{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -4(1sin(2\u03c0(2|(-3x^2 - 4x + 5) - 1| - 3) - 3) - 3) - 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "487", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 1cos(1\u03c0((-1(-3|(3x^2 - 3x + 3) - 3| + 2) + 3)/(2(-3|(3x^2 - 3x + 3) - 3| + 2) + 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": "How many local maxima does the function f(x) = (2(1|(-2e^(-2(-4x^2 - 1)) - 2) + 3| - 3))/(3(1|(-2e^(-2(-4x^2 - 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": "40", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 2sin(3\u03c0(-2(-1|(-3|x - 1| - 2) - 2|)^2 + 3(-1|(-3|x - 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": "454", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 2(-2cos(2\u03c0(3(-2x - 2) + 2) - 2) - 1) - 2 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": "Determine the count of local maxima for the function f(x) = 1sin(2\u03c0(-3(3|((-2x)/(2x - 1))| - 3)^2 + 1(3|((-2x)/(2x - 1))| - 3) - 5) - 1) 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 total count of local extrema points for the function f(x) = -2e^(2(-4(-2((1x - 3)/(2x + 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 total number of local minima and maxima for f(x) = 2(5(-1cos(2\u03c0(5x^2 - 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": "477", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = (1((1(1(-2sin(2\u03c0x - 3) - 2) - 3) + 1)/(3(1(-2sin(2\u03c0x - 3) - 2) - 3) + 2)) - 3)/(2((1(1(-2sin(2\u03c0x - 3) - 2) - 3) + 1)/(3(1(-2sin(2\u03c0x - 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": "20", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 5(-2sin(3\u03c0(-1|(2|x - 1| - 2) + 1| + 1) - 1) - 2)^2 + 5(-2sin(3\u03c0(-1|(2|x - 1| - 2) + 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": "122", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -4(-1sin(2\u03c0(2|(-5x - 3) + 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": "399", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = (-1(1(5(3sin(1\u03c0x - 2) - 3) - 2)) + 3)/(-3(1(5(3sin(1\u03c0x - 2) - 3) - 2)) + 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": "Find the number of local maximum points for f(x) = -1|(5(1cos(3\u03c0(2|x| - 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": "61", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -2(-5(-2cos(1\u03c0((2x + 2)/(2x)) + 2) + 2)^2 - 4(-2cos(1\u03c0((2x + 2)/(2x)) + 2) + 2) + 1) - 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 minima does the function f(x) = 1|((2(-2cos(2\u03c0(-3x - 3) + 2) - 2) - 2)/(-3(-2cos(2\u03c0(-3x - 3) + 2) - 2))) - 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 minima does the function f(x) = 3(1(-2cos(2\u03c0((3x + 3)/(1x)) - 1) + 3)^2 + 1(-2cos(2\u03c0((3x + 3)/(1x)) - 1) + 3) + 3)^2 + 4(1(-2cos(2\u03c0((3x + 3)/(1x)) - 1) + 3)^2 + 1(-2cos(2\u03c0((3x + 3)/(1x)) - 1) + 3) + 3) - 2 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": "Find the total number of local minima and maxima for f(x) = 1(3sin(2\u03c0((1(-2|x + 3| - 1) - 2)/(1(-2|x + 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": "9", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -1((3(2(1cos(3\u03c0x + 3)) + 1) + 2)/(1(2(1cos(3\u03c0x + 3)) + 1)))^2 - 4((3(2(1cos(3\u03c0x + 3)) + 1) + 2)/(1(2(1cos(3\u03c0x + 3)) + 1))) - 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) = (-1(3|((-1(-4x^2 - 2x + 1) + 2)/(2(-4x^2 - 2x + 1))) + 3| - 3) - 2)/(-1(3|((-1(-4x^2 - 2x + 1) + 2)/(2(-4x^2 - 2x + 1))) + 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": "How many local minima does the function f(x) = -1(-3|(3(-1sin(3\u03c0x + 1) + 3)^2 + 4(-1sin(3\u03c0x + 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": "30", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = 3(3sin(3\u03c0((3(-4x + 3))/(1(-4x + 3) + 1)) - 2) + 3)^2 + 1(3sin(3\u03c0((3(-4x + 3))/(1(-4x + 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": "19", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = (-2(-4(-2cos(2\u03c0(1|x + 2| + 2) + 3) - 2) - 5) + 3)/(-1(-4(-2cos(2\u03c0(1|x + 2| + 2) + 3) - 2) - 5) + 2) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = (-2((-2(3(2cos(2\u03c0x - 2))^2 - 3(2cos(2\u03c0x - 2)) + 1) + 1)/(1(3(2cos(2\u03c0x - 2))^2 - 3(2cos(2\u03c0x - 2)) + 1) + 2)) + 3)/(-3((-2(3(2cos(2\u03c0x - 2))^2 - 3(2cos(2\u03c0x - 2)) + 1) + 1)/(1(3(2cos(2\u03c0x - 2))^2 - 3(2cos(2\u03c0x - 2)) + 1) + 2)) - 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 minima for the function f(x) = (1(-1cos(3\u03c0((1(-1x) + 2)/(-2(-1x) + 3)) + 3) + 1) + 2)/(2(-1cos(3\u03c0((1(-1x) + 2)/(-2(-1x) + 3)) + 3) + 1) + 3) 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) = (1(3cos(2\u03c0(-1(2|x + 1|)^2 + 5(2|x + 1|) - 5) - 1) + 2) - 2)/(-3(3cos(2\u03c0(-1(2|x + 1|)^2 + 5(2|x + 1|) - 5) - 1) + 2)) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "278", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = (-1(-2|((-1(1cos(2\u03c0x + 3) + 2) - 3)/(2(1cos(2\u03c0x + 3) + 2) - 1)) - 1| + 1) + 1)/(-2(-2|((-1(1cos(2\u03c0x + 3) + 2) - 3)/(2(1cos(2\u03c0x + 3) + 2) - 1)) - 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": "How many local extrema (minima and maxima combined) does the function f(x) = (-2(-5(3sin(1\u03c0(-2x) + 3) + 1)^2 - 1(3sin(1\u03c0(-2x) + 3) + 1) - 3) + 1)/(-1(-5(3sin(1\u03c0(-2x) + 3) + 1)^2 - 1(3sin(1\u03c0(-2x) + 3) + 1) - 3) + 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": "Find the number of local minimum points for f(x) = -3sin(3\u03c0(1(-1|((1x - 1)/(-3x - 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": "13", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 3|(-5(-1cos(2\u03c0(5x + 3) + 2) - 3) + 2)| have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "100", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 3cos(1\u03c0(-1|((2(-5x^2 - 3x - 1) + 3)/(-1(-5x^2 - 3x - 1) - 1)) + 3| - 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 total number of local minima and maxima for f(x) = (-3(3(-2(-2sin(1\u03c0x) + 1) + 3)^2 + 5(-2(-2sin(1\u03c0x) + 1) + 3)))/(3(3(-2(-2sin(1\u03c0x) + 1) + 3)^2 + 5(-2(-2sin(1\u03c0x) + 1) + 3)) + 2) 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": "Find the number of local maximum points for f(x) = -2cos(3\u03c0((-1(2|(4x + 1) - 2|) - 3)/(-2(2|(4x + 1) - 2|) - 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": "Determine the total count of local extrema points for the function f(x) = -2cos(2\u03c0((3(1|(4x + 1) + 3|) - 1)/(2(1|(4x + 1) + 3|) - 1)) + 3) - 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) = 1cos(3\u03c0(5(3|(-2|x + 3| - 1) + 1| - 3)^2 - 4(3|(-2|x + 3| - 1) + 1| - 3) + 4)) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "172", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -3(-1(-3|(1cos(1\u03c0x - 3)) - 3| + 3)^2 + 3(-3|(1cos(1\u03c0x - 3)) - 3| + 3) + 5)^2 - 5(-1(-3|(1cos(1\u03c0x - 3)) - 3| + 3)^2 + 3(-3|(1cos(1\u03c0x - 3)) - 3| + 3) + 5) - 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(-2(3cos(3\u03c0(2x^2 + 4x - 1) + 3)) + 3)^2 - 1(-2(3cos(3\u03c0(2x^2 + 4x - 1) + 3)) + 3) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "449", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -1e^(-2(-4(-1|(-3x - 1) - 3|)^2 - 2(-1|(-3x - 1) - 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 number of local minimum points for