2 + 3x + 4) + 1)/(3(-5x^2 + 3x + 4) + 2))| + 3) - 2) - 1) + 3))^2 - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 4(3|(-3|(-5(3(1x^2 - 5x - 2)^2 + 2(1x^2 - 5x - 2) - 4)^2 + 3(3(1x^2 - 5x - 2)^2 + 2(1x^2 - 5x - 2) - 4) + 3) + 2| - 1) + 1|)^2 - 1(3|(-3|(-5(3(1x^2 - 5x - 2)^2 + 2(1x^2 - 5x - 2) - 4)^2 + 3(3(1x^2 - 5x - 2)^2 + 2(1x^2 - 5x - 2) - 4) + 3) + 2| - 1) + 1|) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 5((1(-1cos(3\u03c0(-4(2|(-1x + 1) - 2| + 3) + 4) + 1) + 3) - 3)/(-2(-1cos(3\u03c0(-4(2|(-1x + 1) - 2| + 3) + 4) + 1) + 3))) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "481", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -3(-1|((-2(-2e^(-1(-3|(-4x^2 + 4x + 1) + 2| + 1)) + 3) - 3)/(3(-2e^(-1(-3|(-4x^2 + 4x + 1) + 2| + 1)) + 3) - 2)) - 1| - 1)^2 - 3(-1|((-2(-2e^(-1(-3|(-4x^2 + 4x + 1) + 2| + 1)) + 3) - 3)/(3(-2e^(-1(-3|(-4x^2 + 4x + 1) + 2| + 1)) + 3) - 2)) - 1| - 1) - 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 5((1((-1(-1(1(3|x - 1| - 3)^2 - 3(3|x - 1| - 3) + 2)^2 + 1) + 2)/(1(-1(1(3|x - 1| - 3)^2 - 3(3|x - 1| - 3) + 2)^2 + 1) + 2)) + 3)/(-1((-1(-1(1(3|x - 1| - 3)^2 - 3(3|x - 1| - 3) + 2)^2 + 1) + 2)/(1(-1(1(3|x - 1| - 3)^2 - 3(3|x - 1| - 3) + 2)^2 + 1) + 2)) + 2))^2 - 5((1((-1(-1(1(3|x - 1| - 3)^2 - 3(3|x - 1| - 3) + 2)^2 + 1) + 2)/(1(-1(1(3|x - 1| - 3)^2 - 3(3|x - 1| - 3) + 2)^2 + 1) + 2)) + 3)/(-1((-1(-1(1(3|x - 1| - 3)^2 - 3(3|x - 1| - 3) + 2)^2 + 1) + 2)/(1(-1(1(3|x - 1| - 3)^2 - 3(3|x - 1| - 3) + 2)^2 + 1) + 2)) + 2)) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -4(2((2(1(1cos(3\u03c0(3|x + 2| - 1) - 2) - 1)^2 + 3(1cos(3\u03c0(3|x + 2| - 1) - 2) - 1) + 4) + 3)/(2(1(1cos(3\u03c0(3|x + 2| - 1) - 2) - 1)^2 + 3(1cos(3\u03c0(3|x + 2| - 1) - 2) - 1) + 4)))^2 + 5((2(1(1cos(3\u03c0(3|x + 2| - 1) - 2) - 1)^2 + 3(1cos(3\u03c0(3|x + 2| - 1) - 2) - 1) + 4) + 3)/(2(1(1cos(3\u03c0(3|x + 2| - 1) - 2) - 1)^2 + 3(1cos(3\u03c0(3|x + 2| - 1) - 2) - 1) + 4))) - 5) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "180", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -1|(-2(-1(2cos(1\u03c0(-1|(-3|x + 1| + 3) + 2| - 3) - 1) - 2) - 3)^2 - 3) - 3| + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -1|(-3|(-4(-2e^(-1((-1(4x^2 + 4x - 2) + 2)/(-2(4x^2 + 4x - 2) - 2))) + 2)^2 - 5(-2e^(-1((-1(4x^2 + 4x - 2) + 2)/(-2(4x^2 + 4x - 2) - 2))) + 2) + 4) + 2| + 1) + 1| + 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -1sin(2\u03c0(-5(5(-4(5((-2x)/(1x + 1)) + 3)^2 + 3(5((-2x)/(1x + 1)) + 3) - 4) - 5)^2 + 5(5(-4(5((-2x)/(1x + 1)) + 3)^2 + 3(5((-2x)/(1x + 1)) + 3) - 4) - 5) + 4) - 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 3|(-1(-3|(-4(-3(1sin(1\u03c0x - 3) - 1)^2 + 1(1sin(1\u03c0x - 3) - 1) - 3)^2 + 5(-3(1sin(1\u03c0x - 3) - 1)^2 + 1(1sin(1\u03c0x - 3) - 1) - 3) + 5)| + 3)^2 - 4(-3|(-4(-3(1sin(1\u03c0x - 3) - 1)^2 + 1(1sin(1\u03c0x - 3) - 1) - 3)^2 + 5(-3(1sin(1\u03c0x - 3) - 1)^2 + 1(1sin(1\u03c0x - 3) - 1) - 3) + 5)| + 3) - 1) + 1| - 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -4(1sin(3\u03c0(-2|((-1(4(-2|x - 1| + 3)^2 + 1(-2|x - 1| + 3) - 1) + 2)/(1(4(-2|x - 1| + 3)^2 + 1(-2|x - 1| + 3) - 1))) + 2| - 3) + 3)) - 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "43", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = 1|(-1((2(-3sin(3\u03c0((-3(3|x - 1|) - 3)/(-3(3|x - 1|) + 4)) - 2) + 3) - 1)/(-2(-3sin(3\u03c0((-3(3|x - 1|) - 3)/(-3(3|x - 1|) + 4)) - 2) + 3) - 1))^2 + 4((2(-3sin(3\u03c0((-3(3|x - 1|) - 3)/(-3(3|x - 1|) + 4)) - 2) + 3) - 1)/(-2(-3sin(3\u03c0((-3(3|x - 1|) - 3)/(-3(3|x - 1|) + 4)) - 2) + 3) - 1)) + 4) - 2| + 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "64", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = (2(-5(3|(2|(2(2cos(2\u03c0x - 1) - 3)^2 - 5(2cos(2\u03c0x - 1) - 3) - 2)| + 3) + 1|) - 5))/(-1(-5(3|(2|(2(2cos(2\u03c0x - 1) - 3)^2 - 5(2cos(2\u03c0x - 1) - 3) - 2)| + 3) + 1|) - 5) - 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -1(-2(-1(1sin(2\u03c0(3|((3x + 3)/(1x)) - 1| - 2) - 2))^2 - 2(1sin(2\u03c0(3|((3x + 3)/(1x)) - 1| - 2) - 2)) + 4)^2 - 2(-1(1sin(2\u03c0(3|((3x + 3)/(1x)) - 1| - 2) - 2))^2 - 2(1sin(2\u03c0(3|((3x + 3)/(1x)) - 1| - 2) - 2)) + 4) - 5)^2 + 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "46", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -2(-4((-1(-2|(1|((1x - 2)/(-1x + 3))| - 3) - 3| + 3) - 3)/(1(-2|(1|((1x - 2)/(-1x + 3))| - 3) - 3| + 3) + 1))^2 + 4((-1(-2|(1|((1x - 2)/(-1x + 3))| - 3) - 3| + 3) - 3)/(1(-2|(1|((1x - 2)/(-1x + 3))| - 3) - 3| + 3) + 1))) + 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 3(1cos(2\u03c0(-4((-2(1(-2x^2 + 3x) + 4) - 2)/(2(1(-2x^2 + 3x) + 4) + 1))^2 - 2((-2(1(-2x^2 + 3x) + 4) - 2)/(2(1(-2x^2 + 3x) + 4) + 1)) + 1) - 1) + 2)^2 - 5(1cos(2\u03c0(-4((-2(1(-2x^2 + 3x) + 4) - 2)/(2(1(-2x^2 + 3x) + 4) + 1))^2 - 2((-2(1(-2x^2 + 3x) + 4) - 2)/(2(1(-2x^2 + 3x) + 4) + 1)) + 1) - 1) + 2) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = (2(1cos(1\u03c0(-3(-4(-1((-3x + 2)/(-1x - 2))^2 - 5((-3x + 2)/(-1x - 2))) - 5)^2 + 1(-4(-1((-3x + 2)/(-1x - 2))^2 - 5((-3x + 2)/(-1x - 2))) - 5)) + 3) + 1) - 2)/(-2(1cos(1\u03c0(-3(-4(-1((-3x + 2)/(-1x - 2))^2 - 5((-3x + 2)/(-1x - 2))) - 5)^2 + 1(-4(-1((-3x + 2)/(-1x - 2))^2 - 5((-3x + 2)/(-1x - 2))) - 5)) + 3) + 1) - 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "251", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = (3((-2(2(5((-1(1x^2 - 4x - 1) - 2)/(-1(1x^2 - 4x - 1)))^2 - 1)^2 + 3(5((-1(1x^2 - 4x - 1) - 2)/(-1(1x^2 - 4x - 1)))^2 - 1) + 4) + 3)/(-1(2(5((-1(1x^2 - 4x - 1) - 2)/(-1(1x^2 - 4x - 1)))^2 - 1)^2 + 3(5((-1(1x^2 - 4x - 1) - 2)/(-1(1x^2 - 4x - 1)))^2 - 1) + 4) - 3)) - 1)/(2((-2(2(5((-1(1x^2 - 4x - 1) - 2)/(-1(1x^2 - 4x - 1)))^2 - 1)^2 + 3(5((-1(1x^2 - 4x - 1) - 2)/(-1(1x^2 - 4x - 1)))^2 - 1) + 4) + 3)/(-1(2(5((-1(1x^2 - 4x - 1) - 2)/(-1(1x^2 - 4x - 1)))^2 - 1)^2 + 3(5((-1(1x^2 - 4x - 1) - 2)/(-1(1x^2 - 4x - 1)))^2 - 1) + 4) - 3)) + 3) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 2cos(2\u03c0((-2((2(-2|(1(3x + 2)^2 + 2(3x + 2) - 5) - 2| + 3) + 1)/(2(-2|(1(3x + 2)^2 + 2(3x + 2) - 5) - 2| + 3) - 3)) + 1)/(-2((2(-2|(1(3x + 2)^2 + 2(3x + 2) - 5) - 2| + 3) + 1)/(2(-2|(1(3x + 2)^2 + 2(3x + 2) - 5) - 2| + 3) - 3)) - 2)) - 3) + 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = (-3(3(2(2|((-1(1sin(3\u03c0x + 1) + 1) + 2)/(-3(1sin(3\u03c0x + 1) + 1) + 2)) + 2| - 2) + 1) + 2) - 1)/(2(3(2(2|((-1(1sin(3\u03c0x + 1) + 1) + 2)/(-3(1sin(3\u03c0x + 1) + 1) + 2)) + 2| - 2) + 1) + 2) + 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "180", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = -5(-1((-1(-1sin(3\u03c0(-3|(3|x| - 1)| - 3) + 2) + 2))/(1(-1sin(3\u03c0(-3|(3|x| - 1)| - 3) + 2) + 2) + 2))^2 + 3((-1(-1sin(3\u03c0(-3|(3|x| - 1)| - 3) + 2) + 2))/(1(-1sin(3\u03c0(-3|(3|x| - 1)| - 3) + 2) + 2) + 2)) - 2) - 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "269", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 2|((-3(1|(-1|((-1((2x + 2)/(-3x + 4)) - 1)/(1((2x + 2)/(-3x + 4)) - 2)) - 1| - 3) + 3| - 2) + 3)/(-1(1|(-1|((-1((2x + 2)/(-3x + 4)) - 1)/(1((2x + 2)/(-3x + 4)) - 2)) - 1| - 3) + 3| - 2) + 3)) - 3| have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -3(-2(1cos(2\u03c0(4(5(-3x - 2)^2 - 5(-3x - 2) - 3)^2 + 4(5(-3x - 2)^2 - 5(-3x - 2) - 3) + 5)) - 2)^2 - 5(1cos(2\u03c0(4(5(-3x - 2)^2 - 5(-3x - 2) - 3)^2 + 4(5(-3x - 2)^2 - 5(-3x - 2) - 3) + 5)) - 2) + 4)^2 - 2(-2(1cos(2\u03c0(4(5(-3x - 2)^2 - 5(-3x - 2) - 3)^2 + 4(5(-3x - 2)^2 - 5(-3x - 2) - 3) + 5)) - 2)^2 - 5(1cos(2\u03c0(4(5(-3x - 2)^2 - 5(-3x - 2) - 3)^2 + 4(5(-3x - 2)^2 - 5(-3x - 2) - 3) + 5)) - 2) + 4) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 1|((-2(3cos(3\u03c0(-1(3(-5x + 1)^2 - 3(-5x + 1) - 5)^2 + 3(3(-5x + 1)^2 - 3(-5x + 1) - 5) - 4) - 3) + 1) - 3)/(-1(3cos(3\u03c0(-1(3(-5x + 1)^2 - 3(-5x + 1) - 5)^2 + 3(3(-5x + 1)^2 - 3(-5x + 1) - 5) - 4) - 3) + 1) - 1)) + 1| + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -3(3|(3|(-2((-1(-1|x - 3| + 2) + 2)/(2(-1|x - 3| + 2) - 1)) + 3) + 3| - 1) + 3| + 1) + 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 2(2((-2((-2(2(3cos(2\u03c0x + 2) + 3) - 4) - 1)/(-1(2(3cos(2\u03c0x + 2) + 3) - 4) + 2)) - 1)/(-3((-2(2(3cos(2\u03c0x + 2) + 3) - 4) - 1)/(-1(2(3cos(2\u03c0x + 2) + 3) - 4) + 2)) - 2)) + 1)^2 - 1(2((-2((-2(2(3cos(2\u03c0x + 2) + 3) - 4) - 1)/(-1(2(3cos(2\u03c0x + 2) + 3) - 4) + 2)) - 1)/(-3((-2(2(3cos(2\u03c0x + 2) + 3) - 4) - 1)/(-1(2(3cos(2\u03c0x + 2) + 3) - 4) + 2)) - 2)) + 1) + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "24", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 4((-2(2((-2(3(3cos(1\u03c0x - 3))^2 + 5(3cos(1\u03c0x - 3)) - 2) - 1)/(3(3(3cos(1\u03c0x - 3))^2 + 5(3cos(1\u03c0x - 3)) - 2) + 2)) + 1) + 1)/(3(2((-2(3(3cos(1\u03c0x - 3))^2 + 5(3cos(1\u03c0x - 3)) - 2) - 1)/(3(3(3cos(1\u03c0x - 3))^2 + 5(3cos(1\u03c0x - 3)) - 2) + 2)) + 1) + 3)) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = 1|(2|(-1sin(1\u03c0(2(-1|(-4x^2 + 2x - 4) + 1| + 2) + 3) - 3) + 2) - 1|) + 2| - 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "264", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -3((-2(2cos(1\u03c0(2|((1(-1x^2 - 5x - 5) + 2)/(-2(-1x^2 - 5x - 5) + 3)) - 2| - 2) + 1)))/(1(2cos(1\u03c0(2|((1(-1x^2 - 5x - 5) + 2)/(-2(-1x^2 - 5x - 5) + 3)) - 2| - 2) + 1)) - 3))^2 - 5((-2(2cos(1\u03c0(2|((1(-1x^2 - 5x - 5) + 2)/(-2(-1x^2 - 5x - 5) + 3)) - 2| - 2) + 1)))/(1(2cos(1\u03c0(2|((1(-1x^2 - 5x - 5) + 2)/(-2(-1x^2 - 5x - 5) + 3)) - 2| - 2) + 1)) - 3)) + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = (3(3(2(-1(1(1sin(1\u03c0x + 2) + 3) - 1)^2 - 5(1(1sin(1\u03c0x + 2) + 3) - 1) - 1) + 5)^2 - 2(2(-1(1(1sin(1\u03c0x + 2) + 3) - 1)^2 - 5(1(1sin(1\u03c0x + 2) + 3) - 1) - 1) + 5) + 5) - 2)/(3(3(2(-1(1(1sin(1\u03c0x + 2) + 3) - 1)^2 - 5(1(1sin(1\u03c0x + 2) + 3) - 1) - 1) + 5)^2 - 2(2(-1(1(1sin(1\u03c0x + 2) + 3) - 1)^2 - 5(1(1sin(1\u03c0x + 2) + 3) - 1) - 1) + 5) + 5)) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = (-3(3(-3(-1|(2((2x + 2)/(1x)) - 1) - 1| + 1)^2 - 1(-1|(2((2x + 2)/(1x)) - 1) - 1| + 1) + 1)^2 + 2(-3(-1|(2((2x + 2)/(1x)) - 1) - 1| + 1)^2 - 1(-1|(2((2x + 2)/(1x)) - 1) - 1| + 1) + 1) + 5) - 1)/(-1(3(-3(-1|(2((2x + 2)/(1x)) - 1) - 1| + 1)^2 - 1(-1|(2((2x + 2)/(1x)) - 1) - 1| + 1) + 1)^2 + 2(-3(-1|(2((2x + 2)/(1x)) - 1) - 1| + 1)^2 - 1(-1|(2((2x + 2)/(1x)) - 1) - 1| + 1) + 1) + 5)) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = -1|((-2(-1|((2(-3|(-3sin(2\u03c0x + 2) + 2) + 2| + 1) - 1)/(2(-3|(-3sin(2\u03c0x + 2) + 2) + 2| + 1) + 1))| + 1) - 3)/(-1(-1|((2(-3|(-3sin(2\u03c0x + 2) + 2) + 2| + 1) - 1)/(2(-3|(-3sin(2\u03c0x + 2) + 2) + 2| + 1) + 1))| + 1) + 3)) + 1| + 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = -1(3sin(3\u03c0(-1(1|(-3(-3|x + 3| - 1) - 3) + 3| + 1)^2 + 2) + 3) + 3)^2 + 4(3sin(3\u03c0(-1(1|(-3(-3|x + 3| - 1) - 3) + 3| + 1)^2 + 2) + 3) + 3) + 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "124", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 2((3(3cos(1\u03c0(-2|(-3|(1x - 4) - 3| - 1) + 1| + 1) - 3) - 1) - 3)/(2(3cos(1\u03c0(-2|(-3|(1x - 4) - 3| - 1) + 1| + 1) - 3) - 1))) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "119", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -2cos(2\u03c0((-1(-2(-3|((3(2|x + 1| - 1) - 2)/(3(2|x + 1| - 1))) + 1|)^2 - 3(-3|((3(2|x + 1| - 1) - 2)/(3(2|x + 1| - 1))) + 1|) - 5) - 2)/(-3(-2(-3|((3(2|x + 1| - 1) - 2)/(3(2|x + 1| - 1))) + 1|)^2 - 3(-3|((3(2|x + 1| - 1) - 2)/(3(2|x + 1| - 1))) + 1|) - 5) + 1)) - 1) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = (-3(-2|(5(-3|(-1((2x - 3)/(-2x)) - 5) + 1| + 2)^2 + 1(-3|(-1((2x - 3)/(-2x)) - 5) + 1| + 2) + 3)| + 1) - 1)/(-2(-2|(5(-3|(-1((2x - 3)/(-2x)) - 5) + 1| + 2)^2 + 1(-3|(-1((2x - 3)/(-2x)) - 5) + 1| + 2) + 3)| + 1) + 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -2(-1(2(-2sin(2\u03c0(3(2|x - 3| + 3))) + 1)^2 - 5) + 2)^2 + 4(-1(2(-2sin(2\u03c0(3(2|x - 3| + 3))) + 1)^2 - 5) + 2) - 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "708", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -5(-1(4(5(3sin(3\u03c0(1x + 4) - 2) - 2)^2 - 4(3sin(3\u03c0(1x + 4) - 2) - 2) + 2)^2 - 2(5(3sin(3\u03c0(1x + 4) - 2) - 2)^2 - 4(3sin(3\u03c0(1x + 4) - 2) - 2) + 2) + 1)^2 + 5(4(5(3sin(3\u03c0(1x + 4) - 2) - 2)^2 - 4(3sin(3\u03c0(1x + 4) - 2) - 2) + 2)^2 - 2(5(3sin(3\u03c0(1x + 4) - 2) - 2)^2 - 4(3sin(3\u03c0(1x + 4) - 2) - 2) + 2) + 1) + 2)^2 + 3(-1(4(5(3sin(3\u03c0(1x + 4) - 2) - 2)^2 - 4(3sin(3\u03c0(1x + 4) - 2) - 2) + 2)^2 - 2(5(3sin(3\u03c0(1x + 4) - 2) - 2)^2 - 4(3sin(3\u03c0(1x + 4) - 2) - 2) + 2) + 1)^2 + 5(4(5(3sin(3\u03c0(1x + 4) - 2) - 2)^2 - 4(3sin(3\u03c0(1x + 4) - 2) - 2) + 2)^2 - 2(5(3sin(3\u03c0(1x + 4) - 2) - 2)^2 - 4(3sin(3\u03c0(1x + 4) - 2) - 2) + 2) + 1) + 2) + 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 2|(-1cos(3\u03c0(4(2(2(2|x + 1| + 1) - 1) + 2) - 2) + 1) + 2) + 1| + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -1|(-3cos(1\u03c0(-2(-2|(-2(4x + 4)^2 - 2(4x + 4)) - 2| - 3) + 5) + 3) + 1) + 3| - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "201", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -5(1|((-3(4((-2(-3cos(2\u03c0x - 2) + 1) + 3)/(-2(-3cos(2\u03c0x - 2) + 1) - 2)) - 2))/(2(4((-2(-3cos(2\u03c0x - 2) + 1) + 3)/(-2(-3cos(2\u03c0x - 2) + 1) - 2)) - 2)))| - 1)^2 - 2(1|((-3(4((-2(-3cos(2\u03c0x - 2) + 1) + 3)/(-2(-3cos(2\u03c0x - 2) + 1) - 2)) - 2))/(2(4((-2(-3cos(2\u03c0x - 2) + 1) + 3)/(-2(-3cos(2\u03c0x - 2) + 1) - 2)) - 2)))| - 1) + 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "126", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = 1e^(-2(-3|(-3(-1|(4(4x^2 + 2x - 1)^2 - 2(4x^2 + 2x - 1)) - 3| + 1) - 4) + 3| + 3)) + 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -3|(1((-1(-1(-4(1x^2 - 5x + 5) + 1)^2 + 5(-4(1x^2 - 5x + 5) + 1) - 3) - 1)/(3(-1(-4(1x^2 - 5x + 5) + 1)^2 + 5(-4(1x^2 - 5x + 5) + 1) - 3) - 1))^2 + 1((-1(-1(-4(1x^2 - 5x + 5) + 1)^2 + 5(-4(1x^2 - 5x + 5) + 1) - 3) - 1)/(3(-1(-4(1x^2 - 5x + 5) + 1)^2 + 5(-4(1x^2 - 5x + 5) + 1) - 3) - 1)) - 3) + 2| - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 4(4(1((3(-3e^(-2(-1x^2 - 4x - 1)) - 2) + 1)/(-1(-3e^(-2(-1x^2 - 4x - 1)) - 2) + 2)) + 4) - 2)^2 - 4(4(1((3(-3e^(-2(-1x^2 - 4x - 1)) - 2) + 1)/(-1(-3e^(-2(-1x^2 - 4x - 1)) - 2) + 2)) + 4) - 2) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "99", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = (2(-1sin(1\u03c0(3(-1|((-1(-2|x + 3| + 1) - 2)/(-2(-2|x + 3| + 1) - 3))| + 3)^2 - 3(-1|((-1(-2|x + 3| + 1) - 2)/(-2(-2|x + 3| + 1) - 3))| + 3) - 2) + 1) - 1) - 3)/(2(-1sin(1\u03c0(3(-1|((-1(-2|x + 3| + 1) - 2)/(-2(-2|x + 3| + 1) - 3))| + 3)^2 - 3(-1|((-1(-2|x + 3| + 1) - 2)/(-2(-2|x + 3| + 1) - 3))| + 3) - 2) + 1) - 1) - 1) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "54", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 3|(2(5(-4(2sin(1\u03c0((-3x - 2)/(3x - 2)) + 3) - 1) - 5) + 4)^2 - 3(5(-4(2sin(1\u03c0((-3x - 2)/(3x - 2)) + 3) - 1) - 5) + 4) - 1)| + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = -1|((2(-1(-3|((-3((1x - 2)/(-3x + 4)) + 2)/(-1((1x - 2)/(-3x + 4)) + 2)) - 2| - 2) - 1))/(2(-1(-3|((-3((1x - 2)/(-3x + 4)) + 2)/(-1((1x - 2)/(-3x + 4)) + 2)) - 2| - 2) - 1) - 3)) + 3| + 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 2(1sin(2\u03c0(-3((-2(2(1x + 5)^2 + 5(1x + 5)) + 3)/(-3(2(1x + 5)^2 + 5(1x + 5)) - 3))^2 + 2((-2(2(1x + 5)^2 + 5(1x + 5)) + 