f(x) = -2(5(1|(-3sin(1\u03c0x + 3)) - 1| - 3)^2 + 3(1|(-3sin(1\u03c0x + 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": "11", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 1|(-1sin(3\u03c0(-2(-2x - 5)^2 - 5(-2x - 5))) + 3)| - 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "505", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 2(1cos(1\u03c0(1(-1x^2 - 4x)^2 + 1(-1x^2 - 4x) + 2)) + 2)^2 + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "185", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -3(-4(1|(3|x + 2|) - 3| - 3) + 3)^2 - 1(-4(1|(3|x + 2|) - 3| - 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 extrema (minima and maxima combined) does the function f(x) = -2|(1cos(1\u03c0((-2((-2x + 2)/(1x)) + 2)/(-1((-2x + 2)/(1x)) + 2)) + 1) + 2) - 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": "How many local minima does the function f(x) = 1sin(2\u03c0(-1(-3((3x + 1)/(-1x + 3))^2 + 4)^2 - 3(-3((3x + 1)/(-1x + 3))^2 + 4) + 2)) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "184", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = (-1(3cos(3\u03c0(-1|((1x - 1)/(-3x - 3))| + 1) + 2)) + 1)/(-3(3cos(3\u03c0(-1|((1x - 1)/(-3x - 3))| + 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": "Determine the count of local minima for the function f(x) = (1((1(1|(-3cos(2\u03c0x - 3) + 1) + 2| - 1) - 1)/(-3(1|(-3cos(2\u03c0x - 3) + 1) + 2| - 1))))/(3((1(1|(-3cos(2\u03c0x - 3) + 1) + 2| - 1) - 1)/(-3(1|(-3cos(2\u03c0x - 3) + 1) + 2| - 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": "Find the number of local maximum points for f(x) = 2sin(2\u03c0((-2(-2|(1x - 3) - 1| + 1) - 3)/(-3(-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": "10", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -3e^(2(5(4((-2x + 1)/(2x + 2))^2 + 1((-2x + 1)/(2x + 2)) - 3) - 2)) + 2 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": "How many local maxima does the function f(x) = -5(3|(1cos(3\u03c0(1x^2 - 2x + 1)) + 3) - 2| + 2) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "287", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = 2(-2|(3|((1x - 1)/(-2x - 1)) + 1| + 2) - 2| + 2)^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 number of local minimum points for f(x) = (2(-3(-5(-3cos(3\u03c0x + 3) - 2) + 3) + 1))/(-1(-3(-5(-3cos(3\u03c0x + 3) - 2) + 3) + 1) + 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": "How many local minima does the function f(x) = -1cos(1\u03c0(3(3(2x^2 + 5x + 3)^2 + 2(2x^2 + 5x + 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": "93", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = -4(3(-1cos(1\u03c0((-3x + 2)/(-3x))) + 2) - 1)^2 + 5(3(-1cos(1\u03c0((-3x + 2)/(-3x))) + 2) - 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 minimum points for f(x) = (3(-1|(-3sin(2\u03c0(3x - 5) - 3) - 1) - 3| - 2) + 2)/(2(-1|(-3sin(2\u03c0(3x - 5) - 3) - 1) - 3| - 2) + 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": "Determine the count of local maxima for the function f(x) = 3sin(3\u03c0(1|((3((-2x + 1)/(-2x + 3)) + 3)/(-3((-2x + 1)/(-2x + 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": "7", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 1(2(2sin(3\u03c0(-4x^2 - 2x + 4) + 1) - 2) - 2)^2 - 5(2(2sin(3\u03c0(-4x^2 - 2x + 4) + 1) - 2) - 2) - 2 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 total count of local extrema points for the function f(x) = -2(1|(1(3sin(2\u03c0x - 3) - 1) + 2) + 2| + 2)^2 - 1(1|(1(3sin(2\u03c0x - 3) - 1) + 2) + 2| + 2) + 5 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) = -1|(2|(1(-3|x + 1| - 2)^2 + 5(-3|x + 1| - 2) - 3)| - 1) + 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": "Find the number of local minimum points for f(x) = 3cos(3\u03c0((1(1(-5x + 1)))/(3(1(-5x + 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": "Determine the total count of local extrema points for the function f(x) = 1(-1cos(2\u03c0(2(1x + 5)^2 + 4(1x + 5) - 2) - 1) + 3) 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((2(4(-2sin(3\u03c0x + 1) - 3)^2 + 5(-2sin(3\u03c0x + 1) - 3) + 5))/(3(4(-2sin(3\u03c0x + 1) - 3)^2 + 5(-2sin(3\u03c0x + 1) - 3) + 5) - 1))^2 - 4((2(4(-2sin(3\u03c0x + 1) - 3)^2 + 5(-2sin(3\u03c0x + 1) - 3) + 5))/(3(4(-2sin(3\u03c0x + 1) - 3)^2 + 5(-2sin(3\u03c0x + 1) - 3) + 5) - 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": "Find the number of local minimum points for f(x) = (2((1(-2cos(1\u03c0(-1x + 2) + 3)) + 1)/(2(-2cos(1\u03c0(-1x + 2) + 3)))))/(2((1(-2cos(1\u03c0(-1x + 2) + 3)) + 1)/(2(-2cos(1\u03c0(-1x + 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": "How many local extrema (minima and maxima combined) does the function f(x) = 5((3(-4(3cos(3\u03c0x + 2) + 3) - 3) + 3)/(-2(-4(3cos(3\u03c0x + 2) + 3) - 3) - 1))^2 - 3((3(-4(3cos(3\u03c0x + 2) + 3) - 3) + 3)/(-2(-4(3cos(3\u03c0x + 2) + 3) - 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 total count of local extrema points for the function f(x) = -1sin(1\u03c0((-2(2|((-3x - 3)/(3x - 2)) + 3|) + 2)/(-2(2|((-3x - 3)/(3x - 2)) + 3|) + 3)) + 3) - 1 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 maxima does the function f(x) = -4(-3sin(1\u03c0(5(1|x + 2| + 1) + 2) + 2) - 1) + 1 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 maximum points for f(x) = -3|((-3(-3cos(1\u03c0(3|x| + 3) + 1) - 3) - 1)/(-2(-3cos(1\u03c0(3|x| + 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": "59", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -4(-1|(3(-4x^2 + 5x + 3)^2 + 4(-4x^2 + 5x + 3) - 3) + 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) = -1(1cos(3\u03c0(-2|(-3x - 5)| - 1) + 3) + 3)^2 - 3(1cos(3\u03c0(-2|(-3x - 5)| - 1) + 3) + 3) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "361", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -2(-1|(1(3sin(2\u03c0x + 2) + 3) + 2) + 2| - 3)^2 - 3(-1|(1(3sin(2\u03c0x + 2) + 3) + 2) + 2| - 3) + 4 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 minima for the function f(x) = -4(1|(-2(-2sin(3\u03c0x - 1) + 3)^2 + 2(-2sin(3\u03c0x - 1) + 3) - 1) - 3| - 3)^2 - 3(1|(-2(-2sin(3\u03c0x - 1) + 3)^2 + 2(-2sin(3\u03c0x - 1) + 3) - 1) - 3| - 3) + 5 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 minima for the function f(x) = -5(-1sin(2\u03c0(3((2x - 2)/(-1x))^2 - 5((2x - 2)/(-1x)) + 5) + 3) - 2) + 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "70", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = 2|(-2sin(2\u03c0((3(-3|x + 3| - 3) + 3)/(-2(-3|x + 3| - 3) - 2)) - 1) + 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 minima for the function f(x) = -2|(-4(-3(-2|x - 2|)^2 - 4(-2|x - 2|)) - 5) + 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": "Find the number of local maximum points for f(x) = -1((-1(1|(-1cos(3\u03c0x + 1) - 1) + 2| - 3) + 1)/(-2(1|(-1cos(3\u03c0x + 1) - 1) + 2| - 3) - 3))^2 - 5((-1(1|(-1cos(3\u03c0x + 1) - 1) + 2| - 3) + 1)/(-2(1|(-1cos(3\u03c0x + 1) - 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": "143", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -1sin(1\u03c0(3|(-5(-1|x - 1| + 3)^2 - 2(-1|x - 1| + 3) + 4) - 3|) - 2) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "255", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = (3(2sin(1\u03c0((-2(-3|x + 1| + 1) + 3)/(-2(-3|x + 1| + 1) - 1)) + 3) + 3) - 1)/(-3(2sin(1\u03c0((-2(-3|x + 1| + 1) + 3)/(-2(-3|x + 1| + 