3)/(-3(2(1x + 5)^2 + 5(1x + 5)) - 3))) - 2) + 3) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "56", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = (2((3(4(3sin(1\u03c0(5((2x + 1)/(2x + 2))^2 - 2((2x + 1)/(2x + 2)) - 3) - 1) + 1)^2 + 4(3sin(1\u03c0(5((2x + 1)/(2x + 2))^2 - 2((2x + 1)/(2x + 2)) - 3) - 1) + 1) + 2) + 3)/(-3(4(3sin(1\u03c0(5((2x + 1)/(2x + 2))^2 - 2((2x + 1)/(2x + 2)) - 3) - 1) + 1)^2 + 4(3sin(1\u03c0(5((2x + 1)/(2x + 2))^2 - 2((2x + 1)/(2x + 2)) - 3) - 1) + 1) + 2) - 2)) - 2)/(-3((3(4(3sin(1\u03c0(5((2x + 1)/(2x + 2))^2 - 2((2x + 1)/(2x + 2)) - 3) - 1) + 1)^2 + 4(3sin(1\u03c0(5((2x + 1)/(2x + 2))^2 - 2((2x + 1)/(2x + 2)) - 3) - 1) + 1) + 2) + 3)/(-3(4(3sin(1\u03c0(5((2x + 1)/(2x + 2))^2 - 2((2x + 1)/(2x + 2)) - 3) - 1) + 1)^2 + 4(3sin(1\u03c0(5((2x + 1)/(2x + 2))^2 - 2((2x + 1)/(2x + 2)) - 3) - 1) + 1) + 2) - 2)) - 1) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "49", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -3(1(-2((2(2(1sin(2\u03c0x - 2) - 3) - 3) + 2)/(-2(2(1sin(2\u03c0x - 2) - 3) - 3) + 3))^2 + 4((2(2(1sin(2\u03c0x - 2) - 3) - 3) + 2)/(-2(2(1sin(2\u03c0x - 2) - 3) - 3) + 3))) + 2)^2 + 5(1(-2((2(2(1sin(2\u03c0x - 2) - 3) - 3) + 2)/(-2(2(1sin(2\u03c0x - 2) - 3) - 3) + 3))^2 + 4((2(2(1sin(2\u03c0x - 2) - 3) - 3) + 2)/(-2(2(1sin(2\u03c0x - 2) - 3) - 3) + 3))) + 2) - 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = 1(1(-4(1|(-2|(-1x^2 - 1x + 4) - 3| - 2) + 2|)^2 + 5(1|(-2|(-1x^2 - 1x + 4) - 3| - 2) + 2|) + 4) - 5)^2 - 2(1(-4(1|(-2|(-1x^2 - 1x + 4) - 3| - 2) + 2|)^2 + 5(1|(-2|(-1x^2 - 1x + 4) - 3| - 2) + 2|) + 4) - 5) + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 5(2(-5(5((1(2cos(3\u03c0x + 3) + 1) + 3)/(1(2cos(3\u03c0x + 3) + 1) - 2))^2 - 3((1(2cos(3\u03c0x + 3) + 1) + 3)/(1(2cos(3\u03c0x + 3) + 1) - 2)) - 4) - 5)^2 - 3(-5(5((1(2cos(3\u03c0x + 3) + 1) + 3)/(1(2cos(3\u03c0x + 3) + 1) - 2))^2 - 3((1(2cos(3\u03c0x + 3) + 1) + 3)/(1(2cos(3\u03c0x + 3) + 1) - 2)) - 4) - 5) + 5) - 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "119", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = 4(3|(-1sin(2\u03c0(-2(-5(2|x + 1| - 2) + 2) - 3) + 2)) - 1| + 1)^2 + 2(3|(-1sin(2\u03c0(-2(-5(2|x + 1| - 2) + 2) - 3) + 2)) - 1| + 1) + 5 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "494", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = (-2(3sin(3\u03c0(-2|(3(1|(2x + 2) - 1| + 2)^2 + 4(1|(2x + 2) - 1| + 2) + 4) + 1|) - 2) - 1) - 1)/(3(3sin(3\u03c0(-2|(3(1|(2x + 2) - 1| + 2)^2 + 4(1|(2x + 2) - 1| + 2) + 4) + 1|) - 2) - 1) + 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "488", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -3(-2(3|(-1cos(1\u03c0(5(-1|x| + 3) + 2) + 3) + 3) - 2| - 1) + 1)^2 - 4 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "100", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -3|(3|(5(-1sin(1\u03c0(-2|(2x + 5) - 2| + 3) + 1) - 1)^2 - 3(-1sin(1\u03c0(-2|(2x + 5) - 2| + 3) + 1) - 1))| - 3) - 3| in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "160", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 4(-3(-1((-2((3(-2|x - 1| - 1) + 3)/(-1(-2|x - 1| - 1) - 1)))/(3((3(-2|x - 1| - 1) + 3)/(-1(-2|x - 1| - 1) - 1)) + 3))^2 + 1((-2((3(-2|x - 1| - 1) + 3)/(-1(-2|x - 1| - 1) - 1)))/(3((3(-2|x - 1| - 1) + 3)/(-1(-2|x - 1| - 1) - 1)) + 3)) + 3) + 5) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "44", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 5((2(-1|(-1cos(3\u03c0(-2(-2x - 3)^2 + 3) - 2) + 3) - 1| - 3) - 2)/(2(-1|(-1cos(3\u03c0(-2(-2x - 3)^2 + 3) - 2) + 3) - 1| - 3) + 2))^2 + 5 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "495", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -2cos(2\u03c0(-3(-1(2(4(5x^2 + 3x - 4)^2 + 5(5x^2 + 3x - 4) + 5)^2 - 2(4(5x^2 + 3x - 4)^2 + 5(5x^2 + 3x - 4) + 5)) - 1)) + 2) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "23", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = 1|(-1|(-5(1(-2(-1|x - 3| + 1)^2 - 5(-1|x - 3| + 1) - 1)^2 - 1(-2(-1|x - 3| + 1)^2 - 5(-1|x - 3| + 1) - 1) - 5)^2 + 1(1(-2(-1|x - 3| + 1)^2 - 5(-1|x - 3| + 1) - 1)^2 - 1(-2(-1|x - 3| + 1)^2 - 5(-1|x - 3| + 1) - 1) - 5) - 5)| - 1)| - 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 4(2((-2(-1e^(-1(3(-1x^2 - 3x + 2) + 4)) + 2))/(-3(-1e^(-1(3(-1x^2 - 3x + 2) + 4)) + 2) + 4))^2 + 4((-2(-1e^(-1(3(-1x^2 - 3x + 2) + 4)) + 2))/(-3(-1e^(-1(3(-1x^2 - 3x + 2) + 4)) + 2) + 4)) - 1) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -5((3((-2(-3(2(-2sin(1\u03c0x + 3) + 2) - 2)^2 + 2(2(-2sin(1\u03c0x + 3) + 2) - 2) + 3) + 1)/(-1(-3(2(-2sin(1\u03c0x + 3) + 2) - 2)^2 + 2(2(-2sin(1\u03c0x + 3) + 2) - 2) + 3) - 3)) - 1)/(-3((-2(-3(2(-2sin(1\u03c0x + 3) + 2) - 2)^2 + 2(2(-2sin(1\u03c0x + 3) + 2) - 2) + 3) + 1)/(-1(-3(2(-2sin(1\u03c0x + 3) + 2) - 2)^2 + 2(2(-2sin(1\u03c0x + 3) + 2) - 2) + 3) - 3)) - 3)) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -1(-1((-1(-1sin(1\u03c0((-2(-3|x| + 1) + 3)/(-2(-3|x| + 1))) - 2) + 1) - 1)/(-3(-1sin(1\u03c0((-2(-3|x| + 1) + 3)/(-2(-3|x| + 1))) - 2) + 1) + 2)) + 3) - 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -2(3|((1(1sin(3\u03c0(3|(-2|x + 2| - 3) + 1| + 3) + 1) + 2) - 3)/(1(1sin(3\u03c0(3|(-2|x + 2| - 3) + 1| + 3) + 1) + 2))) - 1| - 3) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "359", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = 2cos(2\u03c0(5(3((-3(-3|(-1x^2 - 3x - 1) + 2| - 3))/(1(-3|(-1x^2 - 3x - 1) + 2| - 3) + 2))^2 + 1((-3(-3|(-1x^2 - 3x - 1) + 2| - 3))/(1(-3|(-1x^2 - 3x - 1) + 2| - 3) + 2)) + 2)^2 + 3) - 1) - 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "214", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -1((2(-1(2(3(-1x^2 - 2x + 2)^2 - 5(-1x^2 - 2x + 2) - 1) - 5)^2 - 5(2(3(-1x^2 - 2x + 2)^2 - 5(-1x^2 - 2x + 2) - 1) - 5) + 2) + 1)/(-2(-1(2(3(-1x^2 - 2x + 2)^2 - 5(-1x^2 - 2x + 2) - 1) - 5)^2 - 5(2(3(-1x^2 - 2x + 2)^2 - 5(-1x^2 - 2x + 2) - 1) - 5) + 2))) + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 1(-3|((-2(2|((3(3|x + 3| + 3) + 3)/(-2(3|x + 3| + 3) + 3)) + 2|) - 1)/(3(2|((3(3|x + 3| + 3) + 3)/(-2(3|x + 3| + 3) + 3)) + 2|))) + 2| - 1)^2 + 2(-3|((-2(2|((3(3|x + 3| + 3) + 3)/(-2(3|x + 3| + 3) + 3)) + 2|) - 1)/(3(2|((3(3|x + 3| + 3) + 3)/(-2(3|x + 3| + 3) + 3)) + 2|))) + 2| - 1) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 3sin(2\u03c0((3((-2((-2(-1(4x - 4)^2 - 3(4x - 4) - 1) - 1)/(3(-1(4x - 4)^2 - 3(4x - 4) - 1))) - 3)/(1((-2(-1(4x - 4)^2 - 3(4x - 4) - 1) - 1)/(3(-1(4x - 4)^2 - 3(4x - 4) - 1))) + 1)) + 2)/(3((-2((-2(-1(4x - 4)^2 - 3(4x - 4) - 1) - 1)/(3(-1(4x - 4)^2 - 3(4x - 4) - 1))) - 3)/(1((-2(-1(4x - 4)^2 - 3(4x - 4) - 1) - 1)/(3(-1(4x - 4)^2 - 3(4x - 4) - 1))) + 1)) - 2))) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 2(3sin(3\u03c0(-3|(1(1|(-1x - 1) + 1| + 3)^2 + 2(1|(-1x - 1) + 1| + 3) + 2) + 1| + 3) - 1) - 3) + 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "230", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -1|(1(-3(5(-2|(-5x^2 + 3x) + 3| + 1)^2 + 5) + 4) - 1) + 1| - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -5(2|((-2(1(2(1|x - 1| + 1)^2 - 3(1|x - 1| + 1) + 2)^2 - 1(2(1|x - 1| + 1)^2 - 3(1|x - 1| + 1) + 2) - 3) - 3)/(-2(1(2(1|x - 1| + 1)^2 - 3(1|x - 1| + 1) + 2)^2 - 1(2(1|x - 1| + 1)^2 - 3(1|x - 1| + 1) + 2) - 3) + 3)) - 1| - 1)^2 + 1(2|((-2(1(2(1|x - 1| + 1)^2 - 3(1|x - 1| + 1) + 2)^2 - 1(2(1|x - 1| + 1)^2 - 3(1|x - 1| + 1) + 2) - 3) - 3)/(-2(1(2(1|x - 1| + 1)^2 - 3(1|x - 1| + 1) + 2)^2 - 1(2(1|x - 1| + 1)^2 - 3(1|x - 1| + 1) + 2) - 3) + 3)) - 1| - 1) + 4 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = (-3(3(1(-2cos(1\u03c0(-3|(-2x^2 + 5x + 3) + 1| - 3) + 2)) + 4) - 1) + 2)/(-1(3(1(-2cos(1\u03c0(-3|(-2x^2 + 5x + 3) + 1| - 3) + 2)) + 4) - 1) - 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "469", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = 2(2cos(1\u03c0(2|(-3(-2|((-3x + 1)/(-3x)) - 2| + 1) - 2) + 1| + 2) - 2) + 3) + 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 2|(-4((1(1(1(-2cos(2\u03c0x - 2)) - 2) - 1) - 3)/(-1(1(1(-2cos(2\u03c0x - 2)) - 2) - 1)))^2 - 3((1(1(1(-2cos(2\u03c0x - 2)) - 2) - 1) - 3)/(-1(1(1(-2cos(2\u03c0x - 2)) - 2) - 1))) + 1) + 3| - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = 4(2(3|(-3(4(-2x - 2) - 4)^2 + 4(4(-2x - 2) - 4) + 4) + 3| - 2) - 4)^2 - 4(2(3|(-3(4(-2x - 2) - 4)^2 + 4(4(-2x - 2) - 4) + 4) + 3| - 2) - 4) - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 1sin(3\u03c0(-4(-1|(1|(1(-2|x - 2| - 2)^2 + 5(-2|x - 2| - 2) + 2) + 1|) - 1|)^2 + 2(-1|(1|(1(-2|x - 2| - 2)^2 + 5(-2|x - 2| - 2) + 2) + 1|) - 1|) - 3) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "87", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 1(-4(3(2cos(2\u03c0((-1(-1x + 1) + 2)/(3(-1x + 1) + 3)) + 3) + 3) - 1)^2 - 1) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 5(-1|(-3(2sin(1\u03c0(5(4x^2 - 2x)^2 - 3(4x^2 - 2x) - 1) + 1) - 2)^2 + 4(2sin(1\u03c0(5(4x^2 - 2x)^2 - 3(4x^2 - 2x) - 1) + 1) - 2) + 5) + 3| - 3)^2 + 5(-1|(-3(2sin(1\u03c0(5(4x^2 - 2x)^2 - 3(4x^2 - 2x) - 1) + 1) - 2)^2 + 4(2sin(1\u03c0(5(4x^2 - 2x)^2 - 3(4x^2 - 2x) - 1) + 1) - 2) + 5) + 3| - 3) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = (2(-1|((3((3(1((-2x + 1)/(-1x)) + 4) + 3)/(-2(1((-2x + 1)/(-1x)) + 4) - 2)) + 3)/(-2((3(1((-2x + 1)/(-1x)) + 4) + 3)/(-2(1((-2x + 1)/(-1x)) + 4) - 2)) - 1))| - 2) - 1)/(2(-1|((3((3(1((-2x + 1)/(-1x)) + 4) + 3)/(-2(1((-2x + 1)/(-1x)) + 4) - 2)) + 3)/(-2((3(1((-2x + 1)/(-1x)) + 4) + 3)/(-2(1((-2x + 1)/(-1x)) + 4) - 2)) - 1))| - 2) + 3) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "54", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 1cos(3\u03c0(-4((2(-1(-2|(5x + 5) + 1| + 2) + 1) - 3)/(-3(-1(-2|(5x + 5) + 1| + 2) + 1) - 1)) - 1) + 2) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 5(-2(1|(-3(3(3cos(3\u03c0x + 2) + 1)^2 + 2(3cos(3\u03c0x + 2) + 1) + 4)^2 - 1(3(3cos(3\u03c0x + 2) + 1)^2 + 2(3cos(3\u03c0x + 2) + 1) + 4) - 1) + 1| - 3) + 5)^2 + 5(-2(1|(-3(3(3cos(3\u03c0x + 2) + 1)^2 + 2(3cos(3\u03c0x + 2) + 1) + 4)^2 - 1(3(3cos(3\u03c0x + 2) + 1)^2 + 2(3cos(3\u03c0x + 2) + 1) + 4) - 1) + 1| - 3) + 5) + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "45", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 2|(3|(-4(-3sin(2\u03c0(-2(5x - 3) + 4) - 2) - 2)^2 - 2(-3sin(2\u03c0(-2(5x - 3) + 4) - 2) - 2) - 2) - 3|) - 3| + 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "587", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = (3(3|(2(5(-4(-2sin(1\u03c0x + 2) - 3)^2 + 5(-2sin(1\u03c0x + 2) - 3) + 4) - 4)^2 + 1(5(-4(-2sin(1\u03c0x + 2) - 3)^2 + 5(-2sin(1\u03c0x + 2) - 3) + 4) - 4)) + 2| + 3) - 2)/(-1(3|(2(5(-4(-2sin(1\u03c0x + 2) - 3)^2 + 5(-2sin(1\u03c0x + 2) - 3) + 4) - 4)^2 + 1(5(-4(-2sin(1\u03c0x + 2) - 3)^2 + 5(-2sin(1\u03c0x + 2) - 3) + 4) - 4)) + 2| + 3) + 3) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 2(2(-5(-3cos(1\u03c0(1|((-3x - 1)/(-1x + 2))| + 1)) + 2) + 3)^2 - 5(-5(-3cos(1\u03c0(1|((-3x - 1)/(-1x + 2))| + 1)) + 2) + 3) - 3)^2 - 3(2(-5(-3cos(1\u03c0(1|((-3x - 1)/(-1x + 2))| + 1)) + 2) + 3)^2 - 5(-5(-3cos(1\u03c0(1|((-3x - 1)/(-1x + 2))| + 1)) + 2) + 3) - 3) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "51", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -2|(2|(-3(-3(5(1|x + 2| - 2))^2 + 2(5(1|x + 2| - 2)) + 1)^2 - 3) - 3| - 3) + 3| - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -3|(1(-3|(3e^(-1(-3(-3|x + 3| + 3) - 4)) - 1)| - 2) + 3) + 3| + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -3(1(1cos(2\u03c0(-1(2|(5x^2 + 4x + 5) + 2| + 1)^2 + 3(2|(5x^2 + 4x + 5) + 2| + 1) + 4) + 3) - 2)^2 - 3(1cos(2\u03c0(-1(2|(5x^2 + 4x + 5) + 2| + 1)^2 + 3(2|(5x^2 + 4x + 5) + 2| + 1) + 4) + 3) - 2) + 2)^2 + 4(1(1cos(2\u03c0(-1(2|(5x^2 + 4x + 5) + 2| + 1)^2 + 3(2|(5x^2 + 4x + 5) + 2| + 1) + 4) + 3) - 2)^2 - 3(1cos(2\u03c0(-1(2|(5x^2 + 4x + 5) + 2| + 1)^2 + 3(2|(5x^2 + 4x + 5) + 2| + 1) + 4) + 3) - 2) + 2) + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "81", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -2cos(2\u03c0((-1(-3(-5(-2|(1x^2 + 1x - 2) + 1| + 3)^2 - 4(-2|(1x^2 + 1x - 2) + 1| + 3) - 1)^2 - 4(-5(-2|(1x^2 + 1x - 2) + 1| + 3)^2 - 4(-2|(1x^2 + 1x - 2) + 1| + 3) - 1)) - 1)/(2(-3(-5(-2|(1x^2 + 1x - 2) + 1| + 3)^2 - 4(-2|(1x^2 + 1x - 2) + 1| + 3) - 1)^2 - 4(-5(-2|(1x^2 + 1x - 2) + 1| + 3)^2 - 4(-2|(1x^2 + 1x - 2) + 1| + 3) - 1)) - 1)) - 2) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = (2(1e^(-1(-3(3((2(-1x) - 2)/(-3(-1x) - 3)) - 4) - 1)) + 2) - 2)/(-1(1e^(-1(-3(3((2(-1x) - 2)/(-3(-1x) - 3)) - 4) - 1)) + 2) - 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = (3(4(-1cos(3\u03c0(4(-4(4x + 1)^2 - 5(4x + 1) + 1) + 5)) - 1)^2 - 4(-1cos(3\u03c0(4(-4(4x + 1)^2 - 5(4x + 1) + 1) + 5)) - 1) - 3) + 3)/(3(4(-1cos(3\u03c0(4(-4(4x + 1)^2 - 5(4x + 1) + 1) + 5)) - 1)^2 - 4(-1cos(3\u03c0(4(-4(4x + 1)^2 - 5(4x + 1) + 1) + 5)) - 1) - 3) - 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "85", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -3|(2cos(1\u03c0(-5((-3(4(2x^2 - 4x) - 5) - 3)/(-2(4(2x^2 - 4x) - 5) - 1)) - 3) - 3)) + 3| - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = (3(-3(4((-2(-3(2|x + 2| - 3)^2 - 5(2|x + 2| - 3) + 3) - 1)/(2(-3(2|x + 2| - 3)^2 - 5(2|x + 2| - 3) + 3) + 2))^2 + 3((-2(-3(2|x + 2| - 3)^2 - 5(2|x + 2| - 3) + 3) - 1)/(2(-3(2|x + 2| - 3)^2 - 5(2|x + 2| - 3) + 3) + 2)) - 1)^2 - 5))/(1(-3(4((-2(-3(2|x + 2| - 3)^2 - 5(2|x + 2| - 3) + 3) - 1)/(2(-3(2|x + 2| - 3)^2 - 5(2|x + 2| - 3) + 3) + 2))^2 + 3((-2(-3(2|x + 2| - 3)^2 - 5(2|x + 2| - 3) + 3) - 1)/(2(-3(2|x + 2| - 3)^2 - 5(2|x + 2| - 3) + 3) + 2)) - 1)^2 - 5)) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -1((2(-5(2((3(2sin(3\u03c0x + 2) + 1) + 3)/(-2(2sin(3\u03c0x + 2) + 1))) + 1)^2 + 2(2((3(2sin(3\u03c0x + 2) + 1) + 3)/(-2(2sin(3\u03c0x + 2) + 1))) + 1) - 1) + 2)/(-3(-5(2((3(2sin(3\u03c0x + 2) + 1) + 3)/(-2(2sin(3\u03c0x + 2) + 1))) + 1)^2 + 2(2((3(2sin(3\u03c0x + 2) + 1) + 3)/(-2(2sin(3\u03c0x + 2) + 1))) + 1) - 1) - 3))^2 + 4((2(-5(2((3(2sin(3\u03c0x + 2) + 1) + 3)/(-2(2sin(3\u03c0x + 2) + 1))) + 1)^2 + 2(2((3(2sin(3\u03c0x + 2) + 1) + 3)/(-2(2sin(3\u03c0x + 2) + 1))) + 1) - 1) + 2)/(-3(-5(2((3(2sin(3\u03c0x + 2) + 1) + 3)/(-2(2sin(3\u03c0x + 2) + 1))) + 1)^2 + 2(2((3(2sin(3\u03c0x + 2) + 1) + 3)/(-2(2sin(3\u03c0x + 2) + 1))) + 1) - 1) - 3)) - 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "207", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = 1(-2|(1(-1sin(3\u03c0(2|((3x)/(1x + 3)) + 2| + 1) + 2) + 3)^2 - 3) - 3| + 1)^2 + 2(-2|(1(-1sin(3\u03c0(2|((3x)/(1x + 3)) + 2| + 1) + 2) + 3)^2 - 3) - 3| + 1) - 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "81", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -1sin(1\u03c0((-1((1(-4((-3(2x - 5) + 1)/(-1(2x - 5) + 3))) + 2)/(-3(-4((-3(2x - 5) + 1)/(-1(2x - 5) + 3))) - 2)) - 2)/(1((1(-4((-3(2x - 5) + 1)/(-1(2x - 5) + 3))) + 2)/(-3(-4((-3(2x - 5) + 1)/(-1(2x - 5) + 3))) - 2)))) + 3) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 2|(1|(2|(3(2cos(1\u03c0(-3|x - 1| + 1)) - 2) - 3)| - 1) - 3| - 2) + 2| + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -2(4((-2(1(-2(-3x^2 + 1x + 4) + 4) - 2) + 3)/(-3(1(-2(-3x^2 + 1x + 4) + 4) - 2) + 1))^2 - 3((-2(1(-2(-3x^2 + 1x + 4) + 4) - 2) + 3)/(-3(1(-2(-3x^2 + 1x + 4) + 4) - 2) + 1)) - 2)^2 - 2(4((-2(1(-2(-3x^2 + 1x + 4) + 4) - 2) + 3)/(-3(1(-2(-3x^2 + 1x + 4) + 4) - 2) + 1))^2 - 3((-2(1(-2(-3x^2 + 1x + 4) + 