1) - 1)) + 3) + 3) - 3) in the interval [-10, 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) = 2|(-2sin(3\u03c0(-1|((2x + 2)/(-2x - 1)) + 1| - 2)) + 3)| + 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": "Determine the count of local maxima for the function f(x) = (2((-2(-1sin(2\u03c0(5x^2 + 4x - 4) + 2) - 3) - 1)/(-1(-1sin(2\u03c0(5x^2 + 4x - 4) + 2) - 3) - 2)) - 3)/(3((-2(-1sin(2\u03c0(5x^2 + 4x - 4) + 2) - 3) - 1)/(-1(-1sin(2\u03c0(5x^2 + 4x - 4) + 2) - 3) - 2)) + 2) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "166", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -3(3(-2|(3cos(1\u03c0x + 1) + 3) + 3| - 1) + 1)^2 + 3(3(-2|(3cos(1\u03c0x + 1) + 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": "20", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -2sin(3\u03c0(1(-1(2x - 5) - 1) + 3) - 3) - 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": "Find the total number of local minima and maxima for f(x) = 1|(-2|(3sin(3\u03c0((-1x + 2)/(-2x + 3)) - 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": "21", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 1cos(1\u03c0(1(1(2|x|) + 2)^2 - 5(1(2|x|) + 2) - 5) + 2) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "567", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = (1((3(1cos(3\u03c0((2x + 1)/(-1x + 2)) - 2)) - 3)/(1(1cos(3\u03c0((2x + 1)/(-1x + 2)) - 2)) + 2)) - 3)/(-1((3(1cos(3\u03c0((2x + 1)/(-1x + 2)) - 2)) - 3)/(1(1cos(3\u03c0((2x + 1)/(-1x + 2)) - 2)) + 2)) - 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 extrema (minima and maxima combined) does the function f(x) = 2|(2cos(1\u03c0(1((2x)/(-1x + 3))^2 + 2((2x)/(-1x + 3)) + 1) - 3) - 2) - 2| - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "98", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -4(5(-4(-3cos(2\u03c0x) - 1) + 2) - 5)^2 + 1(5(-4(-3cos(2\u03c0x) - 1) + 2) - 5) + 1 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 number of local maximum points for f(x) = (-1(-2(-1sin(2\u03c0(5x^2 + 5x + 2) + 3) - 3) + 2) + 1)/(3(-2(-1sin(2\u03c0(5x^2 + 5x + 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": "206", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -2(-2sin(2\u03c0(-2((-3x - 1)/(1x - 2))^2 - 4((-3x - 1)/(1x - 2)) + 1) + 3) + 3) 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 total count of local extrema points for the function f(x) = (-3((3(1|(-1sin(1\u03c0x + 3) + 1)| + 1) + 3)/(2(1|(-1sin(1\u03c0x + 3) + 1)| + 1) - 3)) + 2)/(-1((3(1|(-1sin(1\u03c0x + 3) + 1)| + 1) + 3)/(2(1|(-1sin(1\u03c0x + 3) + 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": "Determine the count of local minima for the function f(x) = -1(1(-3sin(3\u03c0((1x + 1)/(2x - 1)) + 3) + 3)^2 + 2(-3sin(3\u03c0((1x + 1)/(2x - 1)) + 3) + 3) - 5)^2 + 5(1(-3sin(3\u03c0((1x + 1)/(2x - 1)) + 3) + 3)^2 + 2(-3sin(3\u03c0((1x + 1)/(2x - 1)) + 3) + 3) - 5) - 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": "Determine the count of local maxima for the function f(x) = 3|(3|(2sin(3\u03c0(5x^2 - 4x - 2) + 3) - 2) - 2|) + 3| - 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "245", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = (-1(-3|((-1(-3|x| + 2) - 3)/(-3(-3|x| + 2) - 3)) + 2| + 3) + 1)/(-3(-3|((-1(-3|x| + 2) - 3)/(-3(-3|x| + 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": "5", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = (-3(5(3|(2sin(1\u03c0x - 1) + 2) - 3| + 2)) + 1)/(3(5(3|(2sin(1\u03c0x - 1) + 2) - 3| + 2)) + 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": "How many local extrema (minima and maxima combined) does the function f(x) = 3|(-2(2sin(3\u03c0(-1x - 2) + 2) - 1)^2 + 1(2sin(3\u03c0(-1x - 2) + 2) - 1) + 5) - 1| - 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": "Find the number of local minimum points for f(x) = (3(4(-1e^(-1(3x - 3)) + 1) + 5) - 2)/(2(4(-1e^(-1(3x - 3)) + 1) + 5) + 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) = -2|(1sin(2\u03c0(-5(-1x^2 - 2)^2 + 5(-1x^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": "139", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 2|(-1|(-3sin(2\u03c0((2x - 2)/(1x + 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": "98", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -1(-2sin(3\u03c0(-1|((1x - 2)/(-3x - 2)) + 2| + 1) + 2) + 2) - 4 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 maximum points for f(x) = 3cos(3\u03c0(1|(-3(-3|x| + 2) + 4) - 3| - 3) + 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "270", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = (3((1(-3cos(3\u03c0((-3x + 2)/(2x + 3)) + 1) - 3) - 3)/(-1(-3cos(3\u03c0((-3x + 2)/(2x + 3)) + 1) - 3) + 2)) - 1)/(1((1(-3cos(3\u03c0((-3x + 2)/(2x + 3)) + 1) - 3) - 3)/(-1(-3cos(3\u03c0((-3x + 2)/(2x + 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": "61", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 2(-4((-1(1cos(2\u03c0x + 3) + 2) + 3)/(3(1cos(2\u03c0x + 3) + 2) + 2)) - 2)^2 - 3(-4((-1(1cos(2\u03c0x + 3) + 2) + 3)/(3(1cos(2\u03c0x + 3) + 2) + 2)) - 2) - 4 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) = 2cos(2\u03c0(4((1(1x + 1) + 2)/(1(1x + 1)))^2 - 5((1(1x + 1) + 2)/(1(1x + 1))) - 3)) - 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "105", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = -3|(3(1cos(1\u03c0(-1|x + 2|) + 1) - 3)^2 - 1(1cos(1\u03c0(-1|x + 2|) + 1) - 3)) - 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) = -3(-2(1|(1cos(2\u03c0x - 2) + 3) + 1|) + 4) - 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) = -3|(2(2(1x^2 + 5x - 3)^2 - 4(1x^2 + 5x - 3) + 3)^2 - 5) - 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 extrema (minima and maxima combined) does the function f(x) = -2((2((2(3|x + 3| - 2) - 2)/(2(3|x + 3| - 2) - 1)) + 2)/(2((2(3|x + 3| - 2) - 2)/(2(3|x + 3| - 2) - 1)) - 3))^2 - 3((2((2(3|x + 3| - 2) - 2)/(2(3|x + 3| - 2) - 1)) + 2)/(2((2(3|x + 3| - 2) - 2)/(2(3|x + 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": "5", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -1cos(1\u03c0(-3|((-3(1|x - 3| - 3) - 1)/(1(1|x - 3| - 3) - 2)) - 2|) - 2) + 2 where -10 \u2264 x \u2264 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) = -5((3(-1cos(1\u03c0(2x + 2) + 3)) - 1)/(1(-1cos(1\u03c0(2x + 2) + 3)) - 2))^2 + 3((3(-1cos(1\u03c0(2x + 2) + 3)) - 1)/(1(-1cos(1\u03c0(2x + 2) + 3)) - 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": "Find the total number of local minima and maxima for f(x) = 3|(3sin(1\u03c0(1|(1|x - 3| + 3)| + 2) - 1) - 3) - 3| - 2 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": "How many local minima does the function f(x) = -1|(3(2|(2e^(1x) - 2) - 2| - 3)^2 + 3(2|(2e^(1x) - 2) - 2| - 3) - 4)| + 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) = 3|(3(-2sin(2\u03c0(3x - 4) - 2) - 1)^2 + 5(-2sin(2\u03c0(3x - 4) - 2) - 1))| + 2 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": "Determine the total count of local extrema points for the function f(x) = -2(1|(2(-1x^2 - 5x + 2)^2 + 3(-1x^2 - 5x + 2) - 1) - 2|) + 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": "Determine the total count of local extrema points for the function f(x) = 4(-1(-2(-1|x + 1| + 1)^2 - 2(-1|x + 1| + 1) - 1) - 4)^2 + 1(-1(-2(-1|x + 1| + 1)^2 - 2(-1|x + 1| + 1) - 1) - 4) + 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": "Determine the count