4) - 2) + 3)/(-3(1(-2(-3x^2 + 1x + 4) + 4) - 2) + 1)) - 2) + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 3|(-5(-5((-1(5(-3|x - 2| + 1)^2 - 2(-3|x - 2| + 1) + 1) + 3)/(2(5(-3|x - 2| + 1)^2 - 2(-3|x - 2| + 1) + 1) - 1))^2 - 3((-1(5(-3|x - 2| + 1)^2 - 2(-3|x - 2| + 1) + 1) + 3)/(2(5(-3|x - 2| + 1)^2 - 2(-3|x - 2| + 1) + 1) - 1)) + 3) - 5) - 2| - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = 1(-2(4((3((-1(2x^2 - 4x) + 3)/(2(2x^2 - 4x) - 3)))/(1((-1(2x^2 - 4x) + 3)/(2(2x^2 - 4x) - 3)) - 3))^2 - 2((3((-1(2x^2 - 4x) + 3)/(2(2x^2 - 4x) - 3)))/(1((-1(2x^2 - 4x) + 3)/(2(2x^2 - 4x) - 3)) - 3)) + 1)^2 + 1(4((3((-1(2x^2 - 4x) + 3)/(2(2x^2 - 4x) - 3)))/(1((-1(2x^2 - 4x) + 3)/(2(2x^2 - 4x) - 3)) - 3))^2 - 2((3((-1(2x^2 - 4x) + 3)/(2(2x^2 - 4x) - 3)))/(1((-1(2x^2 - 4x) + 3)/(2(2x^2 - 4x) - 3)) - 3)) + 1) - 1)^2 + 5(-2(4((3((-1(2x^2 - 4x) + 3)/(2(2x^2 - 4x) - 3)))/(1((-1(2x^2 - 4x) + 3)/(2(2x^2 - 4x) - 3)) - 3))^2 - 2((3((-1(2x^2 - 4x) + 3)/(2(2x^2 - 4x) - 3)))/(1((-1(2x^2 - 4x) + 3)/(2(2x^2 - 4x) - 3)) - 3)) + 1)^2 + 1(4((3((-1(2x^2 - 4x) + 3)/(2(2x^2 - 4x) - 3)))/(1((-1(2x^2 - 4x) + 3)/(2(2x^2 - 4x) - 3)) - 3))^2 - 2((3((-1(2x^2 - 4x) + 3)/(2(2x^2 - 4x) - 3)))/(1((-1(2x^2 - 4x) + 3)/(2(2x^2 - 4x) - 3)) - 3)) + 1) - 1) - 5 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 1|(-3(-1|(-3((-1(-2x^2 - 2x + 4))/(-2(-2x^2 - 2x + 4) - 2)) - 1) + 3| + 1)^2 + 1)| - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -2|(-1|(-2((-1(2(1sin(3\u03c0x) + 1) + 3) + 1)/(2(2(1sin(3\u03c0x) + 1) + 3) + 2))^2 - 4((-1(2(1sin(3\u03c0x) + 1) + 3) + 1)/(2(2(1sin(3\u03c0x) + 1) + 3) + 2)) + 4) + 3| - 1)| + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -2(-4(2|(1(-3cos(1\u03c0((1x - 2)/(-2x - 3))) - 1) + 4) - 3| - 3)^2 + 2(2|(1(-3cos(1\u03c0((1x - 2)/(-2x - 3))) - 1) + 4) - 3| - 3) + 1) - 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = 5(1(-3|(-3(1(5x^2 - 2)^2 - 5(5x^2 - 2) + 1)^2 - 3(1(5x^2 - 2)^2 - 5(5x^2 - 2) + 1) - 2)| - 2)^2 + 2(-3|(-3(1(5x^2 - 2)^2 - 5(5x^2 - 2) + 1)^2 - 3(1(5x^2 - 2)^2 - 5(5x^2 - 2) + 1) - 2)| - 2) - 2)^2 + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -1(2(-5(2|(-2sin(3\u03c0(-2|x + 2| + 2) - 2) + 2) - 1| - 1) - 2)^2 - 2) + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = (-2(1(-2(-1sin(1\u03c0((3(1x + 2) - 3)/(1(1x + 2) + 2)) + 3) + 3) - 5) + 3))/(3(1(-2(-1sin(1\u03c0((3(1x + 2) - 3)/(1(1x + 2) + 2)) + 3) + 3) - 5) + 3) - 2) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "59", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -2((2(-1(2|(4(1|x - 3| - 1)^2 - 1(1|x - 3| - 1) - 2) - 3| + 2)^2 + 2) + 3)/(-2(-1(2|(4(1|x - 3| - 1)^2 - 1(1|x - 3| - 1) - 2) - 3| + 2)^2 + 2) + 3)) + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = (2((1(-2sin(3\u03c0(-1|(-2|(-5x + 1) - 1| + 3) - 2| - 2) + 1)) - 3)/(-1(-2sin(3\u03c0(-1|(-2|(-5x + 1) - 1| + 3) - 2| - 2) + 1)) - 3)) - 2)/(-3((1(-2sin(3\u03c0(-1|(-2|(-5x + 1) - 1| + 3) - 2| - 2) + 1)) - 3)/(-1(-2sin(3\u03c0(-1|(-2|(-5x + 1) - 1| + 3) - 2| - 2) + 1)) - 3)) + 4) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "601", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = (3(-1|(-1sin(3\u03c0(2|((-3(3|x - 2| - 3) - 3)/(-3(3|x - 2| - 3) + 1)) + 3| - 3) + 1) - 1)|) + 2)/(-2(-1|(-1sin(3\u03c0(2|((-3(3|x - 2| - 3) - 3)/(-3(3|x - 2| - 3) + 1)) + 3| - 3) + 1) - 1)|) + 3) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 1((3(1(2(-2sin(3\u03c0(5x^2 - 2x - 3) + 1) + 2) + 5)^2 + 2(2(-2sin(3\u03c0(5x^2 - 2x - 3) + 1) + 2) + 5) + 1))/(-3(1(2(-2sin(3\u03c0(5x^2 - 2x - 3) + 1) + 2) + 5)^2 + 2(2(-2sin(3\u03c0(5x^2 - 2x - 3) + 1) + 2) + 5) + 1) + 2))^2 - 3((3(1(2(-2sin(3\u03c0(5x^2 - 2x - 3) + 1) + 2) + 5)^2 + 2(2(-2sin(3\u03c0(5x^2 - 2x - 3) + 1) + 2) + 5) + 1))/(-3(1(2(-2sin(3\u03c0(5x^2 - 2x - 3) + 1) + 2) + 5)^2 + 2(2(-2sin(3\u03c0(5x^2 - 2x - 3) + 1) + 2) + 5) + 1) + 2)) + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "156", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -3(2(-1(2cos(2\u03c0((1(1x - 1) + 3)/(2(1x - 1) - 1)) - 3) + 2)^2 - 2))^2 + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "26", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = 2cos(2\u03c0(-3(2|(2|(3((3x - 2)/(2x + 2)) + 5) - 2| - 1) - 2| + 3) - 2) - 3) - 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "127", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 3(5((-2(-1sin(2\u03c0(1(-3x + 3) + 3) - 1) + 2) - 1)/(2(-1sin(2\u03c0(1(-3x + 3) + 3) - 1) + 2) - 3)) + 5) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = (2(-1(1(2|(-2|(1|x - 2| - 1) - 1| + 3) - 1| - 3)^2 - 3(2|(-2|(1|x - 2| - 1) - 1| + 3) - 1| - 3) - 1)^2 - 4(1(2|(-2|(1|x - 2| - 1) - 1| + 3) - 1| - 3)^2 - 3(2|(-2|(1|x - 2| - 1) - 1| + 3) - 1| - 3) - 1) - 5) + 2)/(1(-1(1(2|(-2|(1|x - 2| - 1) - 1| + 3) - 1| - 3)^2 - 3(2|(-2|(1|x - 2| - 1) - 1| + 3) - 1| - 3) - 1)^2 - 4(1(2|(-2|(1|x - 2| - 1) - 1| + 3) - 1| - 3)^2 - 3(2|(-2|(1|x - 2| - 1) - 1| + 3) - 1| - 3) - 1) - 5)) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -4((3(-1sin(3\u03c0(-2(3|(-3x - 2) - 1| + 1)) - 1) + 3) - 3)/(-2(-1sin(3\u03c0(-2(3|(-3x - 2) - 1| + 1)) - 1) + 3) + 3))^2 + 5((3(-1sin(3\u03c0(-2(3|(-3x - 2) - 1| + 1)) - 1) + 3) - 3)/(-2(-1sin(3\u03c0(-2(3|(-3x - 2) - 1| + 1)) - 1) + 3) + 3)) - 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "780", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = (-2(-2(-2e^(1(-5(-3|(5x + 5) + 1| + 2)^2 + 1(-3|(5x + 5) + 1| + 2) + 1)) - 2) + 5) + 3)/(-3(-2(-2e^(1(-5(-3|(5x + 5) + 1| + 2)^2 + 1(-3|(5x + 5) + 1| + 2) + 1)) - 2) + 5)) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -1(-1|(3cos(1\u03c0(-5(2(-2|x + 3| + 3)^2 + 1(-2|x + 3| + 3) + 3) - 4)) + 1) + 1| - 3) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "492", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = 3(1(-2cos(2\u03c0(-3|(-2(-2x - 5)^2 - 3(-2x - 5)) - 2| + 3) - 1) + 1)^2 - 3(-2cos(2\u03c0(-3|(-2(-2x - 5)^2 - 3(-2x - 5)) - 2| + 3) - 1) + 1) - 2)^2 - 2(1(-2cos(2\u03c0(-3|(-2(-2x - 5)^2 - 3(-2x - 5)) - 2| + 3) - 1) + 1)^2 - 3(-2cos(2\u03c0(-3|(-2(-2x - 5)^2 - 3(-2x - 5)) - 2| + 3) - 1) + 1) - 2) + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "148", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 1|(-1(-5((-2(-2|(-1x^2 + 3x - 3)|) - 3)/(-3(-2|(-1x^2 + 3x - 3)|) + 1))^2 + 2((-2(-2|(-1x^2 + 3x - 3)|) - 3)/(-3(-2|(-1x^2 + 3x - 3)|) + 1)) - 1)^2 - 1(-5((-2(-2|(-1x^2 + 3x - 3)|) - 3)/(-3(-2|(-1x^2 + 3x - 3)|) + 1))^2 + 2((-2(-2|(-1x^2 + 3x - 3)|) - 3)/(-3(-2|(-1x^2 + 3x - 3)|) + 1)) - 1) + 2) - 2| - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = 1|(1((-1(1|((-1((-2x + 1)/(-2x + 3)) - 3)/(-2((-2x + 1)/(-2x + 3)) - 2))|) - 2)/(2(1|((-1((-2x + 1)/(-2x + 3)) - 3)/(-2((-2x + 1)/(-2x + 3)) - 2))|)))^2 + 3((-1(1|((-1((-2x + 1)/(-2x + 3)) - 3)/(-2((-2x + 1)/(-2x + 3)) - 2))|) - 2)/(2(1|((-1((-2x + 1)/(-2x + 3)) - 3)/(-2((-2x + 1)/(-2x + 3)) - 2))|))) - 1) + 3| - 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -2|(4(-1(-1(2cos(3\u03c0((1x - 2)/(-1x + 3)) - 3) - 2)^2 + 2(2cos(3\u03c0((1x - 2)/(-1x + 3)) - 3) - 2) + 1) - 3) + 3) - 3| + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "43", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -5(-2|(3(-2e^(2(1|(-3|x - 1| + 2) + 1| - 2)) + 3) + 2) + 1| + 2) - 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -3cos(3\u03c0(2|(3(1|((-1(-2x - 5) + 3)/(-3(-2x - 5) + 2)) - 2| + 3) + 2)| + 3) + 2) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 1(-2|(1(-3cos(1\u03c0(-1(1x - 2) - 4) - 1) + 1)^2 + 3(-3cos(1\u03c0(-1(1x - 2) - 4) - 1) + 1) + 1) + 2|) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = 3|(-4(2cos(1\u03c0(-1|(-1|(-2x + 2) + 3| + 1) + 1| + 1)) + 3) + 1) - 1| + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 1|(-1(2|((2(-1|(-2sin(2\u03c0x - 2) + 2) + 1| + 1))/(1(-1|(-2sin(2\u03c0x - 2) + 2) + 1| + 1) + 3)) - 1| - 2) + 5)| + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "119", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -2sin(3\u03c0(2(2(-2|(-5(-1x + 2)^2 + 2(-1x + 2) - 4)| + 1) - 4) + 1) - 1) - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "219", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = (-2(-3(3e^(1(1((2(-2x^2 + 3x + 3) - 3)/(2(-2x^2 + 3x + 3)))^2 - 3((2(-2x^2 + 3x + 3) - 3)/(2(-2x^2 + 3x + 3))) - 3)) - 3)^2 - 1) - 3)/(-1(-3(3e^(1(1((2(-2x^2 + 3x + 3) - 3)/(2(-2x^2 + 3x + 3)))^2 - 3((2(-2x^2 + 3x + 3) - 3)/(2(-2x^2 + 3x + 3))) - 3)) - 3)^2 - 1) + 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -1|(-1|(-5(-4(-4(1x^2 - 3x + 1))^2 - 5(-4(1x^2 - 3x + 1)) + 2)^2 + 5)| - 3) + 2| + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 5(-1((-2(-3cos(1\u03c0(4(2x^2 + 3x - 1)^2 - 2)) + 3) - 1)/(3(-3cos(1\u03c0(4(2x^2 + 3x - 1)^2 - 2)) + 3) + 3))^2 + 3)^2 - 5(-1((-2(-3cos(1\u03c0(4(2x^2 + 3x - 1)^2 - 2)) + 3) - 1)/(3(-3cos(1\u03c0(4(2x^2 + 3x - 1)^2 - 2)) + 3) + 3))^2 + 3) + 5 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "228", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = (-3(3(3sin(3\u03c0(-1(3(-5x - 5) - 5)) + 1) - 3)^2 - 4(3sin(3\u03c0(-1(3(-5x - 5) - 5)) + 1) - 3) - 1) - 2)/(-2(3(3sin(3\u03c0(-1(3(-5x - 5) - 5)) + 1) - 3)^2 - 4(3sin(3\u03c0(-1(3(-5x - 5) - 5)) + 1) - 3) - 1) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "81", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = (-3(-2((-2(2|(-1|((-1x)/(2x - 1)) - 2| + 1) - 3| + 2) + 2)/(-2(2|(-1|((-1x)/(2x - 1)) - 2| + 1) - 3| + 2) - 3)) - 4))/(2(-2((-2(2|(-1|((-1x)/(2x - 1)) - 2| + 1) - 3| + 2) + 2)/(-2(2|(-1|((-1x)/(2x - 1)) - 2| + 1) - 3| + 2) - 3)) - 4)) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "217", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -2(2e^(-1(-3(5(-2(-1|x| + 1)^2 - 3(-1|x| + 1))^2 + 4(-2(-1|x| + 1)^2 - 3(-1|x| + 1)) + 1)^2 + 2(5(-2(-1|x| + 1)^2 - 3(-1|x| + 1))^2 + 4(-2(-1|x| + 1)^2 - 3(-1|x| + 1)) + 1) + 1)) - 2)^2 + 1(2e^(-1(-3(5(-2(-1|x| + 1)^2 - 3(-1|x| + 1))^2 + 4(-2(-1|x| + 1)^2 - 3(-1|x| + 1)) + 1)^2 + 2(5(-2(-1|x| + 1)^2 - 3(-1|x| + 1))^2 + 4(-2(-1|x| + 1)^2 - 3(-1|x| + 1)) + 1) + 1)) - 2) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "24", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -4(-3((-2(3cos(3\u03c0(1(4x^2 + 4x) + 3) + 3) - 3) + 3)/(3(3cos(3\u03c0(1(4x^2 + 4x) + 3) + 3) - 3) + 3))^2 + 3((-2(3cos(3\u03c0(1(4x^2 + 4x) + 3) + 3) - 3) + 3)/(3(3cos(3\u03c0(1(4x^2 + 4x) + 3) + 3) - 3) + 3)) - 5)^2 + 2(-3((-2(3cos(3\u03c0(1(4x^2 + 4x) + 3) + 3) - 3) + 3)/(3(3cos(3\u03c0(1(4x^2 + 4x) + 3) + 3) - 3) + 3))^2 + 3((-2(3cos(3\u03c0(1(4x^2 + 4x) + 3) + 3) - 3) + 3)/(3(3cos(3\u03c0(1(4x^2 + 4x) + 3) + 3) - 3) + 3)) - 5) + 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "457", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -1(-3|(5(2(3cos(3\u03c0(-3x^2 + 1x + 5) - 1) - 1)^2 - 2(3cos(3\u03c0(-3x^2 + 1x + 5) - 1) - 1))^2 - 2(2(3cos(3\u03c0(-3x^2 + 1x + 5) - 1) - 1)^2 - 2(3cos(3\u03c0(-3x^2 + 1x + 5) - 1) - 1)) - 1) - 3| + 2)^2 - 2(-3|(5(2(3cos(3\u03c0(-3x^2 + 1x + 5) - 1) - 1)^2 - 2(3cos(3\u03c0(-3x^2 + 1x + 5) - 1) - 1))^2 - 2(2(3cos(3\u03c0(-3x^2 + 1x + 5) - 1) - 1)^2 - 2(3cos(3\u03c0(-3x^2 + 1x + 5) - 1) - 1)) - 1) - 3| + 2) + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "70", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 2cos(2\u03c0(-1|(1|((-2(-2((2x + 1)/(2x + 3))^2 - 5((2x + 1)/(2x + 3)) - 2) - 1)/(3(-2((2x + 1)/(2x + 3))^2 - 5((2x + 1)/(2x + 3)) - 2) - 2)) - 2| - 2) + 1| + 1) - 2) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -1cos(2\u03c0(-2(-2((2((3(1x^2 + 3x - 3))/(-3(1x^2 + 3x - 3) - 3)) - 2)/(1((3(1x^2 + 3x - 3))/(-3(1x^2 + 3x - 3) - 3)) - 2)) - 4) - 3) + 3) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 3|(-4(5(-3sin(3\u03c0(-3(2|x + 3| + 2) + 4) - 1) - 2)^2 + 5(-3sin(3\u03c0(-3(2|x + 3| + 2) + 4) - 1) - 2))^2 + 4(5(-3sin(3\u03c0(-3(2|x + 3| + 2) + 4) - 1) - 2)^2 + 5(-3sin(3\u03c0(-3(2|x + 3| + 2) + 4) - 1) - 2)))| + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "411", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = (2(2((2((-3(3(2|x + 3| - 1)^2 - 5(2|x + 3| - 1) - 4) + 1)/(2(3(2|x + 3| - 1)^2 - 5(2|x + 3| - 1) - 4) + 1)) + 3)/(2((-3(3(2|x + 3| - 1)^2 - 5(2|x + 3| - 1) - 4) + 1)/(2(3(2|x + 3| - 1)^2 - 5(2|x + 3| - 1) - 4) + 1)) + 1))^2 - 1((2((-3(3(2|x + 3| - 1)^2 - 5(2|x + 3| - 1) - 4) + 1)/(2(3(2|x + 3| - 1)^2 - 5(2|x + 3| - 1) - 4) + 1)) + 3)/(2((-3(3(2|x + 3| - 1)^2 - 5(2|x + 3| - 1) - 4) + 1)/(2(3(2|x + 3| - 1)^2 - 5(2|x + 3| - 1) - 4) + 1)) + 1)) - 1) - 3)/(1(2((2((-3(3(2|x + 3| - 1)^2 - 5(2|x + 3| - 1) - 4) + 1)/(2(3(2|x + 3| - 1)^2 - 5(2|x + 3| - 1) - 4) + 1)) + 3)/(2((-3(3(2|x + 3| - 1)^2 - 5(2|x + 3| - 1) - 4) + 1)/(2(3(2|x + 3| - 1)^2 - 5(2|x + 3| - 1) - 4) + 1)) + 1))^2 - 1((2((-3(3(2|x + 3| - 1)^2 - 5(2|x + 3| - 1) - 4) + 1)/(2(3(2|x + 3| - 1)^2 - 5(2|x + 3| - 1) - 4) + 1)) + 3)/(2((-3(3(2|x + 3| - 1)^2 - 5(2|x + 3| - 1) - 4) + 1)/(2(3(2|x + 3| - 1)^2 - 5(2|x + 3| - 1) - 4) + 1)) + 1)) - 1) - 2) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 1|(-2((1(-2(-2(1x) - 2)^2 - 1(-2(1x) - 2) + 2) + 2)/(1(-2(-2(1x) - 2)^2 - 1(-2(1x) - 2) + 2)))^2 - 2((1(-2(-2(1x) - 2)^2 - 1(-2(1x) - 2) + 2) + 2)/(1(-2(-2(1x) - 2)^2 - 1(-2(1x) - 2) + 2))) + 2) - 3| - 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = 2((1(-3(-3(-5(-1sin(3\u03c0x + 2) + 1)^2 + 4(-1sin(3\u03c0x + 2) + 1) + 1) + 3) - 4))/(-3(-3(-3(-5(-1sin(3\u03c0x + 2) + 1)^2 + 4(-1sin(3\u03c0x + 2) + 1) + 1) + 3) - 4) + 1)) + 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 3|((-2(-5(2(3|(1x^2 + 3x - 1) + 1| + 3)^2 + 5(3|(1x^2 + 3x - 1) + 1| + 3) - 3)^2 + 3(2(3|(1x^2 + 3x - 1) + 1| + 3)^2 + 5(3|(1x^2 + 3x - 1) + 1| + 3) - 3) - 5) - 1)/(-3(-5(2(3|(1x^2 + 3x - 1) + 1| + 3)^2 + 5(3|(1x^2 + 3x - 1) + 1| + 3) - 3)^2 + 3(2(3|(1x^2 + 3x - 1) + 1| + 3)^2 + 5(3|(1x^2 + 3x - 1) + 1| + 3) - 3) - 5) - 3)) + 1| - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = (-3(5(-1|(5(5(1x^2 - 5x + 3)^2 - 4(1x^2 - 5x + 3) + 1)^2 - 4(5(1x^2 - 5x + 3)^2 - 4(1x^2 - 5x + 3) + 1) - 4) - 2| - 1)^2 + 1(-1|(5(5(1x^2 - 5x + 3)^2 - 4(1x^2 - 5x + 3) + 1)^2 - 4(5(1x^2 - 5x + 3)^2 - 4(1x^2 - 5x + 3) + 1) - 4) - 2| - 1) + 1) - 2)/(2(5(-1|(5(5(1x^2 - 5x + 3)^2 - 4(1x^2 - 5x + 3) + 1)^2 - 4(5(1x^2 - 5x + 3)^2 - 4(1x^2 - 5x + 3) + 1) - 4) - 2| - 1)^2 + 1(-1|(5(5(1x^2 - 5x + 3)^2 - 4(1x^2 - 5x + 3) + 1)^2 - 4(5(1x^2 - 5x + 3)^2 - 4(1x^2 - 5x + 3) + 1) - 4) - 2| - 1) + 1) - 1) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "145", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 2(2(1|(4(-5(1sin(2\u03c0x - 3) + 1) + 5) + 5) - 1| + 3) - 4) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "77", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = (-2(-1|(-1sin(1\u03c0(1(-3|(-1|x + 3| + 3) - 1| + 2)^2 - 3(-3|(-1|x + 3| + 3) - 1| + 2) + 5) + 3)) + 3| - 1) + 1)/(-1(-1|(-1sin(1\u03c0(1(-3|(-1|x + 3| + 3) - 1| + 2)^2 - 3(-3|(-1|x + 3| + 3) - 1| + 2) + 5) + 3)) + 3| - 1) + 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "266", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 2(-2(-2cos(2\u03c0(-3((-1(-2x - 2) - 3)/(2(-2x - 2) + 2))^2 + 5((-1(-2x - 2) - 3)/(2(-2x - 2) + 2)) + 4) + 1) - 3)^2 - 3(-2cos(2\u03c0(-3((-1(-2x - 2) - 3)/(2(-2x - 2) + 2))^2 + 5((-1(-2x - 2) - 3)/(2(-2x - 2) + 2)) + 4) + 1) - 3) + 1) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -1|(-5(3(2e^(1(-1|(2|x + 1| + 2) - 3| + 3)))^2 - 1(2e^(1(-1|(2|x + 1| + 2) - 3| + 3))) + 4) + 5) + 2| where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = 3|(1sin(1\u03c0(-2(-5((2(1|x + 3| - 3) - 1)/(1(1|x + 3| - 3) + 3)) - 3)^2 + 1(-5((2(1|x + 3| - 3) - 1)/(1(1|x + 3| - 3) + 3)) - 3) - 3) + 3) - 3) - 1| - 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "224", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = (-3((3(-2(-4(2(5x^2 - 2x + 4) + 3)^2 + 2)^2 - 1(-4(2(5x^2 - 2x + 4) + 3)^2 + 2) - 4) - 1)/(1(-2(-4(2(5x^2 - 2x + 4) + 3)^2 + 2)^2 - 1(-4(2(5x^2 - 2x + 4) + 3)^2 + 2) - 4) + 3)) - 3)/(2((3(-2(-4(2(5x^2 - 2x + 4) + 3)^2 + 2)^2 - 1(-4(2(5x^2 - 2x + 4) + 3)^2 + 2) - 4) - 1)/(1(-2(-4(2(5x^2 - 2x + 4) + 3)^2 + 2)^2 - 1(-4(2(5x^2 - 2x + 4) + 3)^2 + 2) - 4) + 3))) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -3((2((-3(3(-1e^(-2(-2x^2 - 5)) - 3) - 1) - 3)/(-1(3(-1e^(-2(-2x^2 - 5)) - 3) - 1) + 3)) + 2)/(-3((-3(3(-1e^(-2(-2x^2 - 5)) - 3) - 1) - 3)/(-1(3(-1e^(-2(-2x^2 - 5)) - 3) - 1) + 3))))^2 + 4((2((-3(3(-1e^(-2(-2x^2 - 5)) - 3) - 1) - 3)/(-1(3(-1e^(-2(-2x^2 - 5)) - 3) - 1) + 3)) + 2)/(-3((-3(3(-1e^(-2(-2x^2 - 5)) - 3) - 1) - 3)/(-1(3(-1e^(-2(-2x^2 - 5)) - 3) - 1) + 3)))) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "66", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -2|((-3(-2(3(-2|(3sin(1\u03c0x - 2) - 3) + 1| - 3) - 3)^2 - 4(3(-2|(3sin(1\u03c0x - 2) - 3) + 1| - 3) - 3) - 5))/(-3(-2(3(-2|(3sin(1\u03c0x - 2) - 3) + 1| - 3) - 3)^2 - 4(3(-2|(3sin(1\u03c0x - 2) - 3) + 1| - 3) - 3) - 5) + 2)) - 1| + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 1(-2|(-3(-2cos(3\u03c0(-3(1x^2 - 2x)^2 - 1(1x^2 - 2x) - 4) - 3) - 2)^2 + 3(-2cos(3\u03c0(-3(1x^2 - 2x)^2 - 1(1x^2 - 2x) - 4) - 3) - 2) + 1) + 3|)^2 + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "94", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 4(-1(2(-1sin(1\u03c0(1(-1x^2 + 3x - 1) + 1) + 2) - 2)^2 - 4(-1sin(1\u03c0(1(-1x^2 + 3x - 1) + 1) + 2) - 2) + 2) - 4) - 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "103", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = (-1((-3(-2|(1(3|((1x - 2)/(-3x + 4))| - 1)^2 - 1(3|((1x - 2)/(-3x + 4))| - 1)) - 3| - 2))/(3(-2|(1(3|((1x - 2)/(-3x + 4))| - 1)^2 - 1(3|((1x - 2)/(-3x + 4))| - 1)) - 3| - 2) + 3)) + 1)/(3((-3(-2|(1(3|((1x - 2)/(-3x + 4))| - 1)^2 - 1(3|((1x - 2)/(-3x + 4))| - 1)) - 3| - 2))/(3(-2|(1(3|((1x - 2)/(-3x + 4))| - 1)^2 - 1(3|((1x - 2)/(-3x + 4))| - 1)) - 3| - 2) + 3)) - 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 2((-3(-1(5(2(-2cos(2\u03c0x + 3) + 1)^2 - 5(-2cos(2\u03c0x + 3) + 1) - 4)^2 + 1(2(-2cos(2\u03c0x + 3) + 1)^2 - 5(-2cos(2\u03c0x + 3) + 1) - 4) + 3)^2 - 2) + 2)/(3(-1(5(2(-2cos(2\u03c0x + 3) + 1)^2 - 5(-2cos(2\u03c0x + 3) + 1) - 4)^2 + 1(2(-2cos(2\u03c0x + 3) + 1)^2 - 5(-2cos(2\u03c0x + 3) + 1) - 4) + 3)^2 - 2) + 3)) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = (3(-3|(-2|((-3(3(1e^(2x) - 3)^2 + 3(1e^(2x) - 3) + 5))/(1(3(1e^(2x) - 3)^2 + 3(1e^(2x) - 3) + 5) + 3)) + 3| + 3) + 2| + 2) - 3)/(1(-3|(-2|((-3(3(1e^(2x) - 3)^2 + 3(1e^(2x) - 3) + 5))/(1(3(1e^(2x) - 3)^2 + 3(1e^(2x) - 3) + 5) + 3)) + 3| + 3) + 2| + 2) + 1) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -3(-4(3sin(2\u03c0((2((-1(2|x| - 2) - 3)/(3(2|x| - 2) + 2)) + 3)/(-2((-1(2|x| - 2) - 3)/(3(2|x| - 2) + 2)) + 1)) + 3)) + 1)^2 + 2(-4(3sin(2\u03c0((2((-1(2|x| - 2) - 3)/(3(2|x| - 2) + 2)) + 3)/(-2((-1(2|x| - 2) - 3)/(3(2|x| - 2) + 2)) + 1)) + 3)) + 1) - 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "25", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -3|(5(-3(2cos(2\u03c0(2|(-2x)| - 2) + 3) - 1) - 4)^2 - 1(-3(2cos(2\u03c0(2|(-2x)| - 2) + 3) - 1) - 4) - 3) - 1| - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "319", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -2(-3(2|((-2(4(1x - 4)^2 + 4(1x - 4) - 1) - 1)/(-3(4(1x - 4)^2 + 4(1x - 4) - 1) + 4)) + 1| + 1)^2 + 5(2|((-2(4(1x - 4)^2 + 4(1x - 4) - 1) - 1)/(-3(4(1x - 4)^2 + 4(1x - 4) - 1) + 4)) + 1| + 1)) + 5 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = 3|((3(-1sin(3\u03c0((-3(-2(-2x + 5)^2 - 5(-2x + 5) - 4))/(-1(-2(-2x + 5)^2 - 5(-2x + 5) - 4) - 2)) - 3) - 2) - 1)/(1(-1sin(3\u03c0((-3(-2(-2x + 5)^2 - 5(-2x + 5) - 4))/(-1(-2(-2x + 5)^2 - 5(-2x + 5) - 4) - 2)) - 3) - 2) + 1)) - 3| + 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "46", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -2(4((3(3sin(2\u03c0(2((3x - 2)/(-3x + 1))^2 - 2((3x - 2)/(-3x + 1)) + 3) + 2) + 3))/(-3(3sin(2\u03c0(2((3x - 2)/(-3x + 1))^2 - 2((3x - 2)/(-3x + 1)) + 3) + 2) + 3) + 4)) - 1) + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = (-1((3(-2sin(3\u03c0(1|(1|(3x^2 - 5x + 5) - 3| - 2) - 2| + 2) - 1) - 3) - 2)/(2(-2sin(3\u03c0(1|(1|(3x^2 - 5x + 5) - 3| - 2) - 2| + 2) - 1) - 3) + 1)))/(-1((3(-2sin(3\u03c0(1|(1|(3x^2 - 5x + 5) - 3| - 2) - 2| + 2) - 1) - 3) - 2)/(2(-2sin(3\u03c0(1|(1|(3x^2 - 5x + 5) - 3| - 2) - 2| + 2) - 1) - 3) + 1)) - 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "136", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = (2(-5(2|(-2(-1|(-1x - 4) - 3| + 3) - 2) + 3|)^2 + 1(2|(-2(-1|(-1x - 4) - 3| + 3) - 2) + 3|) + 1) - 3)/(2(-5(2|(-2(-1|(-1x - 4) - 3| + 3) - 2) + 3|)^2 + 1(2|(-2(-1|(-1x - 4) - 3| + 3) - 2) + 3|) + 1) + 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -1sin(3\u03c0(-4((-2(-2((1(2|x + 3| - 3) - 1)/(-1(2|x + 3| - 3) + 2))^2 - 5((1(2|x + 3| - 3) - 1)/(-1(2|x + 3| - 3) + 2)) + 4))/(-2(-2((1(2|x + 3| - 3) - 1)/(-1(2|x + 3| - 3) + 2))^2 - 5((1(2|x + 3| - 3) - 1)/(-1(2|x + 3| - 3) + 2)) + 4) + 3)) - 2) - 3) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "24", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -2cos(1\u03c0(-2|(-1(-2|(3((-3x)/(-3x + 4)) + 4) + 3| - 3)^2 + 3) + 3|)) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "214", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -1(1(1(-1(-5(-5x^2 - 5x - 1) - 5)^2 + 1(-5(-5x^2 - 5x - 1) - 5) - 1)^2 + 4(-1(-5(-5x^2 - 5x - 1) - 5)^2 + 1(-5(-5x^2 - 5x - 1) - 5) - 1) + 2)^2 + 3(1(-1(-5(-5x^2 - 5x - 1) - 5)^2 + 1(-5(-5x^2 - 5x - 1) - 5) - 1)^2 + 4(-1(-5(-5x^2 - 5x - 1) - 5)^2 + 1(-5(-5x^2 - 5x - 1) - 5) - 1) + 2) - 2) + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 3(-1cos(3\u03c0(-5(-4(1((3x - 1)/(2x - 1))^2 + 1((3x - 1)/(2x - 1)) - 5)^2 - 2(1((3x - 1)/(2x - 1))^2 + 1((3x - 1)/(2x - 1)) - 5) + 3)^2 + 2(-4(1((3x - 1)/(2x - 1))^2 + 1((3x - 1)/(2x - 1)) - 5)^2 - 2(1((3x - 1)/(2x - 1))^2 + 1((3x - 1)/(2x - 1)) - 5) + 3) + 4) - 3) - 3)^2 - 4(-1cos(3\u03c0(-5(-4(1((3x - 1)/(2x - 1))^2 + 1((3x - 1)/(2x - 1)) - 5)^2 - 2(1((3x - 1)/(2x - 1))^2 + 1((3x - 1)/(2x - 1)) - 5) + 3)^2 + 2(-4(1((3x - 1)/(2x - 1))^2 + 1((3x - 1)/(2x - 1)) - 5)^2 - 2(1((3x - 1)/(2x - 1))^2 + 1((3x - 1)/(2x - 1)) - 5) + 3) + 4) - 3) - 3) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "123", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = -1|(-3(2(4(2|(-2x - 3) + 2| - 3)^2 + 2(2|(-2x - 3) + 2| - 3) + 1) - 5))| - 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = 4((1(-1(-3|(2cos(3\u03c0(4x + 2) - 1) + 1) - 2| + 3)^2 - 1(-3|(2cos(3\u03c0(4x + 2) - 1) + 1) - 2| + 3) + 3) - 1)/(-3(-1(-3|(2cos(3\u03c0(4x + 2) - 1) + 1) - 2| + 3)^2 - 1(-3|(2cos(3\u03c0(4x + 2) - 1) + 1) - 2| + 3) + 3) - 3))^2 + 5((1(-1(-3|(2cos(3\u03c0(4x + 2) - 1) + 1) - 2| + 3)^2 - 1(-3|(2cos(3\u03c0(4x + 2) - 1) + 1) - 2| + 3) + 3) - 1)/(-3(-1(-3|(2cos(3\u03c0(4x + 2) - 1) + 1) - 2| + 3)^2 - 1(-3|(2cos(3\u03c0(4x + 2) - 1) + 1) - 2| + 3) + 3) - 3)) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "380", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = (1((-3(3|(-1(-2(3x^2 - 5x)^2 - 1(3x^2 - 5x) - 3)^2 + 4(-2(3x^2 - 5x)^2 - 1(3x^2 - 5x) - 3) - 4) - 1|))/(-2(3|(-1(-2(3x^2 - 5x)^2 - 1(3x^2 - 5x) - 3)^2 + 4(-2(3x^2 - 5x)^2 - 1(3x^2 - 5x) - 3) - 4) - 1|) + 3)) + 1)/(1((-3(3|(-1(-2(3x^2 - 5x)^2 - 1(3x^2 - 5x) - 3)^2 + 4(-2(3x^2 - 5x)^2 - 1(3x^2 - 5x) - 3) - 4) - 1|))/(-2(3|(-1(-2(3x^2 - 5x)^2 - 1(3x^2 - 5x) - 3)^2 + 4(-2(3x^2 - 5x)^2 - 1(3x^2 - 5x) - 3) - 4) - 1|) + 3))) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 4((1((3((-3((2(1x^2 - 5x - 2) + 3)/(1(1x^2 - 5x - 2) + 1)) + 3)/(2((2(1x^2 - 5x - 2) + 3)/(1(1x^2 - 5x - 2) + 1)) - 1)))/(1((-3((2(1x^2 - 5x - 2) + 3)/(1(1x^2 - 5x - 2) + 1)) + 3)/(2((2(1x^2 - 5x - 2) + 3)/(1(1x^2 - 5x - 2) + 1)) - 1)))) - 2)/(2((3((-3((2(1x^2 - 5x - 2) + 3)/(1(1x^2 - 5x - 2) + 1)) + 3)/(2((2(1x^2 - 5x - 2) + 3)/(1(1x^2 - 5x - 2) + 1)) - 1)))/(1((-3((2(1x^2 - 5x - 2) + 3)/(1(1x^2 - 5x - 2) + 1)) + 3)/(2((2(1x^2 - 5x - 2) + 3)/(1(1x^2 - 5x - 2) + 1)) - 1)))) + 3)) - 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "72", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = -1|(2(1(-3cos(2\u03c0(-2|((3x - 2)/(-1x + 2)) + 1| - 3) + 1) - 3) + 4)^2 + 3(1(-3cos(2\u03c0(-2|((3x - 2)/(-1x + 2)) + 1| - 3) + 1) - 3) + 4) - 5) + 2| - 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "98", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 3|(3sin(3\u03c0(-3(2(-2|((3x + 2)/(1x - 3)) + 2| + 3)^2 - 1(-2|((3x + 2)/(1x - 3)) + 2| + 3) - 2)^2 + 1(2(-2|((3x + 2)/(1x - 3)) + 2| + 3)^2 - 1(-2|((3x + 2)/(1x - 3)) + 2| + 3) - 2) + 4) - 2) + 3) + 1| + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "86", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = (1((-3(-5(1(-2sin(3\u03c0(-3|x - 2| + 2) + 3) - 1) - 1) - 2) - 3)/(1(-5(1(-2sin(3\u03c0(-3|x - 2| + 2) + 3) - 1) - 1) - 2) - 2)))/(1((-3(-5(1(-2sin(3\u03c0(-3|x - 2| + 2) + 3) - 1) - 1) - 2) - 3)/(1(-5(1(-2sin(3\u03c0(-3|x - 2| + 2) + 3) - 1) - 1) - 2) - 2)) - 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "91", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = (-3(3|(-5(-1e^(-2(-1(-3x - 5) - 5)) + 2) + 2) + 3| + 1) - 2)/(1(3|(-5(-1e^(-2(-1(-3x - 5) - 5)) + 2) + 2) + 3| + 1) + 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -3cos(3\u03c0(-2|(-4(-1|((-1(3x - 4) + 1)/(-1(3x - 4) + 3)) + 1| - 3) + 4) + 1| - 2) - 3) - 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "81", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -2|(-1cos(3\u03c0(-5(-2|(-2|(-2|x| - 2) - 3| + 1) + 3| + 3)^2 - 4(-2|(-2|(-2|x| - 2) - 3| + 1) + 3| + 3) + 5) - 2)) + 3| + 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "126", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 3|(-1(3sin(1\u03c0((-2(1((-3x - 2)/(1x))^2 + 4((-3x - 2)/(1x)) + 1) - 2)/(2(1((-3x - 2)/(1x))^2 + 4((-3x - 2)/(1x)) + 1) - 1)) - 1) - 2) - 1)| - 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = (-1(-3(2sin(2\u03c0(-1|(2|(2|x + 2| - 3) + 3| + 1) - 1| + 3) - 3) + 3) + 2) + 3)/(2(-3(2sin(2\u03c0(-1|(2|(2|x + 2| - 3) + 3| + 1) - 1| + 3) - 3) + 3) + 2) + 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -3(-4(-1|((3(2e^(2(3x - 3))) - 1)/(-3(2e^(2(3x - 3))) - 1)) - 2| - 1)^2 - 1(-1|((3(2e^(2(3x - 3))) - 1)/(-3(2e^(2(3x - 3))) - 1)) - 2| - 1) - 1)^2 + 4(-4(-1|((3(2e^(2(3x - 3))) - 1)/(-3(2e^(2(3x - 3))) - 1)) - 2| - 1)^2 - 1(-1|((3(2e^(2(3x - 3))) - 1)/(-3(2e^(2(3x - 3))) - 1)) - 2| - 1) - 1) - 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = (1(4(2(3sin(1\u03c0((1((-1x - 1)/(2x - 3)) + 2)/(2((-1x - 1)/(2x - 3))))))^2 - 3(3sin(1\u03c0((1((-1x - 1)/(2x - 3)) + 2)/(2((-1x - 1)/(2x - 3)))))) - 4)^2 - 3(2(3sin(1\u03c0((1((-1x - 1)/(2x - 3)) + 2)/(2((-1x - 1)/(2x - 3))))))^2 - 3(3sin(1\u03c0((1((-1x - 1)/(2x - 3)) + 2)/(2((-1x - 1)/(2x - 3)))))) - 4) - 3) + 3)/(-2(4(2(3sin(1\u03c0((1((-1x - 1)/(2x - 3)) + 2)/(2((-1x - 1)/(2x - 3))))))^2 - 3(3sin(1\u03c0((1((-1x - 1)/(2x - 3)) + 2)/(2((-1x - 1)/(2x - 3)))))) - 4)^2 - 3(2(3sin(1\u03c0((1((-1x - 1)/(2x - 3)) + 2)/(2((-1x - 1)/(2x - 3))))))^2 - 3(3sin(1\u03c0((1((-1x - 1)/(2x - 3)) + 2)/(2((-1x - 1)/(2x - 3)))))) - 4) - 3) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "67", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -3|(1(-3((-3(3(2cos(2\u03c0x + 1) + 2) + 3) - 3)/(-2(3(2cos(2\u03c0x + 1) + 2) + 3) + 3))) - 3) - 1| - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 2sin(3\u03c0((2(-1(-5(-3|(3|x + 1| - 1) - 3| + 1)^2 + 1(-3|(3|x + 1| - 1) - 3| + 1) + 4)^2 - 5(-5(-3|(3|x + 1| - 1) - 3| + 1)^2 + 1(-3|(3|x + 1| - 1) - 3| + 1) + 4) + 4) + 3)/(-2(-1(-5(-3|(3|x + 1| - 1) - 3| + 1)^2 + 1(-3|(3|x + 1| - 1) - 3| + 1) + 4)^2 - 5(-5(-3|(3|x + 1| - 1) - 3| + 1)^2 + 1(-3|(3|x + 1| - 1) - 3| + 1) + 4) + 4) + 3))) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -1(-5(-1sin(2\u03c0(3|(-5(5x^2 + 3x + 4) - 3)|) - 3) - 2)^2 + 5(-1sin(2\u03c0(3|(-5(5x^2 + 3x + 4) - 3)|) - 3) - 2) - 5)^2 - 4(-5(-1sin(2\u03c0(3|(-5(5x^2 + 3x + 4) - 3)|) - 3) - 2)^2 + 5(-1sin(2\u03c0(3|(-5(5x^2 + 3x + 4) - 3)|) - 3) - 2) - 5) + 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "147", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = 3(-2(-1(3(-4(-1sin(2\u03c0x + 1) + 3)^2 - 5) + 4)^2 - 1(3(-4(-1sin(2\u03c0x + 1) + 3)^2 - 5) + 4) + 1)^2 + 5(-1(3(-4(-1sin(2\u03c0x + 1) + 3)^2 - 5) + 4)^2 - 1(3(-4(-1sin(2\u03c0x + 1) + 3)^2 - 5) + 4) + 1) - 4)^2 + 2(-2(-1(3(-4(-1sin(2\u03c0x + 1) + 3)^2 - 5) + 4)^2 - 1(3(-4(-1sin(2\u03c0x + 1) + 3)^2 - 5) + 4) + 1)^2 + 5(-1(3(-4(-1sin(2\u03c0x + 1) + 3)^2 - 5) + 4)^2 - 1(3(-4(-1sin(2\u03c0x + 1) + 3)^2 - 5) + 4) + 1) - 4) + 4 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -2(1|(3|((3(-3|(-3x - 2) + 1| - 2) + 3)/(-2(-3|(-3x - 2) + 1| - 2) - 2)) + 2| + 2) - 1| + 2) - 4 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "122", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -1|((1(3sin(1\u03c0(-3|((2(-1|x + 2| + 1) - 1)/(1(-1|x + 2| + 1) + 1))| + 1) + 2)) - 2)/(-2(3sin(1\u03c0(-3|((2(-1|x + 2| + 1) - 1)/(1(-1|x + 2| + 1) + 1))| + 1) + 2)) + 3)) + 3| + 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "57", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 5(2|(-1|((2(-1((-1x - 3)/(-3x))^2 - 3((-1x - 3)/(-3x)) - 3) + 3)/(-1(-1((-1x - 3)/(-3x))^2 - 3((-1x - 3)/(-3x)) - 3) - 2)) - 3| + 1) + 1| + 3)^2 + 1(2|(-1|((2(-1((-1x - 3)/(-3x))^2 - 3((-1x - 3)/(-3x)) - 3) + 3)/(-1(-1((-1x - 3)/(-3x))^2 - 3((-1x - 3)/(-3x)) - 3) - 2)) - 3| + 1) + 1| + 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = 2(1|(-2|(-4(5(-4x + 1)^2 - 1(-4x + 1) - 3)^2 - 3(5(-4x + 1)^2 - 1(-4x + 1) - 3) + 3)| - 1) + 1| + 1)^2 - 5(1|(-2|(-4(5(-4x + 1)^2 - 1(-4x + 1) - 3)^2 - 3(5(-4x + 1)^2 - 1(-4x + 1) - 3) + 3)| - 1) + 1| + 1) - 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = (2(1(-1|(5(5(4x) - 5)^2 + 1(5(4x) - 5) - 3) + 2|)^2 - 3(-1|(5(5(4x) - 5)^2 + 1(5(4x) - 5) - 3) + 2|) - 1) + 2)/(3(1(-1|(5(5(4x) - 5)^2 + 1(5(4x) - 5) - 3) + 2|)^2 - 3(-1|(5(5(4x) - 5)^2 + 1(5(4x) - 5) - 3) + 2|) - 1) + 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "321", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -5(1(2cos(3\u03c0(3((3(-5x - 5) - 3)/(-2(-5x - 5)))^2 + 1((3(-5x - 5) - 3)/(-2(-5x - 5))) - 1) + 3) + 1) - 5) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "50", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 5((-2(3cos(2\u03c0(-2(-5((-2x - 3)/(1x + 2))) + 2) + 1) - 2) + 2)/(1(3cos(2\u03c0(-2(-5((-2x - 3)/(1x + 2))) + 2) + 1) - 2)))^2 + 4((-2(3cos(2\u03c0(-2(-5((-2x - 3)/(1x + 2))) + 2) + 1) - 2) + 2)/(1(3cos(2\u03c0(-2(-5((-2x - 3)/(1x + 2))) + 2) + 1) - 2))) + 5 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "115", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 5(-2cos(1\u03c0(1((2(-5(-3x^2 + 3x + 4) + 2) + 1)/(-3(-5(-3x^2 + 3x + 4) + 2) + 2))^2 - 3((2(-5(-3x^2 + 3x + 4) + 2) + 1)/(-3(-5(-3x^2 + 3x + 4) + 2) + 2)) + 4) + 1) + 3) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = (-1(1(1(1|(2(-1sin(2\u03c0x + 3) - 2))| + 1)^2 + 3(1|(2(-1sin(2\u03c0x + 3) - 2))| + 1) + 5)^2 - 3(1(1|(2(-1sin(2\u03c0x + 3) - 2))| + 1)^2 + 3(1|(2(-1sin(2\u03c0x + 3) - 2))| + 1) + 5) + 2) + 1)/(-2(1(1(1|(2(-1sin(2\u03c0x + 3) - 2))| + 1)^2 + 3(1|(2(-1sin(2\u03c0x + 3) - 2))| + 1) + 5)^2 - 3(1(1|(2(-1sin(2\u03c0x + 3) - 2))| + 1)^2 + 3(1|(2(-1sin(2\u03c0x + 3) - 2))| + 1) + 5) + 2) + 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = (-1((2(2e^(-1(-4(1|(2x) + 1| - 3)^2 - 2(1|(2x) + 1| - 3) - 2)) + 2) - 3)/(-3(2e^(-1(-4(1|(2x) + 1| - 3)^2 - 2(1|(2x) + 1| - 3) - 2)) + 2) + 4)))/(-2((2(2e^(-1(-4(1|(2x) + 1| - 3)^2 - 2(1|(2x) + 1| - 3) - 2)) + 2) - 3)/(-3(2e^(-1(-4(1|(2x) + 1| - 3)^2 - 2(1|(2x) + 1| - 3) - 2)) + 2) + 4)) - 1) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "51", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -1(-2cos(2\u03c0(-5(1(-3|((-1x - 3)/(1x + 2)) - 2| - 2) + 4)^2 - 5(1(-3|((-1x - 3)/(1x + 2)) - 2| - 2) + 4) - 1)) + 2) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "160", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = (-2(1|(-3cos(3\u03c0(2(1|(4x - 2) + 1| - 2)^2 + 3(1|(4x - 2) + 1| - 2) + 4) + 2) - 3) - 2| - 2) - 3)/(1(1|(-3cos(3\u03c0(2(1|(4x - 2) + 1| - 2)^2 + 3(1|(4x - 2) + 1| - 2) + 4) + 2) - 3) - 2| - 2) + 1) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "105", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = (-3(-2((-1((1(2(-1x^2 + 4x + 5)^2 + 2(-1x^2 + 4x + 5) + 5) + 2)/(-1(2(-1x^2 + 4x + 5)^2 + 2(-1x^2 + 4x + 5) + 5) + 2)) - 1)/(-3((1(2(-1x^2 + 4x + 5)^2 + 2(-1x^2 + 4x + 5) + 5) + 2)/(-1(2(-1x^2 + 4x + 5)^2 + 2(-1x^2 + 4x + 5) + 5) + 2)) - 3))^2 - 5((-1((1(2(-1x^2 + 4x + 5)^2 + 2(-1x^2 + 4x + 5) + 5) + 2)/(-1(2(-1x^2 + 4x + 5)^2 + 2(-1x^2 + 4x + 5) + 5) + 2)) - 1)/(-3((1(2(-1x^2 + 4x + 5)^2 + 2(-1x^2 + 4x + 5) + 5) + 2)/(-1(2(-1x^2 + 4x + 5)^2 + 2(-1x^2 + 4x + 5) + 5) + 2)) - 3)) - 2) - 1)/(-3(-2((-1((1(2(-1x^2 + 4x + 5)^2 + 2(-1x^2 + 4x + 5) + 5) + 2)/(-1(2(-1x^2 + 4x + 5)^2 + 2(-1x^2 + 4x + 5) + 5) + 2)) - 1)/(-3((1(2(-1x^2 + 4x + 5)^2 + 2(-1x^2 + 4x + 5) + 5) + 2)/(-1(2(-1x^2 + 4x + 5)^2 + 2(-1x^2 + 4x + 5) + 5) + 2)) - 3))^2 - 5((-1((1(2(-1x^2 + 4x + 5)^2 + 2(-1x^2 + 4x + 5) + 5) + 2)/(-1(2(-1x^2 + 4x + 5)^2 + 2(-1x^2 + 4x + 5) + 5) + 2)) - 1)/(-3((1(2(-1x^2 + 4x + 5)^2 + 2(-1x^2 + 4x + 5) + 5) + 2)/(-1(2(-1x^2 + 4x + 5)^2 + 2(-1x^2 + 4x + 5) + 5) + 2)) - 3)) - 2) + 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "248", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -4((1((1(2cos(1\u03c0((-1(2|x + 1| + 1) + 2)/(2(2|x + 1| + 1) - 1)) + 1) - 1) + 3)/(-1(2cos(1\u03c0((-1(2|x + 1| + 1) + 2)/(2(2|x + 1| + 1) - 1)) + 1) - 1) + 3)) - 2)/(-2((1(2cos(1\u03c0((-1(2|x + 1| + 1) + 2)/(2(2|x + 1| + 1) - 1)) + 1) - 1) + 3)/(-1(2cos(1\u03c0((-1(2|x + 1| + 1) + 2)/(2(2|x + 1| + 1) - 1)) + 1) - 1) + 3)) - 1))^2 + 4((1((1(2cos(1\u03c0((-1(2|x + 1| + 1) + 2)/(2(2|x + 1| + 1) - 1)) + 1) - 1) + 3)/(-1(2cos(1\u03c0((-1(2|x + 1| + 1) + 2)/(2(2|x + 1| + 1) - 1)) + 1) - 1) + 3)) - 2)/(-2((1(2cos(1\u03c0((-1(2|x + 1| + 1) + 2)/(2(2|x + 1| + 1) - 1)) + 1) - 1) + 3)/(-1(2cos(1\u03c0((-1(2|x + 1| + 1) + 2)/(2(2|x + 1| + 1) - 1)) + 1) - 1) + 3)) - 1)) + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = 1(2|(-1|(1(2sin(2\u03c0(-3x^2 + 2x + 2) - 3) + 1)^2 + 5(2sin(2\u03c0(-3x^2 + 2x + 2) - 3) + 1) - 3) + 2| + 1) - 2| - 1)^2 - 2(2|(-1|(1(2sin(2\u03c0(-3x^2 + 2x + 2) - 3) + 1)^2 + 5(2sin(2\u03c0(-3x^2 + 2x + 2) - 3) + 1) - 3) + 2| + 1) - 2| - 1) - 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "187", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -2|(1(-2sin(3\u03c0(5((1(1x^2 + 2x + 1) - 1)/(3(1x^2 + 2x + 1) - 2))^2 - 4) + 1) + 3)^2 - 2(-2sin(3\u03c0(5((1(1x^2 + 2x + 1) - 1)/(3(1x^2 + 2x + 1) - 2))^2 - 4) + 1) + 3) - 3)| - 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -1(4(1e^(-1(2|(1(-2|x - 1| + 2) - 5)| + 1)) + 1) - 1)^2 - 5(4(1e^(-1(2|(1(-2|x - 1| + 2) - 5)| + 1)) + 1) - 1) + 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = 5((1(1((-2(-1(2x - 4)^2 + 4(2x - 4) - 3) + 2)/(-2(-1(2x - 4)^2 + 4(2x - 4) - 3) - 2))^2 + 3((-2(-1(2x - 4)^2 + 4(2x - 4) - 3) + 2)/(-2(-1(2x - 4)^2 + 4(2x - 4) - 3) - 2)) - 5) + 2)/(-1(1((-2(-1(2x - 4)^2 + 4(2x - 4) - 3) + 2)/(-2(-1(2x - 4)^2 + 4(2x - 4) - 3) - 2))^2 + 3((-2(-1(2x - 4)^2 + 4(2x - 4) - 3) + 2)/(-2(-1(2x - 4)^2 + 4(2x - 4) - 3) - 2)) - 5) + 2))^2 + 3((1(1((-2(-1(2x - 4)^2 + 4(2x - 4) - 3) + 2)/(-2(-1(2x - 4)^2 + 4(2x - 4) - 3) - 2))^2 + 3((-2(-1(2x - 4)^2 + 4(2x - 4) - 3) + 2)/(-2(-1(2x - 4)^2 + 4(2x - 4) - 3) - 2)) - 5) + 2)/(-1(1((-2(-1(2x - 4)^2 + 4(2x - 4) - 3) + 2)/(-2(-1(2x - 4)^2 + 4(2x - 4) - 3) - 2))^2 + 3((-2(-1(2x - 4)^2 + 4(2x - 4) - 3) + 2)/(-2(-1(2x - 4)^2 + 4(2x - 4) - 3) - 2)) - 5) + 2)) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = -1(2cos(3\u03c0(-4(-2(2|((3x + 3)/(2x + 2)) - 3|)^2 + 3(2|((3x + 3)/(2x + 2)) - 3|) - 2)^2 + 4(-2(2|((3x + 3)/(2x + 2)) - 3|)^2 + 3(2|((3x + 3)/(2x + 2)) - 3|) - 2) - 4) - 3) + 3)^2 - 2(2cos(3\u03c0(-4(-2(2|((3x + 3)/(2x + 2)) - 3|)^2 + 3(2|((3x + 3)/(2x + 2)) - 3|) - 2)^2 + 4(-2(2|((3x + 3)/(2x + 2)) - 3|)^2 + 3(2|((3x + 3)/(2x + 2)) - 3|) - 2) - 4) - 3) + 3) + 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 4(1(2((-3((-1(4x^2 - 3x - 5) - 3)/(3(4x^2 - 3x - 5) - 1)))/(-1((-1(4x^2 - 3x - 5) - 3)/(3(4x^2 - 3x - 5) - 1)) - 2)) - 3)^2 - 4(2((-3((-1(4x^2 - 3x - 5) - 3)/(3(4x^2 - 3x - 5) - 1)))/(-1((-1(4x^2 - 3x - 5) - 3)/(3(4x^2 - 3x - 5) - 1)) - 2)) - 3) + 3) - 4 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = (2(-1cos(1\u03c0(-2(-2(1|(2|x - 2| + 1) + 3|)^2 + 5(1|(2|x - 2| + 1) + 3|))^2 - 2(-2(1|(2|x - 2| + 1) + 3|)^2 + 5(1|(2|x - 2| + 1) + 3|)) - 2) - 3)) - 2)/(-1(-1cos(1\u03c0(-2(-2(1|(2|x - 2| + 1) + 3|)^2 + 5(1|(2|x - 2| + 1) + 3|))^2 - 2(-2(1|(2|x - 2| + 1) + 3|)^2 + 5(1|(2|x - 2| + 1) + 3|)) - 2) - 3)) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "91", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -1cos(1\u03c0(1|(1(1|(-1(1x + 1) - 2) + 3| - 2)^2 - 2(1|(-1(1x + 1) - 2) + 3| - 2) + 5) + 1|) - 2) + 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "119", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 1((-2(1(-3|((2(-4x^2 + 1x - 3))/(1(-4x^2 + 1x - 3) - 3)) - 2| - 1) + 3) + 2)/(-3(1(-3|((2(-4x^2 + 1x - 3))/(1(-4x^2 + 1x - 3) - 3)) - 2| - 1) + 3) - 1))^2 - 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -4(-1cos(1\u03c0(2(-2|(-3|(-3|x| - 1) - 2| + 1)| + 3)^2 + 2(-2|(-3|(-3|x| - 1) - 2| + 1)| + 3) + 5) - 1))^2 + 1(-1cos(1\u03c0(2(-2|(-3|(-3|x| - 1) - 2| + 1)| + 3)^2 + 2(-2|(-3|(-3|x| - 1) - 2| + 1)| + 3) + 5) - 1)) + 5 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "149", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 1(-4(-1|(2|(-3(1cos(1\u03c0x - 1) - 1)^2 + 2(1cos(1\u03c0x - 1) - 1) - 4) - 1|) + 1| - 2) - 1)^2 - 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = (-3((-2(2sin(1\u03c0(-3(1(-1x^2 + 2x - 2) - 1) + 2) + 1) - 1))/(2(2sin(1\u03c0(-3(1(-1x^2 + 2x - 2) - 1) + 2) + 1) - 1) - 3)) + 3)/(1((-2(2sin(1\u03c0(-3(1(-1x^2 + 2x - 2) - 1) + 2) + 1) - 1))/(2(2sin(1\u03c0(-3(1(-1x^2 + 2x - 2) - 1) + 2) + 1) - 1) - 3)) - 3) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "56", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = (-1(-2sin(2\u03c0(-5(1(1((-2x + 1)/(-3x + 1))^2 - 4((-2x + 1)/(-3x + 1)) + 2) + 5)^2 - 4(1(1((-2x + 1)/(-3x + 1))^2 - 4((-2x + 1)/(-3x + 1)) + 2) + 5) + 1) + 1) - 3) + 3)/(1(-2sin(2\u03c0(-5(1(1((-2x + 1)/(-3x + 1))^2 - 4((-2x + 1)/(-3x + 1)) + 2) + 5)^2 - 4(1(1((-2x + 1)/(-3x + 1))^2 - 4((-2x + 1)/(-3x + 1)) + 2) + 5) + 1) + 1) - 3)) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "77", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -3(1(5(-2cos(3\u03c0(-5(1|x - 2| - 3) + 3)) + 2)) - 4)^2 - 5(1(5(-2cos(3\u03c0(-5(1|x - 2| - 3) + 3)) + 2)) - 4) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "263", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -1cos(1\u03c0((3(2|(3|(2(-5x^2 + 4x) - 1) + 1| - 1) + 1| - 3))/(1(2|(3|(2(-5x^2 + 4x) - 1) + 1| - 1) + 1| - 3) - 3)) + 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = (2(-2|(-2e^(1(-1|(-5(1|x + 3|)^2 - 3(1|x + 3|) + 5) + 2| + 3)) + 2)| - 1) + 2)/(-2(-2|(-2e^(1(-1|(-5(1|x + 3|)^2 - 3(1|x + 3|) + 5) + 2| + 3)) + 2)| - 1)) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -1|(-2sin(1\u03c0(3(3|(5(-3|x + 2| - 1)^2 + 2(-3|x + 2| - 1) - 4)| + 2) - 3) - 3) + 2)| have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "315", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 3(-3(-2cos(2\u03c0(-3|(3(5x^2 - 1x - 4)^2 + 5(5x^2 - 1x - 4) + 4) - 3| + 2) - 1)) + 3) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "48", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 1(2cos(2\u03c0(-1(-1|(-4((-1x + 1)/(-3x + 2)) + 1)|)^2 + 4(-1|(-4((-1x + 1)/(-3x + 2)) + 1)|) - 3) - 2) + 1)^2 + 3(2cos(2\u03c0(-1(-1|(-4((-1x + 1)/(-3x + 2)) + 1)|)^2 + 4(-1|(-4((-1x + 1)/(-3x + 2)) + 1)|) - 3) - 2) + 1) - 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "53", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -5(1cos(2\u03c0(1(3(-3|(-2x^2 + 3x - 1) - 2|) + 2)^2 - 5(3(-3|(-2x^2 + 3x - 1) - 2|) + 2) - 3) - 1) + 1) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "84", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -3((1(1(-1|(1sin(2\u03c0(-1x + 1) - 2) + 1) + 2| + 3) + 4) + 2)/(-2(1(-1|(1sin(2\u03c0(-1x + 1) - 2) + 1) + 2| + 3) + 4) - 2))^2 - 5((1(1(-1|(1sin(2\u03c0(-1x + 1) - 2) + 1) + 2| + 3) + 4) + 2)/(-2(1(-1|(1sin(2\u03c0(-1x + 1) - 2) + 1) + 2| + 3) + 4) - 2)) + 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 1|(-2|(3|(-3((2(-1|x| + 3) + 3)/(3(-1|x| + 3) + 3))^2 - 2((2(-1|x| + 3) + 3)/(3(-1|x| + 3) + 3)) - 5) - 2|) + 3| + 2) + 1| have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -1|(-1cos(2\u03c0(1|(-3(2(-1x - 1) - 4) - 5) + 2| + 3) + 1)) - 1| - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = -4((2(3|(-3|(3cos(2\u03c0(2x^2 - 2x - 3))) - 2|) + 2| + 1) + 2)/(-1(3|(-3|(3cos(2\u03c0(2x^2 - 2x - 3))) - 2|) + 2| + 1) + 2)) - 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "448", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -1(3((3(-2cos(2\u03c0((-2((1x + 1)/(-1x + 2)))/(-1((1x + 1)/(-1x + 2)) + 2)) + 2) + 3) - 1)/(-2(-2cos(2\u03c0((-2((1x + 1)/(-1x + 2)))/(-1((1x + 1)/(-1x + 2)) + 2)) + 2) + 3) + 3)) - 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -1((3(-3(5(1((-2x - 1)/(3x + 3)) + 2) - 5)^2 - 4(5(1((-2x - 1)/(3x + 3)) + 2) - 5) + 2) + 1)/(-2(-3(5(1((-2x - 1)/(3x + 3)) + 2) - 5)^2 - 4(5(1((-2x - 1)/(3x + 3)) + 2) - 5) + 2) + 1))^2 + 1((3(-3(5(1((-2x - 1)/(3x + 3)) + 2) - 5)^2 - 4(5(1((-2x - 1)/(3x + 3)) + 2) - 5) + 2) + 1)/(-2(-3(5(1((-2x - 1)/(3x + 3)) + 2) - 5)^2 - 4(5(1((-2x - 1)/(3x + 3)) + 2) - 5) + 2) + 1)) - 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = 3(1(-4(-1cos(1\u03c0(3((-3x - 2)/(3x + 3)) - 5)) - 1)^2 + 5(-1cos(1\u03c0(3((-3x - 2)/(3x + 3)) - 5)) - 1) - 3) + 4) - 5 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -2(-4(3|((2((-3(-3cos(1\u03c0x + 1)) + 3)/(-3(-3cos(1\u03c0x + 1)) + 2)) + 3)/(-3((-3(-3cos(1\u03c0x + 1)) + 3)/(-3(-3cos(1\u03c0x + 1)) + 2)))) - 2| + 3)^2 + 5(3|((2((-3(-3cos(1\u03c0x + 1)) + 3)/(-3(-3cos(1\u03c0x + 1)) + 2)) + 3)/(-3((-3(-3cos(1\u03c0x + 1)) + 3)/(-3(-3cos(1\u03c0x + 1)) + 2)))) - 2| + 3))^2 - 4(-4(3|((2((-3(-3cos(1\u03c0x + 1)) + 3)/(-3(-3cos(1\u03c0x + 1)) + 2)) + 3)/(-3((-3(-3cos(1\u03c0x + 1)) + 3)/(-3(-3cos(1\u03c0x + 1)) + 2)))) - 2| + 3)^2 + 5(3|((2((-3(-3cos(1\u03c0x + 1)) + 3)/(-3(-3cos(1\u03c0x + 1)) + 2)) + 3)/(-3((-3(-3cos(1\u03c0x + 1)) + 3)/(-3(-3cos(1\u03c0x + 1)) + 2)))) - 2| + 3)) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 4(2|(-1(1cos(1\u03c0(-2(-3|x + 1| - 2) + 3) + 3) + 2) + 4) - 1|)^2 + 1(2|(-1(1cos(1\u03c0(-2(-3|x + 1| - 2) + 3) + 3) + 2) + 4) - 1|) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = 2((-1(-2((-3(-1(-5x^2 + 4x + 5)^2 - 1(-5x^2 + 4x + 5) - 2) + 2)/(-2(-1(-5x^2 + 4x + 5)^2 - 1(-5x^2 + 4x + 5) - 2) - 3))^2 - 1((-3(-1(-5x^2 + 4x + 5)^2 - 1(-5x^2 + 4x + 5) - 2) + 2)/(-2(-1(-5x^2 + 4x + 5)^2 - 1(-5x^2 + 4x + 5) - 2) - 3))) + 3)/(-2(-2((-3(-1(-5x^2 + 4x + 5)^2 - 1(-5x^2 + 4x + 5) - 2) + 2)/(-2(-1(-5x^2 + 4x + 5)^2 - 1(-5x^2 + 4x + 5) - 2) - 3))^2 - 1((-3(-1(-5x^2 + 4x + 5)^2 - 1(-5x^2 + 4x + 5) - 2) + 2)/(-2(-1(-5x^2 + 4x + 5)^2 - 1(-5x^2 + 4x + 5) - 2) - 3))) - 3))^2 - 3((-1(-2((-3(-1(-5x^2 + 4x + 5)^2 - 1(-5x^2 + 4x + 5) - 2) + 2)/(-2(-1(-5x^2 + 4x + 5)^2 - 1(-5x^2 + 4x + 5) - 2) - 3))^2 - 1((-3(-1(-5x^2 + 4x + 5)^2 - 1(-5x^2 + 4x + 5) - 2) + 2)/(-2(-1(-5x^2 + 4x + 5)^2 - 1(-5x^2 + 4x + 5) - 2) - 3))) + 3)/(-2(-2((-3(-1(-5x^2 + 4x + 5)^2 - 1(-5x^2 + 4x + 5) - 2) + 2)/(-2(-1(-5x^2 + 4x + 5)^2 - 1(-5x^2 + 4x + 5) - 2) - 3))^2 - 1((-3(-1(-5x^2 + 4x + 5)^2 - 1(-5x^2 + 4x + 5) - 2) + 2)/(-2(-1(-5x^2 + 4x + 5)^2 - 1(-5x^2 + 4x + 5) - 2) - 3))) - 3)) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = (-2(-2(3(-2|(-4(2e^(2x)) + 1) - 3| - 2) + 1)^2 + 3(3(-2|(-4(2e^(2x)) + 1) - 3| - 2) + 1) - 4) - 3)/(-2(-2(3(-2|(-4(2e^(2x)) + 1) - 3| - 2) + 1)^2 + 3(3(-2|(-4(2e^(2x)) + 1) - 3| - 2) + 1) - 4) - 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = (2(-2(1((-2(1cos(2\u03c0(1|x + 1|) + 1)) + 3)/(-1(1cos(2\u03c0(1|x + 1|) + 1)) - 2))^2 - 1((-2(1cos(2\u03c0(1|x + 1|) + 1)) + 3)/(-1(1cos(2\u03c0(1|x + 1|) + 1)) - 2)) - 1)^2 - 1(1((-2(1cos(2\u03c0(1|x + 1|) + 1)) + 3)/(-1(1cos(2\u03c0(1|x + 1|) + 1)) - 2))^2 - 1((-2(1cos(2\u03c0(1|x + 1|) + 1)) + 3)/(-1(1cos(2\u03c0(1|x + 1|) + 1)) - 2)) - 1) + 4) - 1)/(-1(-2(1((-2(1cos(2\u03c0(1|x + 1|) + 1)) + 3)/(-1(1cos(2\u03c0(1|x + 1|) + 1)) - 2))^2 - 1((-2(1cos(2\u03c0(1|x + 1|) + 1)) + 3)/(-1(1cos(2\u03c0(1|x + 1|) + 1)) - 2)) - 1)^2 - 1(1((-2(1cos(2\u03c0(1|x + 1|) + 1)) + 3)/(-1(1cos(2\u03c0(1|x + 1|) + 1)) - 2))^2 - 1((-2(1cos(2\u03c0(1|x + 1|) + 1)) + 3)/(-1(1cos(2\u03c0(1|x + 1|) + 1)) - 2)) - 1) + 4) - 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "81", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -1(1|((3(2sin(1\u03c0(3|((-3x + 1)/(-1x - 1)) + 1|)) + 3) + 2)/(2(2sin(1\u03c0(3|((-3x + 1)/(-1x - 1)) + 1|)) + 3) - 1)) - 3| + 3) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "91", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -3|(2|(3(-3|(5(1x^2 - 1x - 1) - 5) - 3| + 1)^2 + 4(-3|(5(1x^2 - 1x - 1) - 5) - 3| + 1) - 3) - 1| + 1) + 1| + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -4(2(3|(-4((-2(-2cos(3\u03c0x + 2) + 3))/(2(-2cos(3\u03c0x + 2) + 3) + 1)) - 2) - 1| - 1))^2 - 2(2(3|(-4((-2(-2cos(3\u03c0x + 2) + 3))/(2(-2cos(3\u03c0x + 2) + 3) + 1)) - 2) - 1| - 1)) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "240", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = (-1(4(-1(-1sin(3\u03c0(-5(-3x^2 - 2)^2 - 2(-3x^2 - 2) - 4) - 1)) - 2) - 1) + 3)/(3(4(-1(-1sin(3\u03c0(-5(-3x^2 - 2)^2 - 2(-3x^2 - 2) - 4) - 1)) - 2) - 1) - 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "148", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = 3|(-5((-2(-5((-1(-2x^2 - 4x + 4) - 3)/(2(-2x^2 - 4x + 4) - 1))^2 + 5) + 1)/(-3(-5((-1(-2x^2 - 4x + 4) - 3)/(2(-2x^2 - 4x + 4) - 1))^2 + 5) + 4)) - 2) + 1| + 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = (-3((2(3(2|(1(-1x + 2)^2 - 3) - 2| - 3)^2 - 2(2|(1(-1x + 2)^2 - 3) - 2| - 3) - 4) + 3)/(3(3(2|(1(-1x + 2)^2 - 3) - 2| - 3)^2 - 2(2|(1(-1x + 2)^2 - 3) - 2| - 3) - 4) - 2)) + 2)/(-3((2(3(2|(1(-1x + 2)^2 - 3) - 2| - 3)^2 - 2(2|(1(-1x + 2)^2 - 3) - 2| - 3) - 4) + 3)/(3(3(2|(1(-1x + 2)^2 - 3) - 2| - 3)^2 - 2(2|(1(-1x + 2)^2 - 3) - 2| - 3) - 4) - 2)) - 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 3(2(2(-2sin(2\u03c0(2((3x - 1)/(1x))^2 - 4((3x - 1)/(1x)) - 5) - 3))^2 + 5(-2sin(2\u03c0(2((3x - 1)/(1x))^2 - 4((3x - 1)/(1x)) - 5) - 3)) - 2) + 2) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "51", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -3(-1((1(1|(-1|(-1x^2 - 4x - 1) + 1| + 3) - 3| - 1) - 2)/(2(1|(-1|(-1x^2 - 4x - 1) + 1| + 3) - 3| - 1)))^2 - 3((1(1|(-1|(-1x^2 - 4x - 1) + 1| + 3) - 3| - 1) - 2)/(2(1|(-1|(-1x^2 - 4x - 1) + 1| + 3) - 3| - 1)))) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 2|(-2|(5(-1|(5(3|x - 3| - 2) + 4) + 3|)^2 + 1(-1|(5(3|x - 3| - 2) + 4) + 3|) - 5) - 2| - 2) - 2| - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = 5(-1sin(1\u03c0(-4((-3(3|(5x + 2) - 2| + 3) - 1)/(2(3|(5x + 2) - 2| + 3) + 3))^2 + 4((-3(3|(5x + 2) - 2| + 3) - 1)/(2(3|(5x + 2) - 2| + 3) + 3)) + 4) - 2) - 3) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 4(3|(-4(-2cos(3\u03c0(5(1x^2 + 5x + 5) - 2) + 3) - 1)^2 + 1(-2cos(3\u03c0(5(1x^2 + 5x + 5) - 2) + 3) - 1) - 3) - 2| + 3) + 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "344", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -1((3(1|((3(-1sin(2\u03c0(5x - 3) - 2) - 1) + 3)/(3(-1sin(2\u03c0(5x - 3) - 2) - 1) + 1)) + 3|) - 3)/(2(1|((3(-1sin(2\u03c0(5x - 3) - 2) - 1) + 3)/(3(-1sin(2\u03c0(5x - 3) - 2) - 1) + 1)) + 3|) - 1)) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "332", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = 3|(5(-4((2(-4(3|x + 1| - 3)^2 + 5(3|x + 1| - 3) + 4) - 3)/(-3(-4(3|x + 1| - 3)^2 + 5(3|x + 1| - 3) + 4) + 2)) - 1) + 2) + 2| + 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 5(-4(-3(2((-3(-1e^(2x) + 2) + 2)/(-3(-1e^(2x) + 2) - 2))^2 + 2((-3(-1e^(2x) + 2) + 2)/(-3(-1e^(2x) + 2) - 2)) - 4)^2 + 2(2((-3(-1e^(2x) + 2) + 2)/(-3(-1e^(2x) + 2) - 2))^2 + 2((-3(-1e^(2x) + 2) + 2)/(-3(-1e^(2x) + 2) - 2)) - 4) + 2)^2 + 1)^2 + 3(-4(-3(2((-3(-1e^(2x) + 2) + 2)/(-3(-1e^(2x) + 2) - 2))^2 + 2((-3(-1e^(2x) + 2) + 2)/(-3(-1e^(2x) + 2) - 2)) - 4)^2 + 2(2((-3(-1e^(2x) + 2) + 2)/(-3(-1e^(2x) + 2) - 2))^2 + 2((-3(-1e^(2x) + 2) + 2)/(-3(-1e^(2x) + 2) - 2)) - 4) + 2)^2 + 1) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -5(2((-2(1(1|(-3e^(-1x) + 2) + 2|)^2 - 1(1|(-3e^(-1x) + 2) + 2|)) + 3)/(1(1(1|(-3e^(-1x) + 2) + 2|)^2 - 1(1|(-3e^(-1x) + 2) + 2|)) + 1))^2 - 3((-2(1(1|(-3e^(-1x) + 2) + 2|)^2 - 1(1|(-3e^(-1x) + 2) + 2|)) + 3)/(1(1(1|(-3e^(-1x) + 2) + 2|)^2 - 1(1|(-3e^(-1x) + 2) + 2|)) + 1)) + 3) - 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -3(5(2(4(-4(-2sin(1\u03c0x - 1) - 1)^2 - 4)^2 + 3(-4(-2sin(1\u03c0x - 1) - 1)^2 - 4) - 5) - 5)^2 - 3(2(4(-4(-2sin(1\u03c0x - 1) - 1)^2 - 4)^2 + 3(-4(-2sin(1\u03c0x - 1) - 1)^2 - 4) - 5) - 5) + 2) + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 4(1(2e^(-1((-1((-1(2|x - 1| - 3) - 1)/(1(2|x - 1| - 3))) - 2)/(-3((-1(2|x - 1| - 3) - 1)/(1(2|x - 1| - 3))) + 2))) + 1)^2 - 4(2e^(-1((-1((-1(2|x - 1| - 3) - 1)/(1(2|x - 1| - 3))) - 2)/(-3((-1(2|x - 1| - 3) - 1)/(1(2|x - 1| - 3))) + 2))) + 1) - 1)^2 + 4(1(2e^(-1((-1((-1(2|x - 1| - 3) - 1)/(1(2|x - 1| - 3))) - 2)/(-3((-1(2|x - 1| - 3) - 1)/(1(2|x - 1| - 3))) + 2))) + 1)^2 - 4(2e^(-1((-1((-1(2|x - 1| - 3) - 1)/(1(2|x - 1| - 3))) - 2)/(-3((-1(2|x - 1| - 3) - 1)/(1(2|x - 1| - 3))) + 2))) + 1) - 1) + 5 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = (-1((2(3(-2|(5(2|x - 2| - 2) - 5)| + 1)^2 + 4(-2|(5(2|x - 2| - 2) - 5)| + 1) + 5) + 2)/(-3(3(-2|(5(2|x - 2| - 2) - 5)| + 1)^2 + 4(-2|(5(2|x - 2| - 2) - 5)| + 1) + 5) - 1)) + 3)/(-1((2(3(-2|(5(2|x - 2| - 2) - 5)| + 1)^2 + 4(-2|(5(2|x - 2| - 2) - 5)| + 1) + 5) + 2)/(-3(3(-2|(5(2|x - 2| - 2) - 5)| + 1)^2 + 4(-2|(5(2|x - 2| - 2) - 5)| + 1) + 5) - 1)) + 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 1|((-2(-3((-3(4(1cos(3\u03c0x) - 1) - 1) + 3)/(-3(4(1cos(3\u03c0x) - 1) - 1) + 1)) + 1) + 1)/(3(-3((-3(4(1cos(3\u03c0x) - 1) - 1) + 3)/(-3(4(1cos(3\u03c0x) - 1) - 1) + 1)) + 1) + 1)) - 2| + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 1sin(1\u03c0(-1(2|(-2(2((3x - 3)/(-3x + 1)) - 1) + 5) + 1|) + 5) - 1) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "24", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -2|(2sin(2\u03c0(-3(1((3((-2x - 1)/(2x - 1)))/(-3((-2x - 1)/(2x - 1)) + 1)) + 2)^2 - 1(1((3((-2x - 1)/(2x - 1)))/(-3((-2x - 1)/(2x - 1)) + 1)) + 2) + 3))) + 3| + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = 2(5(-2(1(3|(-3|x + 1| + 3) - 1|) - 2)^2 + 1(1(3|(-3|x + 1| + 3) - 1|) - 2) + 3)^2 - 3(-2(1(3|(-3|x + 1| + 3) - 1|) - 2)^2 + 1(1(3|(-3|x + 1| + 3) - 1|) - 2) + 3) + 3) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -3(4(-1(-3cos(1\u03c0((-2((3x + 1)/(2x + 2)) - 1)/(1((3x + 1)/(2x + 2)))) + 2) - 2))^2 - 3(-1(-3cos(1\u03c0((-2((3x + 1)/(2x + 2)) - 1)/(1((3x + 1)/(2x + 2)))) + 2) - 2)) - 2) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = -2((-2(-1(2(-1|(-3e^(-2x) + 3) - 3| + 2)^2 - 1(-1|(-3e^(-2x) + 3) - 3| + 2) - 2)^2 - 1(2(-1|(-3e^(-2x) + 3) - 3| + 2)^2 - 1(-1|(-3e^(-2x) + 3) - 3| + 2) - 2) + 4) + 1)/(3(-1(2(-1|(-3e^(-2x) + 3) - 3| + 2)^2 - 1(-1|(-3e^(-2x) + 3) - 3| + 2) - 2)^2 - 1(2(-1|(-3e^(-2x) + 3) - 3| + 2)^2 - 1(-1|(-3e^(-2x) + 3) - 3| + 2) - 2) + 4))) - 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = (-2(3sin(2\u03c0(1(5((-3(-3x^2 + 3x - 4))/(-3(-3x^2 + 3x - 4) + 4)) + 2) - 2) - 1) - 2) - 1)/(2(3sin(2\u03c0(1(5((-3(-3x^2 + 3x - 4))/(-3(-3x^2 + 3x - 4) + 4)) + 2) - 2) - 1) - 2)) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 1(-2(-2cos(1\u03c0(-3(3|(-1x - 3) + 3| + 3) + 3) + 3) - 2)^2 - 3(-2cos(1\u03c0(-3(3|(-1x - 3) + 3| + 3) + 3) + 3) - 2) + 3) + 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "361", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 1(-1(-3|(2(-3cos(3\u03c0((-1x + 2)/(-2x - 1)) + 1) + 3) + 4) - 2| - 2)^2 - 3(-3|(2(-3cos(3\u03c0((-1x + 2)/(-2x - 1)) + 1) + 3) + 4) - 2| - 2) + 4) - 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = -3((-2(-2sin(2\u03c0(1((-2(1x^2 - 2x - 2) - 2)/(-1(1x^2 - 2x - 2) - 3))^2 + 2((-2(1x^2 - 2x - 2) - 2)/(-1(1x^2 - 2x - 2) - 3)) - 3) + 2) + 3))/(-2(-2sin(2\u03c0(1((-2(1x^2 - 2x - 2) - 2)/(-1(1x^2 - 2x - 2) - 3))^2 + 2((-2(1x^2 - 2x - 2) - 2)/(-1(1x^2 - 2x - 2) - 3)) - 3) + 2) + 3) + 1)) - 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "23", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -4(-5(2|(-3e^(2(-3(1|x + 3|)^2 + 2(1|x + 3|) + 5)) + 3) + 1| + 3) + 5)^2 - 1(-5(2|(-3e^(2(-3(1|x + 3|)^2 + 2(1|x + 3|) + 5)) + 3) + 1| + 3) + 5) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = (-1(4(-1(-5(1(5x^2 + 1x + 2)^2 + 5(5x^2 + 1x + 2) + 3)^2 + 5(1(5x^2 + 1x + 2)^2 + 5(5x^2 + 1x + 2) + 3) + 4)^2 - 5(-5(1(5x^2 + 1x + 2)^2 + 5(5x^2 + 1x + 2) + 3)^2 + 5(1(5x^2 + 1x + 2)^2 + 5(5x^2 + 1x + 2) + 3) + 4)) + 1))/(-3(4(-1(-5(1(5x^2 + 1x + 2)^2 + 5(5x^2 + 1x + 2) + 3)^2 + 5(1(5x^2 + 1x + 2)^2 + 5(5x^2 + 1x + 2) + 3) + 4)^2 - 5(-5(1(5x^2 + 1x + 2)^2 + 5(5x^2 + 1x + 2) + 3)^2 + 5(1(5x^2 + 1x + 2)^2 + 5(5x^2 + 1x + 2) + 3) + 4)) + 1) - 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "223", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -3(-3|((2(-2cos(3\u03c0(5(1|x + 3| - 1)^2 + 1(1|x + 3| - 1) + 3) - 3) + 1) - 1)/(-2(-2cos(3\u03c0(5(1|x + 3| - 1)^2 + 1(1|x + 3| - 1) + 3) - 3) + 1) + 3)) - 2| - 2)^2 - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "203", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -1e^(2(-3|((-1(2|((1(3x^2 - 5x) - 2)/(-3(3x^2 - 5x) - 3)) - 1|) + 2)/(1(2|((1(3x^2 - 5x) - 2)/(-3(3x^2 - 5x) - 3)) - 1|) + 2)) + 3| - 1)) - 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = -3|(-5(-1cos(1\u03c0((-3((-1(1|x + 2| - 3) + 1)/(1(1|x + 2| - 3) - 2)) + 2)/(1((-1(1|x + 2| - 3) + 1)/(1(1|x + 2| - 3) - 2)) - 3)) - 2) - 3) + 2) - 2| + 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 2|((-1(1((-1((-3(-3x^2 + 2x + 2) + 2)/(-2(-3x^2 + 2x + 2) - 3)) + 3)/(-2((-3(-3x^2 + 2x + 2) + 2)/(-2(-3x^2 + 2x + 2) - 3)) + 1))^2 - 4((-1((-3(-3x^2 + 2x + 2) + 2)/(-2(-3x^2 + 2x + 2) - 3)) + 3)/(-2((-3(-3x^2 + 2x + 2) + 2)/(-2(-3x^2 + 2x + 2) - 3)) + 1)) - 4) - 3)/(-3(1((-1((-3(-3x^2 + 2x + 2) + 2)/(-2(-3x^2 + 2x + 2) - 3)) + 3)/(-2((-3(-3x^2 + 2x + 2) + 2)/(-2(-3x^2 + 2x + 2) - 3)) + 1))^2 - 4((-1((-3(-3x^2 + 2x + 2) + 2)/(-2(-3x^2 + 2x + 2) - 3)) + 3)/(-2((-3(-3x^2 + 2x + 2) + 2)/(-2(-3x^2 + 2x + 2) - 3)) + 1)) - 4) - 3))| - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -4(1(2(-1(-3cos(3\u03c0(-5x + 1) + 3))^2 + 5(-3cos(3\u03c0(-5x + 1) + 3)) - 1) - 3) - 2) - 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "189", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = (-3(-3|(-1|(4(1sin(3\u03c0(2x - 2)) + 2)^2 + 1(1sin(3\u03c0(2x - 2)) + 2) + 1) - 1| - 3) + 3| - 1) + 3)/(-2(-3|(-1|(4(1sin(3\u03c0(2x - 2)) + 2)^2 + 1(1sin(3\u03c0(2x - 2)) + 2) + 1) - 1| - 3) + 3| - 1) + 1) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = (2(-5((-3(-1(-1cos(1\u03c0(1|x - 1| + 2) + 3) - 2)^2 - 2(-1cos(1\u03c0(1|x - 1| + 2) + 3) - 2) + 1))/(-3(-1(-1cos(1\u03c0(1|x - 1| + 2) + 3) - 2)^2 - 2(-1cos(1\u03c0(1|x - 1| + 2) + 3) - 2) + 1) - 1))^2 - 3((-3(-1(-1cos(1\u03c0(1|x - 1| + 2) + 3) - 2)^2 - 2(-1cos(1\u03c0(1|x - 1| + 2) + 3) - 2) + 1))/(-3(-1(-1cos(1\u03c0(1|x - 1| + 2) + 3) - 2)^2 - 2(-1cos(1\u03c0(1|x - 1| + 2) + 3) - 2) + 1) - 1)) + 4) + 3)/(1(-5((-3(-1(-1cos(1\u03c0(1|x - 1| + 2) + 3) - 2)^2 - 2(-1cos(1\u03c0(1|x - 1| + 2) + 3) - 2) + 1))/(-3(-1(-1cos(1\u03c0(1|x - 1| + 2) + 3) - 2)^2 - 2(-1cos(1\u03c0(1|x - 1| + 2) + 3) - 2) + 1) - 1))^2 - 3((-3(-1(-1cos(1\u03c0(1|x - 1| + 2) + 3) - 2)^2 - 2(-1cos(1\u03c0(1|x - 1| + 2) + 3) - 2) + 1))/(-3(-1(-1cos(1\u03c0(1|x - 1| + 2) + 3) - 2)^2 - 2(-1cos(1\u03c0(1|x - 1| + 2) + 3) - 2) + 1) - 1)) + 4) + 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "61", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = 2|(1|(3|(-5((-2((2x - 1)/(1x + 1)))/(1((2x - 1)/(1x + 1)) + 1))^2 - 2((-2((2x - 1)/(1x + 1)))/(1((2x - 1)/(1x + 1)) + 1)) - 3) + 3|) - 1| + 3) + 3| - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = (1(5((-1(5(2(-1|x + 2| + 3))^2 - 2(2(-1|x + 2| + 3)) - 4) + 3)/(1(5(2(-1|x + 2| + 3))^2 - 2(2(-1|x + 2| + 3)) - 4) + 2))^2 - 3((-1(5(2(-1|x + 2| + 3))^2 - 2(2(-1|x + 2| + 3)) - 4) + 3)/(1(5(2(-1|x + 2| + 3))^2 - 2(2(-1|x + 2| + 3)) - 4) + 2)) - 3) - 1)/(-3(5((-1(5(2(-1|x + 2| + 3))^2 - 2(2(-1|x + 2| + 3)) - 4) + 3)/(1(5(2(-1|x + 2| + 3))^2 - 2(2(-1|x + 2| + 3)) - 4) + 2))^2 - 3((-1(5(2(-1|x + 2| + 3))^2 - 2(2(-1|x + 2| + 3)) - 4) + 3)/(1(5(2(-1|x + 2| + 3))^2 - 2(2(-1|x + 2| + 3)) - 4) + 2)) - 3) + 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 3cos(1\u03c0(-2|(-3|(1|(-5((-2x + 3)/(3x + 2))^2 - 2((-2x + 3)/(3x + 2)) + 2) + 3| + 3) + 3| - 3) - 2| - 2) + 1) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "136", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 1|((-2(2(2|(-1(-2sin(3\u03c0x - 1) - 1)^2 - 2(-2sin(3\u03c0x - 1) - 1) - 2) - 2| + 3) - 2) + 1)/(3(2(2|(-1(-2sin(3\u03c0x - 1) - 1)^2 - 2(-2sin(3\u03c0x - 1) - 1) - 2) - 2| + 3) - 2) - 2)) + 1| have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 3|(-3cos(1\u03c0(4(-2|(1(-3|x - 3| + 3) + 2) - 3| + 1)^2 + 1(-2|(1(-3|x - 3| + 3) + 2) - 3| + 1) - 5))) + 1| + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "372", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 3(-2(1(4((-2(3|x + 1| - 3) + 1)/(1(3|x + 1| - 3) - 2))^2 + 5((-2(3|x + 1| - 3) + 1)/(1(3|x + 1| - 3) - 2)) - 1)^2 - 4(4((-2(3|x + 1| - 3) + 1)/(1(3|x + 1| - 3) - 2))^2 + 5((-2(3|x + 1| - 3) + 1)/(1(3|x + 1| - 3) - 2)) - 1) + 3)^2 - 2(1(4((-2(3|x + 1| - 3) + 1)/(1(3|x + 1| - 3) - 2))^2 + 5((-2(3|x + 1| - 3) + 1)/(1(3|x + 1| - 3) - 2)) - 1)^2 - 4(4((-2(3|x + 1| - 3) + 1)/(1(3|x + 1| - 3) - 2))^2 + 5((-2(3|x + 1| - 3) + 1)/(1(3|x + 1| - 3) - 2)) - 1) + 3) + 2) + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = 2|((2(3|(-2((3(1|x + 2| + 1) - 2)/(-3(1|x + 2| + 1) + 4))^2 + 4((3(1|x + 2| + 1) - 2)/(-3(1|x + 2| + 1) + 4))) - 2| - 3) + 2)/(3(3|(-2((3(1|x + 2| + 1) - 2)/(-3(1|x + 2| + 1) + 4))^2 + 4((3(1|x + 2| + 1) - 2)/(-3(1|x + 2| + 1) + 4))) - 2| - 3) - 2))| where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 1(-4(-1(-2|(2|(2sin(1\u03c0x + 2) - 2) + 2| - 2) + 1| - 2)^2 + 2(-2|(2|(2sin(1\u03c0x + 2) - 2) + 2| - 2) + 1| - 2) - 1)^2 - 4) - 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "72", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 1(-3sin(3\u03c0(-1(-4(2|(-4x + 2) + 1| + 3)^2 + 4(2|(-4x + 2) + 1| + 3) + 1)^2 - 5(-4(2|(-4x + 2) + 1| + 3)^2 + 4(2|(-4x + 2) + 1| + 3) + 1) - 5) + 1) - 2) + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 1(-1cos(2\u03c0(1(4((3((1x + 3)/(3x + 2)))/(-1((1x + 3)/(3x + 2)) - 2))^2 - 2((3((1x + 3)/(3x + 2)))/(-1((1x + 3)/(3x + 2)) - 2)) + 5) + 2) - 2))^2 + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -1((-1((2((-1(-2(-1cos(3\u03c0x - 1) - 1)^2 + 1(-1cos(3\u03c0x - 1) - 1) + 5) + 2)/(-2(-2(-1cos(3\u03c0x - 1) - 1)^2 + 1(-1cos(3\u03c0x - 1) - 1) + 5) - 2)) - 3)/(3((-1(-2(-1cos(3\u03c0x - 1) - 1)^2 + 1(-1cos(3\u03c0x - 1) - 1) + 5) + 2)/(-2(-2(-1cos(3\u03c0x - 1) - 1)^2 + 1(-1cos(3\u03c0x - 1) - 1) + 5) - 2)) + 1)))/(-3((2((-1(-2(-1cos(3\u03c0x - 1) - 1)^2 + 1(-1cos(3\u03c0x - 1) - 1) + 5) + 2)/(-2(-2(-1cos(3\u03c0x - 1) - 1)^2 + 1(-1cos(3\u03c0x - 1) - 1) + 5) - 2)) - 3)/(3((-1(-2(-1cos(3\u03c0x - 1) - 1)^2 + 1(-1cos(3\u03c0x - 1) - 1) + 5) + 2)/(-2(-2(-1cos(3\u03c0x - 1) - 1)^2 + 1(-1cos(3\u03c0x - 1) - 1) + 5) - 2)) + 1)) - 1))^2 - 1((-1((2((-1(-2(-1cos(3\u03c0x - 1) - 1)^2 + 1(-1cos(3\u03c0x - 1) - 1) + 5) + 2)/(-2(-2(-1cos(3\u03c0x - 1) - 1)^2 + 1(-1cos(3\u03c0x - 1) - 1) + 5) - 2)) - 3)/(3((-1(-2(-1cos(3\u03c0x - 1) - 1)^2 + 1(-1cos(3\u03c0x - 1) - 1) + 5) + 2)/(-2(-2(-1cos(3\u03c0x - 1) - 1)^2 + 1(-1cos(3\u03c0x - 1) - 1) + 5) - 2)) + 1)))/(-3((2((-1(-2(-1cos(3\u03c0x - 1) - 1)^2 + 1(-1cos(3\u03c0x - 1) - 1) + 5) + 2)/(-2(-2(-1cos(3\u03c0x - 1) - 1)^2 + 1(-1cos(3\u03c0x - 1) - 1) + 5) - 2)) - 3)/(3((-1(-2(-1cos(3\u03c0x - 1) - 1)^2 + 1(-1cos(3\u03c0x - 1) - 1) + 5) + 2)/(-2(-2(-1cos(3\u03c0x - 1) - 1)^2 + 1(-1cos(3\u03c0x - 1) - 1) + 5) - 2)) + 1)) - 1)) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 3(2e^(-1(1|(-1|(3|(1x^2 + 4x - 3)| - 3) - 3| - 2) - 1| - 1)) + 3) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = (-2(-1(3|(-1cos(2\u03c0((2(3|x - 1| + 1) + 2)/(-1(3|x - 1| + 1) + 2)) - 1) + 3) + 2| + 3) - 5) + 1)/(3(-1(3|(-1cos(2\u03c0((2(3|x - 1| + 1) + 2)/(-1(3|x - 1| + 1) + 2)) - 1) + 3) + 2| + 3) - 5) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -2(-1cos(1\u03c0((2(-2|(1(2x - 2)^2 + 2(2x - 2) - 4) - 2| + 1))/(-2(-2|(1(2x - 2)^2 + 2(2x - 2) - 4) - 2| + 1) - 3)) + 2) + 2) - 4 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = (-2((-2(2cos(2\u03c0(3(1(-1x^2 + 5x + 5)^2 + 4(-1x^2 + 5x + 5) + 3)^2 + 4(1(-1x^2 + 5x + 5)^2 + 4(-1x^2 + 5x + 5) + 3) + 5))) + 2)/(-3(2cos(2\u03c0(3(1(-1x^2 + 5x + 5)^2 + 4(-1x^2 + 5x + 5) + 3)^2 + 4(1(-1x^2 + 5x + 5)^2 + 4(-1x^2 + 5x + 5) + 3) + 5))) + 1)) - 2)/(-1((-2(2cos(2\u03c0(3(1(-1x^2 + 5x + 5)^2 + 4(-1x^2 + 5x + 5) + 3)^2 + 4(1(-1x^2 + 5x + 5)^2 + 4(-1x^2 + 5x + 5) + 3) + 5))) + 2)/(-3(2cos(2\u03c0(3(1(-1x^2 + 5x + 5)^2 + 4(-1x^2 + 5x + 5) + 3)^2 + 4(1(-1x^2 + 5x + 5)^2 + 4(-1x^2 + 5x + 5) + 3) + 5))) + 1))) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "52", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 1(-4(-1sin(2\u03c0(1((3((-1x + 3)/(-3x - 2)))/(-2((-1x + 3)/(-3x - 2)) - 1)) - 3) + 3) + 3) - 4)^2 + 3(-4(-1sin(2\u03c0(1((3((-1x + 3)/(-3x - 2)))/(-2((-1x + 3)/(-3x - 2)) - 1)) - 3) + 3) + 3) - 4) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = 1(2(-2|(1((1(1sin(3\u03c0x - 3) - 1) + 1)/(2(1sin(3\u03c0x - 3) - 1) + 1))^2 + 2((1(1sin(3\u03c0x - 3) - 1) + 1)/(2(1sin(3\u03c0x - 3) - 1) + 1)) - 5) + 3| + 2) - 5) + 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "90", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 2|((1(4(-1cos(2\u03c0(-1|(-1|x - 3| - 2) + 1| - 1) + 3)) + 3) + 2)/(3(4(-1cos(2\u03c0(-1|(-1|x - 3| - 2) + 1| - 1) + 3)) + 3) - 2)) + 2| where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "79", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 1sin(3\u03c0(1|(4(-1(3|(-1x^2 - 2x + 5) - 3| + 2) + 1)^2 + 5(-1(3|(-1x^2 - 2x + 5) - 3| + 2) + 1) + 2) + 2| - 3) + 2) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "84", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -1sin(3\u03c0(-5((3(3|(-2((2x + 1)/(1x + 1)) + 4) - 3| + 1) - 3)/(-3(3|(-2((2x + 1)/(1x + 1)) + 4) - 3| + 1) - 1))^2 + 5((3(3|(-2((2x + 1)/(1x + 1)) + 4) - 3| + 1) - 3)/(-3(3|(-2((2x + 1)/(1x + 1)) + 4) - 3| + 1) - 1)) + 5) - 1) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -2(-3cos(1\u03c0(1(-3|(-1|(-2x - 5) - 2| + 3) + 3| + 3)^2 + 1(-3|(-1|(-2x - 5) - 2| + 3) + 3| + 3) + 3) + 3) + 2) - 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "240", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -2cos(3\u03c0(5((1(1(2|(-3x - 4) + 3| - 3)^2 + 4(2|(-3x - 4) + 3| - 3)) + 2)/(2(1(2|(-3x - 4) + 3| - 3)^2 + 4(2|(-3x - 4) + 3| - 3)) + 2)) + 4) - 3) + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 4(2cos(1\u03c0(4(1(1(5x - 2)^2 - 5(5x - 2) + 4)^2 - 1(1(5x - 2)^2 - 5(5x - 2) + 4) - 2)^2 - 1(1(1(5x - 2)^2 - 5(5x - 2) + 4)^2 - 1(1(5x - 2)^2 - 5(5x - 2) + 4) - 2)) + 2) - 1)^2 + 2(2cos(1\u03c0(4(1(1(5x - 2)^2 - 5(5x - 2) + 4)^2 - 1(1(5x - 2)^2 - 5(5x - 2) + 4) - 2)^2 - 1(1(1(5x - 2)^2 - 5(5x - 2) + 4)^2 - 1(1(5x - 2)^2 - 5(5x - 2) + 4) - 2)) + 2) - 1) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 1(-1|(2cos(1\u03c0(5((-1(-1|x - 1| + 2) - 1)/(-1(-1|x - 1| + 2) - 3))^2 + 1((-1(-1|x - 1| + 2) - 1)/(-1(-1|x - 1| + 2) - 3)) + 4) - 2) + 2) + 3| + 3)^2 + 5(-1|(2cos(1\u03c0(5((-1(-1|x - 1| + 2) - 1)/(-1(-1|x - 1| + 2) - 3))^2 + 1((-1(-1|x - 1| + 2) - 1)/(-1(-1|x - 1| + 2) - 3)) + 4) - 2) + 2) + 3| + 3) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "194", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = -2|(4(2cos(2\u03c0((2(5(-2x + 3)^2 + 4(-2x + 3) - 4))/(3(5(-2x + 3)^2 + 4(-2x + 3) - 4) + 3)) + 2) - 3)^2 + 5(2cos(2\u03c0((2(5(-2x + 3)^2 + 4(-2x + 3) - 4))/(3(5(-2x + 3)^2 + 4(-2x + 3) - 4) + 3)) + 2) - 3)) + 3| + 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = -1(2sin(3\u03c0(1(3(-3(-2|x - 3| - 3)^2 - 5(-2|x - 3| - 3)) + 3) + 4) - 1) + 1)^2 - 5(2sin(3\u03c0(1(3(-3(-2|x - 3| - 3)^2 - 5(-2|x - 3| - 3)) + 3) + 4) - 1) + 1) + 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "155", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 1(5((3((-1(-2cos(3\u03c0((2x + 3)/(3x + 2)) - 2) + 2) + 1)/(-3(-2cos(3\u03c0((2x + 3)/(3x + 2)) - 2) + 2) - 3)) + 2)/(1((-1(-2cos(3\u03c0((2x + 3)/(3x + 2)) - 2) + 2) + 1)/(-3(-2cos(3\u03c0((2x + 3)/(3x + 2)) - 2) + 2) - 3))))^2 - 3)^2 - 2(5((3((-1(-2cos(3\u03c0((2x + 3)/(3x + 2)) - 2) + 2) + 1)/(-3(-2cos(3\u03c0((2x + 3)/(3x + 2)) - 2) + 2) - 3)) + 2)/(1((-1(-2cos(3\u03c0((2x + 3)/(3x + 2)) - 2) + 2) + 1)/(-3(-2cos(3\u03c0((2x + 3)/(3x + 2)) - 2) + 2) - 3))))^2 - 3) + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = (1(-5((-2(3sin(2\u03c0(-4(1x - 4) - 4) + 1) - 2) - 1)/(3(3sin(2\u03c0(-4(1x - 4) - 4) + 1) - 2) + 2)) + 4) + 3)/(-2(-5((-2(3sin(2\u03c0(-4(1x - 4) - 4) + 1) - 2) - 1)/(3(3sin(2\u03c0(-4(1x - 4) - 4) + 1) - 2) + 2)) + 4) + 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = (2((2(-5(2|(-3sin(1\u03c0(5x - 5) - 3) - 2) + 2| - 2)^2 - 4(2|(-3sin(1\u03c0(5x - 5) - 3) - 2) + 2| - 2) + 1) - 1)/(-1(-5(2|(-3sin(1\u03c0(5x - 5) - 3) - 2) + 2| - 2)^2 - 4(2|(-3sin(1\u03c0(5x - 5) - 3) - 2) + 2| - 2) + 1) + 2)) - 2)/(-2((2(-5(2|(-3sin(1\u03c0(5x - 5) - 3) - 2) + 2| - 2)^2 - 4(2|(-3sin(1\u03c0(5x - 5) - 3) - 2) + 2| - 2) + 1) - 1)/(-1(-5(2|(-3sin(1\u03c0(5x - 5) - 3) - 2) + 2| - 2)^2 - 4(2|(-3sin(1\u03c0(5x - 5) - 3) - 2) + 2| - 2) + 1) + 2)) - 2) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "187", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -5(5(-3cos(3\u03c0(-2|(1(-1x - 1) - 3) - 3| + 1)) - 1)^2 + 4(-3cos(3\u03c0(-2|(1(-1x - 1) - 3) - 3| + 1)) - 1) + 5)^2 - 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 2((-3(2(-2cos(2\u03c0(-4(-2|x - 1| + 2)^2 + 1(-2|x - 1| + 2) + 3) - 2) - 1)^2 + 2(-2cos(2\u03c0(-4(-2|x - 1| + 2)^2 + 1(-2|x - 1| + 2) + 3) - 2) - 1) - 3) - 3)/(2(2(-2cos(2\u03c0(-4(-2|x - 1| + 2)^2 + 1(-2|x - 1| + 2) + 3) - 2) - 1)^2 + 2(-2cos(2\u03c0(-4(-2|x - 1| + 2)^2 + 1(-2|x - 1| + 2) + 3) - 2) - 1) - 3) + 1))^2 - 3((-3(2(-2cos(2\u03c0(-4(-2|x - 1| + 2)^2 + 1(-2|x - 1| + 2) + 3) - 2) - 1)^2 + 2(-2cos(2\u03c0(-4(-2|x - 1| + 2)^2 + 1(-2|x - 1| + 2) + 3) - 2) - 1) - 3) - 3)/(2(2(-2cos(2\u03c0(-4(-2|x - 1| + 2)^2 + 1(-2|x - 1| + 2) + 3) - 2) - 1)^2 + 2(-2cos(2\u03c0(-4(-2|x - 1| + 2)^2 + 1(-2|x - 1| + 2) + 3) - 2) - 1) - 3) + 1)) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "256", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = (1(2cos(2\u03c0((1(1((2(4x + 3) + 3)/(2(4x + 3) - 3))^2 - 4) - 1)/(1(1((2(4x + 3) + 3)/(2(4x + 3) - 3))^2 - 4))) - 2) + 1) - 2)/(2(2cos(2\u03c0((1(1((2(4x + 3) + 3)/(2(4x + 3) - 3))^2 - 4) - 1)/(1(1((2(4x + 3) + 3)/(2(4x + 3) - 3))^2 - 4))) - 2) + 1) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = 2|(4((2(-2cos(3\u03c0(5(3|x - 1|) + 5) + 1) - 3) - 2)/(-3(-2cos(3\u03c0(5(3|x - 1|) + 5) + 1) - 3) - 2)) - 4)| - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "819", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -1(3|(-1|(-3e^(-1((3(-1x^2 + 5x))/(1(-1x^2 + 5x) + 3))) - 3) + 1| + 3)| - 2)^2 - 5(3|(-1|(-3e^(-1((3(-1x^2 + 5x))/(1(-1x^2 + 5x) + 3))) - 3) + 1| + 3)| - 2) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = (1(2(2|(-1(2cos(1\u03c0(2x^2 + 2x - 5)) - 3) + 4) - 1| + 2) + 4) + 2)/(1(2(2|(-1(2cos(1\u03c0(2x^2 + 2x - 5)) - 3) + 4) - 1| + 2) + 4)) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "187", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -1|(-3|(-2(-2e^(2(3(-3|x + 1|)^2 + 2(-3|x + 1|) - 3)) - 3) + 2) + 1| + 2) - 1| have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -2(-3(1cos(3\u03c0(-3|(-1(3x^2 - 1x + 5)^2 - 1(3x^2 - 1x + 5) - 5) + 2| + 2) + 1) - 1)^2 - 1(1cos(3\u03c0(-3|(-1(3x^2 - 1x + 5)^2 - 1(3x^2 - 1x + 5) - 5) + 2| + 2) + 1) - 1) - 1)^2 + 2(-3(1cos(3\u03c0(-3|(-1(3x^2 - 1x + 5)^2 - 1(3x^2 - 1x + 5) - 5) + 2| + 2) + 1) - 1)^2 - 1(1cos(3\u03c0(-3|(-1(3x^2 - 1x + 5)^2 - 1(3x^2 - 1x + 5) - 5) + 2| + 2) + 1) - 1) - 1) + 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "65", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -1cos(2\u03c0(-1(1(1|(5(4x^2 - 3x - 4) - 3) - 2| + 1)^2 + 2(1|(5(4x^2 - 3x - 4) - 3) - 2| + 1) - 3) - 5) - 1) + 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 2cos(1\u03c0(-3(-2|(-3(5(1x^2 - 3)^2 + 1(1x^2 - 3) - 1) - 1)| - 1) + 3) + 3) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "169", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -1(-3(1(-4(1|(-5x - 5) + 2| - 2) + 4)^2 + 4(-4(1|(-5x - 5) + 2| - 2) + 4) - 2) - 5)^2 + 1(-3(1(-4(1|(-5x - 5) + 2| - 2) + 4)^2 + 4(-4(1|(-5x - 5) + 2| - 2) + 4) - 2) - 5) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = -2|((-3((-2(-5(-3(-1x - 3)^2 - 5(-1x - 3) + 2) - 1) - 3)/(3(-5(-3(-1x - 3)^2 - 5(-1x - 3) + 2) - 1) + 2)))/(-1((-2(-5(-3(-1x - 3)^2 - 5(-1x - 3) + 2) - 1) - 3)/(3(-5(-3(-1x - 3)^2 - 5(-1x - 3) + 2) - 1) + 2)) - 2)) - 1| in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 3sin(1\u03c0(-1(-1(2(-1(-2x^2 + 3x - 2)^2 - 3(-2x^2 + 3x - 2) - 2) + 2) - 1) + 3)) + 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "239", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = 4(-1(1(-3|(-3(-2cos(2\u03c0x + 3) - 3) + 1)| + 2) + 5)^2 - 3(1(-3|(-3(-2cos(2\u03c0x + 3) - 3) + 1)| + 2) + 5) + 2)^2 - 2(-1(1(-3|(-3(-2cos(2\u03c0x + 3) - 3) + 1)| + 2) + 5)^2 - 3(1(-3|(-3(-2cos(2\u03c0x + 3) - 3) + 1)| + 2) + 5) + 2) - 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -5(2|(1e^(2(3|((-3(-3|x - 2| + 1) + 1)/(3(-3|x - 2| + 1) + 1)) - 3| - 3)) + 1) + 3| - 1)^2 + 4(2|(1e^(2(3|((-3(-3|x - 2| + 1) + 1)/(3(-3|x - 2| + 1) + 1)) - 3| - 3)) + 1) + 3| - 1) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 3(-4((1(-1(4(3|x - 3| - 2)^2 + 2(3|x - 3| - 2) - 1)^2 - 4(4(3|x - 3| - 2)^2 + 2(3|x - 3| - 2) - 1) + 5) + 3)/(2(-1(4(3|x - 3| - 2)^2 + 2(3|x - 3| - 2) - 1)^2 - 4(4(3|x - 3| - 2)^2 + 2(3|x - 3| - 2) - 1) + 5) + 3))^2 + 1((1(-1(4(3|x - 3| - 2)^2 + 2(3|x - 3| - 2) - 1)^2 - 4(4(3|x - 3| - 2)^2 + 2(3|x - 3| - 2) - 1) + 5) + 3)/(2(-1(4(3|x - 3| - 2)^2 + 2(3|x - 3| - 2) - 1)^2 - 4(4(3|x - 3| - 2)^2 + 2(3|x - 3| - 2) - 1) + 5) + 3)) - 5) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = (-3(-1(1|(-3(3|(1x^2 - 5x)| - 1) + 5)|) + 2) + 2)/(-3(-1(1|(-3(3|(1x^2 - 5x)| - 1) + 5)|) + 2) + 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = (3((-2(1|(-3e^(1(-3(4x^2 - 4x + 1)^2 + 1(4x^2 - 4x + 1) - 2))) - 2| - 1) - 2)/(-2(1|(-3e^(1(-3(4x^2 - 4x + 1)^2 + 1(4x^2 - 4x + 1) - 2))) - 2| - 1) - 3)) - 2)/(2((-2(1|(-3e^(1(-3(4x^2 - 4x + 1)^2 + 1(4x^2 - 4x + 1) - 2))) - 2| - 1) - 2)/(-2(1|(-3e^(1(-3(4x^2 - 4x + 1)^2 + 1(4x^2 - 4x + 1) - 2))) - 2| - 1) - 3)) - 1) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 4(-5((-2(-2(3e^(2(2|x - 2| + 3)) - 3)^2 - 1(3e^(2(2|x - 2| + 3)) - 3) + 2) - 3)/(1(-2(3e^(2(2|x - 2| + 3)) - 3)^2 - 1(3e^(2(2|x - 2| + 3)) - 3) + 2) - 3))^2 + 5((-2(-2(3e^(2(2|x - 2| + 3)) - 3)^2 - 1(3e^(2(2|x - 2| + 3)) - 3) + 2) - 3)/(1(-2(3e^(2(2|x - 2| + 3)) - 3)^2 - 1(3e^(2(2|x - 2| + 3)) - 3) + 2) - 3)) - 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = -1(-3(5(-2(-1(2cos(1\u03c0x + 2) - 1) - 2) + 5) + 3))^2 - 4(-3(5(-2(-1(2cos(1\u03c0x + 2) - 1) - 2) + 5) + 3)) + 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = (2(1(-2e^(2(3(-1(1|x - 2| + 1)) - 5)) - 1) - 4) + 1)/(-2(1(-2e^(2(3(-1(1|x - 2| + 1)) - 5)) - 1) - 4) + 3) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -4((1((-3((-2(2cos(2\u03c0((-3x - 1)/(-1x - 2)) - 1) - 3) - 2)/(1(2cos(2\u03c0((-3x - 1)/(-1x - 2)) - 1) - 3))) + 3)/(-2((-2(2cos(2\u03c0((-3x - 1)/(-1x - 2)) - 1) - 3) - 2)/(1(2cos(2\u03c0((-3x - 1)/(-1x - 2)) - 1) - 3))))) + 3)/(-2((-3((-2(2cos(2\u03c0((-3x - 1)/(-1x - 2)) - 1) - 3) - 2)/(1(2cos(2\u03c0((-3x - 1)/(-1x - 2)) - 1) - 3))) + 3)/(-2((-2(2cos(2\u03c0((-3x - 1)/(-1x - 2)) - 1) - 3) - 2)/(1(2cos(2\u03c0((-3x - 1)/(-1x - 2)) - 1) - 3)))))))^2 + 1((1((-3((-2(2cos(2\u03c0((-3x - 1)/(-1x - 2)) - 1) - 3) - 2)/(1(2cos(2\u03c0((-3x - 1)/(-1x - 2)) - 1) - 3))) + 3)/(-2((-2(2cos(2\u03c0((-3x - 1)/(-1x - 2)) - 1) - 3) - 2)/(1(2cos(2\u03c0((-3x - 1)/(-1x - 2)) - 1) - 3))))) + 3)/(-2((-3((-2(2cos(2\u03c0((-3x - 1)/(-1x - 2)) - 1) - 3) - 2)/(1(2cos(2\u03c0((-3x - 1)/(-1x - 2)) - 1) - 3))) + 3)/(-2((-2(2cos(2\u03c0((-3x - 1)/(-1x - 2)) - 1) - 3) - 2)/(1(2cos(2\u03c0((-3x - 1)/(-1x - 2)) - 1) - 3))))))) - 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "49", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 3(-3sin(1\u03c0((3((-2(2(2|x + 3| - 2) - 1))/(1(2(2|x + 3| - 2) - 1) + 3)) - 1)/(-2((-2(2(2|x + 3| - 2) - 1))/(1(2(2|x + 3| - 2) - 1) + 3)) + 3)) - 3))^2 + 4(-3sin(1\u03c0((3((-2(2(2|x + 3| - 2) - 1))/(1(2(2|x + 3| - 2) - 1) + 3)) - 1)/(-2((-2(2(2|x + 3| - 2) - 1))/(1(2(2|x + 3| - 2) - 1) + 3)) + 3)) - 3)) - 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -5((2(2cos(1\u03c0((-1(-3(-5x + 2) - 2) + 3)/(-2(-3(-5x + 2) - 2) - 1)) - 1) - 3) + 2)/(-3(2cos(1\u03c0((-1(-3(-5x + 2) - 2) + 3)/(-2(-3(-5x + 2) - 2) - 1)) - 1) - 3))) + 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -2(-2|(3|(-1(-3|(-1e^(-2x) + 1) + 2| + 2)^2 + 3(-3|(-1e^(-2x) + 1) + 2| + 2) - 2) + 3| + 1) + 1| - 3) - 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = 2|(-2(2(-3|(1cos(1\u03c0((-2x - 1)/(2x + 2)) + 3) - 1)| + 2)^2 + 5(-3|(1cos(1\u03c0((-2x - 1)/(2x + 2)) + 3) - 1)| + 2) - 2)^2 - 1(2(-3|(1cos(1\u03c0((-2x - 1)/(2x + 2)) + 3) - 1)| + 2)^2 + 5(-3|(1cos(1\u03c0((-2x - 1)/(2x + 2)) + 3) - 1)| + 2) - 2) + 5) + 2| + 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = -5(-1((2(-1(1(-2cos(3\u03c0x + 1) + 2) - 3) - 5) - 2)/(-2(-1(1(-2cos(3\u03c0x + 1) + 2) - 3) - 5) + 1))^2 + 4((2(-1(1(-2cos(3\u03c0x + 1) + 2) - 3) - 5) - 2)/(-2(-1(1(-2cos(3\u03c0x + 1) + 2) - 3) - 5) + 1)) - 3)^2 - 2(-1((2(-1(1(-2cos(3\u03c0x + 1) + 2) - 3) - 5) - 2)/(-2(-1(1(-2cos(3\u03c0x + 1) + 2) - 3) - 5) + 1))^2 + 4((2(-1(1(-2cos(3\u03c0x + 1) + 2) - 3) - 5) - 2)/(-2(-1(1(-2cos(3\u03c0x + 1) + 2) - 3) - 5) + 1)) - 3) - 4 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 1|(-1|((1(5(5(1|x + 3| + 1) - 5) - 2) + 2)/(-1(5(5(1|x + 3| + 1) - 5) - 2) + 3)) - 1|) + 2| + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = 1(-3(3(3sin(1\u03c0(1(1|x + 2|)) + 3) - 1)^2 + 5(3sin(1\u03c0(1(1|x + 2|)) + 3) - 1) - 5)^2 - 1(3(3sin(1\u03c0(1(1|x + 2|)) + 3) - 1)^2 + 5(3sin(1\u03c0(1(1|x + 2|)) + 3) - 1) - 5) + 4)^2 + 1(-3(3(3sin(1\u03c0(1(1|x + 2|)) + 3) - 1)^2 + 5(3sin(1\u03c0(1(1|x + 2|)) + 3) - 1) - 5)^2 - 1(3(3sin(1\u03c0(1(1|x + 2|)) + 3) - 1)^2 + 5(3sin(1\u03c0(1(1|x + 2|)) + 3) - 1) - 5) + 4) + 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "55", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = (1(-1(5((2(-5(2sin(1\u03c0x - 3) - 3)^2 + 5(2sin(1\u03c0x - 3) - 3) - 4) + 2)/(2(-5(2sin(1\u03c0x - 3) - 3)^2 + 5(2sin(1\u03c0x - 3) - 3) - 4) + 3))^2 + 5)^2 - 1(5((2(-5(2sin(1\u03c0x - 3) - 3)^2 + 5(2sin(1\u03c0x - 3) - 3) - 4) + 2)/(2(-5(2sin(1\u03c0x - 3) - 3)^2 + 5(2sin(1\u03c0x - 3) - 3) - 4) + 3))^2 + 5) - 1) + 3)/(-1(-1(5((2(-5(2sin(1\u03c0x - 3) - 3)^2 + 5(2sin(1\u03c0x - 3) - 3) - 4) + 2)/(2(-5(2sin(1\u03c0x - 3) - 3)^2 + 5(2sin(1\u03c0x - 3) - 3) - 4) + 3))^2 + 5)^2 - 1(5((2(-5(2sin(1\u03c0x - 3) - 3)^2 + 5(2sin(1\u03c0x - 3) - 3) - 4) + 2)/(2(-5(2sin(1\u03c0x - 3) - 3)^2 + 5(2sin(1\u03c0x - 3) - 3) - 4) + 3))^2 + 5) - 1)) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = 4((-1((-1(-2(-1|(2x - 1) + 3| + 3) - 2) - 1)/(1(-2(-1|(2x - 1) + 3| + 3) - 2) + 2)) + 1)/(-2((-1(-2(-1|(2x - 1) + 3| + 3) - 2) - 1)/(1(-2(-1|(2x - 1) + 3| + 3) - 2) + 2)) + 3))^2 + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = (3((3(-2(-1(3sin(2\u03c0((1x + 2)/(1x)) - 3) + 3)^2 + 2(3sin(2\u03c0((1x + 2)/(1x)) - 3) + 3))^2 + 2(-1(3sin(2\u03c0((1x + 2)/(1x)) - 3) + 3)^2 + 2(3sin(2\u03c0((1x + 2)/(1x)) - 3) + 3)) + 1) - 2)/(3(-2(-1(3sin(2\u03c0((1x + 2)/(1x)) - 3) + 3)^2 + 2(3sin(2\u03c0((1x + 2)/(1x)) - 3) + 3))^2 + 2(-1(3sin(2\u03c0((1x + 2)/(1x)) - 3) + 3)^2 + 2(3sin(2\u03c0((1x + 2)/(1x)) - 3) + 3)) + 1))) + 1)/(2((3(-2(-1(3sin(2\u03c0((1x + 2)/(1x)) - 3) + 3)^2 + 2(3sin(2\u03c0((1x + 2)/(1x)) - 3) + 3))^2 + 2(-1(3sin(2\u03c0((1x + 2)/(1x)) - 3) + 3)^2 + 2(3sin(2\u03c0((1x + 2)/(1x)) - 3) + 3)) + 1) - 2)/(3(-2(-1(3sin(2\u03c0((1x + 2)/(1x)) - 3) + 3)^2 + 2(3sin(2\u03c0((1x + 2)/(1x)) - 3) + 3))^2 + 2(-1(3sin(2\u03c0((1x + 2)/(1x)) - 3) + 3)^2 + 2(3sin(2\u03c0((1x + 2)/(1x)) - 3) + 3)) + 1))) + 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "78", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 2|((1((-3(-1cos(1\u03c0(-3(-2|x - 1| + 2) + 3) + 2) - 1))/(-2(-1cos(1\u03c0(-3(-2|x - 1| + 2) + 3) + 2) - 1) + 3)) - 3)/(3((-3(-1cos(1\u03c0(-3(-2|x - 1| + 2) + 3) + 2) - 1))/(-2(-1cos(1\u03c0(-3(-2|x - 1| + 2) + 3) + 2) - 1) + 3)) + 3)) - 2| - 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "121", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = (2(-2(3sin(1\u03c0(-1((3((1x - 3)/(-2x + 1)) + 2)/(2((1x - 3)/(-2x + 1)) - 1)) + 1)))) - 3)/(3(-2(3sin(1\u03c0(-1((3((1x - 3)/(-2x + 1)) + 2)/(2((1x - 3)/(-2x + 1)) - 1)) + 1)))) - 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 2((2(1|((1((1(-2cos(1\u03c0x + 1) + 2) - 3)/(-2(-2cos(1\u03c0x + 1) + 2) - 3)) + 2)/(-3((1(-2cos(1\u03c0x + 1) + 2) - 3)/(-2(-2cos(1\u03c0x + 1) + 2) - 3)) - 3)) + 3|) - 1)/(3(1|((1((1(-2cos(1\u03c0x + 1) + 2) - 3)/(-2(-2cos(1\u03c0x + 1) + 2) - 3)) + 2)/(-3((1(-2cos(1\u03c0x + 1) + 2) - 3)/(-2(-2cos(1\u03c0x + 1) + 2) - 3)) - 3)) + 3|) + 1))^2 - 2((2(1|((1((1(-2cos(1\u03c0x + 1) + 2) - 3)/(-2(-2cos(1\u03c0x + 1) + 2) - 3)) + 2)/(-3((1(-2cos(1\u03c0x + 1) + 2) - 3)/(-2(-2cos(1\u03c0x + 1) + 2) - 3)) - 3)) + 3|) - 1)/(3(1|((1((1(-2cos(1\u03c0x + 1) + 2) - 3)/(-2(-2cos(1\u03c0x + 1) + 2) - 3)) + 2)/(-3((1(-2cos(1\u03c0x + 1) + 2) - 3)/(-2(-2cos(1\u03c0x + 1) + 2) - 3)) - 3)) + 3|) + 1)) - 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = (3(5(-1(-2|(-1sin(3\u03c0(-1x^2 + 5x - 1) + 2) - 1) + 3| - 3)^2 - 3(-2|(-1sin(3\u03c0(-1x^2 + 5x - 1) + 2) - 1) + 3| - 3) - 5)^2 + 3(-1(-2|(-1sin(3\u03c0(-1x^2 + 5x - 1) + 2) - 1) + 3| - 3)^2 - 3(-2|(-1sin(3\u03c0(-1x^2 + 5x - 1) + 2) - 1) + 3| - 3) - 5) - 1) - 3)/(1(5(-1(-2|(-1sin(3\u03c0(-1x^2 + 5x - 1) + 2) - 1) + 3| - 3)^2 - 3(-2|(-1sin(3\u03c0(-1x^2 + 5x - 1) + 2) - 1) + 3| - 3) - 5)^2 + 3(-1(-2|(-1sin(3\u03c0(-1x^2 + 5x - 1) + 2) - 1) + 3| - 3)^2 - 3(-2|(-1sin(3\u03c0(-1x^2 + 5x - 1) + 2) - 1) + 3| - 3) - 5) - 1) - 2) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "141", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 5(3((3(2|(-2(1x^2 + 4x - 4)^2 + 3(1x^2 + 4x - 4) + 2) - 1|) - 3)/(-3(2|(-2(1x^2 + 4x - 4)^2 + 3(1x^2 + 4x - 4) + 2) - 1|) + 1)) - 4)^2 + 5(3((3(2|(-2(1x^2 + 4x - 4)^2 + 3(1x^2 + 4x - 4) + 2) - 1|) - 3)/(-3(2|(-2(1x^2 + 4x - 4)^2 + 3(1x^2 + 4x - 4) + 2) - 1|) + 1)) - 4) + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 2(2(-5((-1(-3sin(2\u03c0(-2x - 2) - 2) - 2) - 3)/(2(-3sin(2\u03c0(-2x - 2) - 2) - 2))) + 5)^2 - 4(-5((-1(-3sin(2\u03c0(-2x - 2) - 2) - 2) - 3)/(2(-3sin(2\u03c0(-2x - 2) - 2) - 2))) + 5) - 3)^2 + 3(2(-5((-1(-3sin(2\u03c0(-2x - 2) - 2) - 2) - 3)/(2(-3sin(2\u03c0(-2x - 2) - 2) - 2))) + 5)^2 - 4(-5((-1(-3sin(2\u03c0(-2x - 2) - 2) - 2) - 3)/(2(-3sin(2\u03c0(-2x - 2) - 2) - 2))) + 5) - 3) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "56", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 3cos(3\u03c0((-3((3(-1(2(1|x - 1| - 1)^2 - 4(1|x - 1| - 1) - 5)^2 - 3(2(1|x - 1| - 1)^2 - 4(1|x - 1| - 1) - 5) + 5) - 1)/(1(-1(2(1|x - 1| - 1)^2 - 4(1|x - 1| - 1) - 5)^2 - 3(2(1|x - 1| - 1)^2 - 4(1|x - 1| - 1) - 5) + 5) + 1)) - 3)/(2((3(-1(2(1|x - 1| - 1)^2 - 4(1|x - 1| - 1) - 5)^2 - 3(2(1|x - 1| - 1)^2 - 4(1|x - 1| - 1) - 5) + 5) - 1)/(1(-1(2(1|x - 1| - 1)^2 - 4(1|x - 1| - 1) - 5)^2 - 3(2(1|x - 1| - 1)^2 - 4(1|x - 1| - 1) - 5) + 5) + 1)) + 3)) - 2) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = -3cos(2\u03c0(-1(2|(-2((3(3x^2 + 5x - 2) + 2)/(3(3x^2 + 5x - 2) - 2))^2 + 2((3(3x^2 + 5x - 2) + 2)/(3(3x^2 + 5x - 2) - 2)) + 2) + 1| - 2)^2 - 5(2|(-2((3(3x^2 + 5x - 2) + 2)/(3(3x^2 + 5x - 2) - 2))^2 + 2((3(3x^2 + 5x - 2) + 2)/(3(3x^2 + 5x - 2) - 2)) + 2) + 1| - 2) - 2) + 2) + 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "50", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = (1(2cos(2\u03c0(-5((1(-4(-2|x + 1| + 1)^2 - 2(-2|x + 1| + 1) + 1) - 2)/(3(-4(-2|x + 1| + 1)^2 - 2(-2|x + 1| + 1) + 1) - 2)) - 4) + 3) - 2) + 2)/(2(2cos(2\u03c0(-5((1(-4(-2|x + 1| + 1)^2 - 2(-2|x + 1| + 1) + 1) - 2)/(3(-4(-2|x + 1| + 1)^2 - 2(-2|x + 1| + 1) + 1) - 2)) - 4) + 3) - 2) + 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = (3(-1((1(-1cos(2\u03c0(-4((2x - 1)/(-3x + 2))^2 - 4((2x - 1)/(-3x + 2)) - 2) + 1)) + 2)/(3(-1cos(2\u03c0(-4((2x - 1)/(-3x + 2))^2 - 4((2x - 1)/(-3x + 2)) - 2) + 1)) + 1))^2 + 4((1(-1cos(2\u03c0(-4((2x - 1)/(-3x + 2))^2 - 4((2x - 1)/(-3x + 2)) - 2) + 1)) + 2)/(3(-1cos(2\u03c0(-4((2x - 1)/(-3x + 2))^2 - 4((2x - 1)/(-3x + 2)) - 2) + 1)) + 1)) - 3) + 1)/(-3(-1((1(-1cos(2\u03c0(-4((2x - 1)/(-3x + 2))^2 - 4((2x - 1)/(-3x + 2)) - 2) + 1)) + 2)/(3(-1cos(2\u03c0(-4((2x - 1)/(-3x + 2))^2 - 4((2x - 1)/(-3x + 2)) - 2) + 1)) + 1))^2 + 4((1(-1cos(2\u03c0(-4((2x - 1)/(-3x + 2))^2 - 4((2x - 1)/(-3x + 2)) - 2) + 1)) + 2)/(3(-1cos(2\u03c0(-4((2x - 1)/(-3x + 2))^2 - 4((2x - 1)/(-3x + 2)) - 2) + 1)) + 1)) - 3) + 4) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -3(-1(-1((2(-1|(-4x^2 - 1x - 1) + 1|) + 3)/(-1(-1|(-4x^2 - 1x - 1) + 1|)))^2 + 3((2(-1|(-4x^2 - 1x - 1) + 1|) + 3)/(-1(-1|(-4x^2 - 1x - 1) + 1|))) - 4)) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = (3(5(-5(-3|(-3(2cos(1\u03c0x - 1) - 1)^2 - 3(2cos(1\u03c0x - 1) - 1) - 1) + 2| - 1)^2 - 2(-3|(-3(2cos(1\u03c0x - 1) - 1)^2 - 3(2cos(1\u03c0x - 1) - 1) - 1) + 2| - 1) + 3)^2 - 2(-5(-3|(-3(2cos(1\u03c0x - 1) - 1)^2 - 3(2cos(1\u03c0x - 1) - 1) - 1) + 2| - 1)^2 - 2(-3|(-3(2cos(1\u03c0x - 1) - 1)^2 - 3(2cos(1\u03c0x - 1) - 1) - 1) + 2| - 1) + 3) - 1) - 3)/(-2(5(-5(-3|(-3(2cos(1\u03c0x - 1) - 1)^2 - 3(2cos(1\u03c0x - 1) - 1) - 1) + 2| - 1)^2 - 2(-3|(-3(2cos(1\u03c0x - 1) - 1)^2 - 3(2cos(1\u03c0x - 1) - 1) - 1) + 2| - 1) + 3)^2 - 2(-5(-3|(-3(2cos(1\u03c0x - 1) - 1)^2 - 3(2cos(1\u03c0x - 1) - 1) - 1) + 2| - 1)^2 - 2(-3|(-3(2cos(1\u03c0x - 1) - 1)^2 - 3(2cos(1\u03c0x - 1) - 1) - 1) + 2| - 1) + 3) - 1) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "65", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 5(4(-2sin(1\u03c0(-5(2((-3x + 1)/(1x - 2))^2 - 5((-3x + 1)/(1x - 2)) + 5) + 1) - 2) + 1) + 3) + 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "161", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 2|(2cos(3\u03c0(2|((-2(-2((2x + 2)/(3x))^2 - 4((2x + 2)/(3x)) + 1) - 2)/(-2(-2((2x + 2)/(3x))^2 - 4((2x + 2)/(3x)) + 1) - 1)) + 2| - 3) + 2) + 3)| + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = (-3(3|(2cos(1\u03c0(-3(-1|(-3|x + 1| - 1) + 3| + 3) + 2) - 3) + 2) + 2| - 2))/(-2(3|(2cos(1\u03c0(-3(-1|(-3|x + 1| - 1) + 3| + 3) + 2) - 3) + 2) + 2| - 2) - 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "91", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 2sin(1\u03c0(3|(-2(3|(1|(3|x - 1| - 1) + 2| + 1)| + 2)^2 + 3(3|(1|(3|x - 1| - 1) + 2| + 1)| + 2) - 1) - 3|) + 2) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "125", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -3((-1((-3(-1|(-4(-4x^2 + 1x + 4)^2 - 1(-4x^2 + 1x + 4)) - 1| + 3) - 2)/(1(-1|(-4(-4x^2 + 1x + 4)^2 - 1(-4x^2 + 1x + 4)) - 1| + 3) - 2)) + 2)/(3((-3(-1|(-4(-4x^2 + 1x + 4)^2 - 1(-4x^2 + 1x + 4)) - 1| + 3) - 2)/(1(-1|(-4(-4x^2 + 1x + 4)^2 - 1(-4x^2 + 1x + 4)) - 1| + 3) - 2)) - 1))^2 - 2((-1((-3(-1|(-4(-4x^2 + 1x + 4)^2 - 1(-4x^2 + 1x + 4)) - 1| + 3) - 2)/(1(-1|(-4(-4x^2 + 1x + 4)^2 - 1(-4x^2 + 1x + 4)) - 1| + 3) - 2)) + 2)/(3((-3(-1|(-4(-4x^2 + 1x + 4)^2 - 1(-4x^2 + 1x + 4)) - 1| + 3) - 2)/(1(-1|(-4(-4x^2 + 1x + 4)^2 - 1(-4x^2 + 1x + 4)) - 1| + 3) - 2)) - 1)) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 5((-2(4(3cos(2\u03c0(-4(-4x^2 + 1x - 5)^2 + 1) - 2) + 1)) - 3)/(-3(4(3cos(2\u03c0(-4(-4x^2 + 1x - 5)^2 + 1) - 2) + 1)) + 4))^2 + 5((-2(4(3cos(2\u03c0(-4(-4x^2 + 1x - 5)^2 + 1) - 2) + 1)) - 3)/(-3(4(3cos(2\u03c0(-4(-4x^2 + 1x - 5)^2 + 1) - 2) + 1)) + 4)) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "56", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -5(5((-1(2(1|(-1cos(3\u03c0x) + 1) - 3| + 3)^2 - 1(1|(-1cos(3\u03c0x) + 1) - 3| + 3) - 3) + 2)/(-1(2(1|(-1cos(3\u03c0x) + 1) - 3| + 3)^2 - 1(1|(-1cos(3\u03c0x) + 1) - 3| + 3) - 3) - 2))^2 + 4((-1(2(1|(-1cos(3\u03c0x) + 1) - 3| + 3)^2 - 1(1|(-1cos(3\u03c0x) + 1) - 3| + 3) - 3) + 2)/(-1(2(1|(-1cos(3\u03c0x) + 1) - 3| + 3)^2 - 1(1|(-1cos(3\u03c0x) + 1) - 3| + 3) - 3) - 2)) + 5) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "59", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -5((-2(1((1(3|(2cos(3\u03c0x - 1) - 3) - 2|) + 3)/(2(3|(2cos(3\u03c0x - 1) - 3) - 2|) + 3)) + 2) + 3)/(-1(1((1(3|(2cos(3\u03c0x - 1) - 3) - 2|) + 3)/(2(3|(2cos(3\u03c0x - 1) - 3) - 2|) + 3)) + 2) - 2)) + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = -3cos(1\u03c0(-1|(1|((1(-1(-1x + 1) - 4))/(-2(-1(-1x + 1) - 4) + 3)) - 3| + 2) + 3| + 2)) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = 3(2(-5((3((-3(-3cos(1\u03c0x - 3)) + 3)/(-2(-3cos(1\u03c0x - 3)) - 3)) - 2)/(2((-3(-3cos(1\u03c0x - 3)) + 3)/(-2(-3cos(1\u03c0x - 3)) - 3)))) + 4) - 4)^2 - 1(2(-5((3((-3(-3cos(1\u03c0x - 3)) + 3)/(-2(-3cos(1\u03c0x - 3)) - 3)) - 2)/(2((-3(-3cos(1\u03c0x - 3)) + 3)/(-2(-3cos(1\u03c0x - 3)) - 3)))) + 4) - 4) + 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = 1(-3|(1|(4(-1e^(1(5x - 4)) - 1) - 3)| - 3) + 3| - 3) + 5 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -3|(-1sin(1\u03c0(-2(2|(2|((-2x + 3)/(-2x - 2)) + 3| - 2)| + 1)^2 + 4(2|(2|((-2x + 3)/(-2x - 2)) + 3| - 2)| + 1) - 5) + 3) + 2) + 3| + 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "355", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -5(-1(-1|(2|(-3(-3cos(1\u03c0x + 2) - 1)^2 - 4(-3cos(1\u03c0x + 2) - 1) + 3) - 3| - 2) - 3| + 3)^2 + 5(-1|(2|(-3(-3cos(1\u03c0x + 2) - 1)^2 - 4(-3cos(1\u03c0x + 2) - 1) + 3) - 3| - 2) - 3| + 3) + 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -1sin(2\u03c0((2((1((-3(3|(2|x + 2| + 1) - 2| - 2) - 2)/(-3(3|(2|x + 2| + 1) - 2| - 2) + 4)))/(2((-3(3|(2|x + 2| + 1) - 2| - 2) - 2)/(-3(3|(2|x + 2| + 1) - 2| - 2) + 4)) + 3)) + 3)/(3((1((-3(3|(2|x + 2| + 1) - 2| - 2) - 2)/(-3(3|(2|x + 2| + 1) - 2| - 2) + 4)))/(2((-3(3|(2|x + 2| + 1) - 2| - 2) - 2)/(-3(3|(2|x + 2| + 1) - 2| - 2) + 4)) + 3)))) + 1) - 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "64", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -2|((3((2(-5(1|(-5x - 1)| - 2) + 4))/(3(-5(1|(-5x - 1)| - 2) + 4))) + 3)/(-1((2(-5(1|(-5x - 1)| - 2) + 4))/(3(-5(1|(-5x - 1)| - 2) + 4))) + 2)) - 2| - 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "172", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 5((1(1(4((-3(-1x + 2))/(-1(-1x + 2) + 3))^2 - 1) - 1))/(-2(1(4((-3(-1x + 2))/(-1(-1x + 2) + 3))^2 - 1) - 1) - 2))^2 + 2((1(1(4((-3(-1x + 2))/(-1(-1x + 2) + 3))^2 - 1) - 1))/(-2(1(4((-3(-1x + 2))/(-1(-1x + 2) + 3))^2 - 1) - 1) - 2)) - 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -2|(3|(3|((-1(-1cos(3\u03c0(4x - 4)) + 2) - 3)/(-1(-1cos(3\u03c0(4x - 4)) + 2))) - 2| + 1) - 3| + 3) + 3| + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "480", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = (2(2(-3(1(5(1|x + 3| + 3)^2 + 3(1|x + 3| + 3) - 3) - 2) + 1)^2 + 1(-3(1(5(1|x + 3| + 3)^2 + 3(1|x + 3| + 3) - 3) - 2) + 1) - 2) + 2)/(-3(2(-3(1(5(1|x + 3| + 3)^2 + 3(1|x + 3| + 3) - 3) - 2) + 1)^2 + 1(-3(1(5(1|x + 3| + 3)^2 + 3(1|x + 3| + 3) - 3) - 2) + 1) - 2) - 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "91", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -3(5(2(1(5(-2sin(3\u03c0x - 1) + 3)^2 - 3(-2sin(3\u03c0x - 1) + 3) + 5) - 2) + 2)^2 - 2(2(1(5(-2sin(3\u03c0x - 1) + 3)^2 - 3(-2sin(3\u03c0x - 1) + 3) + 5) - 2) + 2) - 4) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "57", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 2cos(3\u03c0(1|((-3(2(2(-1|x + 2| + 1) + 3)^2 - 4(2(-1|x + 2| + 1) + 3) + 2) - 2)/(-1(2(2(-1|x + 2| + 1) + 3)^2 - 4(2(-1|x + 2| + 1) + 3) + 2) + 2)) + 2| - 1) + 1) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "51", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -3(-4((2(-1(1|(-2cos(3\u03c0x) - 2)| + 3) - 2) + 3)/(-2(-1(1|(-2cos(3\u03c0x) - 2)| + 3) - 2) + 3))^2 + 1((2(-1(1|(-2cos(3\u03c0x) - 2)| + 3) - 2) + 3)/(-2(-1(1|(-2cos(3\u03c0x) - 2)| + 3) - 2) + 3)) - 4) - 5 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = 3|(-4(-2sin(3\u03c0(1(2|(1x^2 + 5x - 5) + 2| + 3)^2 - 2(2|(1x^2 + 5x - 5) + 2| + 3) - 3) - 1) + 2)^2 + 3(-2sin(3\u03c0(1(2|(1x^2 + 5x - 5) + 2| + 3)^2 - 2(2|(1x^2 + 5x - 5) + 2| + 3) - 3) - 1) + 2)) + 2| - 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "111", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 2|((-2(1(-1|((-3(1x^2 - 5x + 2) - 2)/(3(1x^2 - 5x + 2) + 3)) + 3|) + 1))/(1(1(-1|((-3(1x^2 - 5x + 2) - 2)/(3(1x^2 - 5x + 2) + 3)) + 3|) + 1) + 2)) + 1| - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -2cos(3\u03c0(-1(3|(-1(-3(1x - 2) + 1)^2 + 2(-3(1x - 2) + 1) - 1) + 3| + 2) - 4) - 1) - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "221", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -2(-3|(-5(5(-3e^(-2(1x^2 - 5x - 5)) + 1)^2 + 5(-3e^(-2(1x^2 - 5x - 5)) + 1) - 3)^2 + 3(5(-3e^(-2(1x^2 - 5x - 5)) + 1)^2 + 5(-3e^(-2(1x^2 - 5x - 5)) + 1) - 3) + 2)| + 2)^2 + 3(-3|(-5(5(-3e^(-2(1x^2 - 5x - 5)) + 1)^2 + 5(-3e^(-2(1x^2 - 5x - 5)) + 1) - 3)^2 + 3(5(-3e^(-2(1x^2 - 5x - 5)) + 1)^2 + 5(-3e^(-2(1x^2 - 5x - 5)) + 1) - 3) + 2)| + 2) + 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = 1((-3(-2(-1(-1cos(1\u03c0(3x^2 - 4x - 2) - 2) + 3) - 2)^2 - 1(-1(-1cos(1\u03c0(3x^2 - 4x - 2) - 2) + 3) - 2) + 1) + 2)/(1(-2(-1(-1cos(1\u03c0(3x^2 - 4x - 2) - 2) + 3) - 2)^2 - 1(-1(-1cos(1\u03c0(3x^2 - 4x - 2) - 2) + 3) - 2) + 1) + 1))^2 + 5((-3(-2(-1(-1cos(1\u03c0(3x^2 - 4x - 2) - 2) + 3) - 2)^2 - 1(-1(-1cos(1\u03c0(3x^2 - 4x - 2) - 2) + 3) - 2) + 1) + 2)/(1(-2(-1(-1cos(1\u03c0(3x^2 - 4x - 2) - 2) + 3) - 2)^2 - 1(-1(-1cos(1\u03c0(3x^2 - 4x - 2) - 2) + 3) - 2) + 1) + 1)) + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "361", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 3(-1cos(2\u03c0(-4(-1((2(-5x^2 - 2x - 4) - 3)/(2(-5x^2 - 2x - 4)))^2 + 1((2(-5x^2 - 2x - 4) - 3)/(2(-5x^2 - 2x - 4)))) + 3) + 1) + 3)^2 + 2(-1cos(2\u03c0(-4(-1((2(-5x^2 - 2x - 4) - 3)/(2(-5x^2 - 2x - 4)))^2 + 1((2(-5x^2 - 2x - 4) - 3)/(2(-5x^2 - 2x - 4)))) + 3) + 1) + 3) + 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -2((3(2sin(2\u03c0(-1(-1|(-3|x + 1| - 2) + 3| - 3)^2 - 3(-1|(-3|x + 1| - 2) + 3| - 3) - 5)) - 1) - 3)/(3(2sin(2\u03c0(-1(-1|(-3|x + 1| - 2) + 3| - 3)^2 - 3(-1|(-3|x + 1| - 2) + 3| - 3) - 5)) - 1) - 2))^2 - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "512", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -3|((-2((-2(4(-1(-4x^2 - 5x + 3)^2 + 5(-4x^2 - 5x + 3) + 5)^2 - 3(-1(-4x^2 - 5x + 3)^2 + 5(-4x^2 - 5x + 3) + 5) + 4) - 1)/(3(4(-1(-4x^2 - 5x + 3)^2 + 5(-4x^2 - 5x + 3) + 5)^2 - 3(-1(-4x^2 - 5x + 3)^2 + 5(-4x^2 - 5x + 3) + 5) + 4) - 1)) + 1)/(2((-2(4(-1(-4x^2 - 5x + 3)^2 + 5(-4x^2 - 5x + 3) + 5)^2 - 3(-1(-4x^2 - 5x + 3)^2 + 5(-4x^2 - 5x + 3) + 5) + 4) - 1)/(3(4(-1(-4x^2 - 5x + 3)^2 + 5(-4x^2 - 5x + 3) + 5)^2 - 3(-1(-4x^2 - 5x + 3)^2 + 5(-4x^2 - 5x + 3) + 5) + 4) - 1)))) + 2| + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = 5(-2|((3(-1(1(1x^2 + 5x) - 4) - 2) - 3)/(-1(-1(1(1x^2 + 5x) - 4) - 2) + 2)) - 2| + 1)^2 - 2(-2|((3(-1(1(1x^2 + 5x) - 4) - 2) - 3)/(-1(-1(1(1x^2 + 5x) - 4) - 2) + 2)) - 2| + 1) + 5 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}