of local maxima for the function f(x) = 1|(-5(5(5x^2 + 4x - 5)^2 + 5(5x^2 + 4x - 5) + 1) - 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 total number of local minima and maxima for f(x) = 1(-3cos(1\u03c0(4(5x^2 + 1x + 2)^2 + 4(5x^2 + 1x + 2) + 3)) - 1) - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "144", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = 1cos(1\u03c0(-3(1|(-1x^2 - 4x + 1)| + 3)^2 - 3(1|(-1x^2 - 4x + 1)| + 3) + 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 maxima does the function f(x) = -4((-1(-2(1cos(1\u03c0x) - 3)^2 - 2(1cos(1\u03c0x) - 3) + 5) - 2)/(3(-2(1cos(1\u03c0x) - 3)^2 - 2(1cos(1\u03c0x) - 3) + 5) + 2)) - 4 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) = 3(-2(3|(3cos(1\u03c0x - 3) - 1) - 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": "Find the number of local maximum points for f(x) = 1((-1(-2(1sin(3\u03c0x - 3) - 3)^2 + 3(1sin(3\u03c0x - 3) - 3) - 1))/(-1(-2(1sin(3\u03c0x - 3) - 3)^2 + 3(1sin(3\u03c0x - 3) - 3) - 1) - 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": "Determine the count of local maxima for the function f(x) = 5(-3(1cos(2\u03c0(1x - 1)) + 1) - 2)^2 - 3(-3(1cos(2\u03c0(1x - 1)) + 1) - 2) + 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": "Determine the total count of local extrema points for the function f(x) = -3(3(-2sin(2\u03c0(-1|x - 2| + 1) - 3) + 1) - 4) 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 maxima for the function f(x) = 1(2|(1((3x)/(-2x))^2 - 5((3x)/(-2x)) + 4) - 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) = -5(3sin(2\u03c0(-3|(1|x - 3| - 1)|) + 1) + 3)^2 + 4(3sin(2\u03c0(-3|(1|x - 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": "243", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 1(-1sin(1\u03c0(4(3|x + 3| + 2)^2 + 4(3|x + 3| + 2) - 1) - 3) - 3)^2 - 3(-1sin(1\u03c0(4(3|x + 3| + 2)^2 + 4(3|x + 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": "209", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 2(3cos(3\u03c0(1((3x - 1)/(-1x - 1))^2 - 4((3x - 1)/(-1x - 1)) + 1) - 3) - 1)^2 - 3(3cos(3\u03c0(1((3x - 1)/(-1x - 1))^2 - 4((3x - 1)/(-1x - 1)) + 1) - 3) - 1) - 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "132", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = 5((-1(3(-1sin(1\u03c0x - 1) - 1) + 3) + 3)/(-3(3(-1sin(1\u03c0x - 1) - 1) + 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": "Find the number of local maximum points for f(x) = 1((-1(-3|(2sin(2\u03c0x) + 3) - 2| - 2) + 2)/(1(-3|(2sin(2\u03c0x) + 3) - 2| - 2))) - 5 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": "Find the total number of local minima and maxima for f(x) = 1|(2(-3cos(2\u03c0(-1x + 1) - 2) - 1)^2 - 1(-3cos(2\u03c0(-1x + 1) - 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": "159", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 3sin(2\u03c0(3(-2|(2x^2 + 3x - 3) + 1|) - 1) - 2) + 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "483", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = (-2(-1sin(3\u03c0(-2|(5x^2 - 2x) + 2| - 1) - 1) + 3) - 1)/(-2(-1sin(3\u03c0(-2|(5x^2 - 2x) + 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": "218", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = 5(1(4(-1cos(1\u03c0x - 2) + 3)^2 - 1(-1cos(1\u03c0x - 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": "How many local extrema (minima and maxima combined) does the function f(x) = 1|(1|(3sin(3\u03c0(4x + 2) - 2) + 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": "Find the number of local minimum points for f(x) = 2cos(3\u03c0(-5(-1|(4x - 5) - 1| + 3) + 2) + 2) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "400", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -5(-1cos(2\u03c0(-1(3x^2 - 4x - 1)^2 - 3(3x^2 - 4x - 1) + 4) + 3) - 1)^2 - 4(-1cos(2\u03c0(-1(3x^2 - 4x - 1)^2 - 3(3x^2 - 4x - 1) + 4) + 3) - 1) + 4 in the interval [-10, 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) = (3((1(2|(-1cos(2\u03c0x + 2) + 2) + 1| - 2) + 3)/(-2(2|(-1cos(2\u03c0x + 2) + 2) + 1| - 2) - 1)))/(1((1(2|(-1cos(2\u03c0x + 2) + 2) + 1| - 2) + 3)/(-2(2|(-1cos(2\u03c0x + 2) + 2) + 1| - 2) - 1)) + 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 1(1cos(2\u03c0(5(-1|x + 1|)^2 - 4(-1|x + 1|) + 5) + 2) + 2)^2 - 3(1cos(2\u03c0(5(-1|x + 1|)^2 - 4(-1|x + 1|) + 5) + 2) + 2) - 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "223", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -5(2sin(2\u03c0((-3(2x^2 - 1x - 4) - 3)/(-3(2x^2 - 1x - 4) + 1)) + 3))^2 + 2(2sin(2\u03c0((-3(2x^2 - 1x - 4) - 3)/(-3(2x^2 - 1x - 4) + 1)) + 3)) - 3 in the interval [-10, 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) = (3(2(1sin(3\u03c0(1x^2 + 4x - 5) + 3))^2 + 1(1sin(3\u03c0(1x^2 + 4x - 5) + 3)) + 1) + 2)/(3(2(1sin(3\u03c0(1x^2 + 4x - 5) + 3))^2 + 1(1sin(3\u03c0(1x^2 + 4x - 5) + 3)) + 1) + 3) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "498", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -4(-2|(-1|(-3sin(3\u03c0x + 1) - 1) - 2| - 1) - 2| + 2)^2 + 3 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": "Find the total number of local minima and maxima for f(x) = -3sin(2\u03c0((-2(-5(-2|x| + 1)^2 - 2(-2|x| + 1) + 5) - 3)/(-2(-5(-2|x| + 1)^2 - 2(-2|x| + 1) + 5) + 3)) + 3) + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "47", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 3|(-1sin(2\u03c0((-3((-2x - 3)/(-3x - 2)) + 2)/(2((-2x - 3)/(-3x - 2)) + 1)) + 2) + 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": "Find the number of local minimum points for f(x) = (2(2(-5(-1sin(1\u03c0x + 1) + 2)^2 + 4(-1sin(1\u03c0x + 1) + 2) - 3)^2 + 4(-5(-1sin(1\u03c0x + 1) + 2)^2 + 4(-1sin(1\u03c0x + 1) + 2) - 3) - 4) + 3)/(3(2(-5(-1sin(1\u03c0x + 1) + 2)^2 + 4(-1sin(1\u03c0x + 1) + 2) - 3)^2 + 4(-5(-1sin(1\u03c0x + 1) + 2)^2 + 4(-1sin(1\u03c0x + 1) + 2) - 3) - 4) - 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": "Determine the count of local maxima for the function f(x) = -2|(3e^(2(4(3x - 4))) + 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 minima does the function f(x) = -3cos(1\u03c0(-3(2((3x - 2)/(2x + 3)) + 2)^2 - 3(2((3x - 2)/(2x + 3)) + 2) + 5) + 2) - 1 have 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) = 2(-2cos(2\u03c0(4(-3x - 2) + 2) - 1) - 2) - 2 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": "Determine the count of local minima for the function f(x) = (2(2(-4(4x^2 + 3x - 2)^2 + 1(4x^2 + 3x - 2) + 3)^2 - 2(-4(4x^2 + 3x - 2)^2 + 1(4x^2 + 3x - 2) + 3) + 4) - 1)/(-3(2(-4(4x^2 + 3x - 2)^2 + 1(4x^2 + 3x - 2) + 3)^2 - 2(-4(4x^2 + 3x - 2)^2 + 1(4x^2 + 3x - 2) + 3) + 4) + 2) 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) = 1(-2|(-3sin(2\u03c0(1|x + 2| + 1) - 3) - 3)| + 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": "Determine the total count of local extrema points for the function f(x) = -3(-2sin(2\u03c0(-4(1x^2 - 3x - 1) - 4) - 3) + 2)^2 + 2(-2sin(2\u03c0(-4(1x^2 - 3x - 1) - 4) - 3) + 2) - 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "450", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = 3(3|(-2cos(1\u03c0((1x)/(-2x - 1)) - 3) + 3) + 2| + 3)^2 + 5(3|(-2cos(1\u03c0((1x)/(-2x - 1)) - 3) + 3) + 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": "Find the total number of local minima and maxima for f(x) = -3(5((1(-2sin(3\u03c0x - 2) + 2) - 1)/(-2(-2sin(3\u03c0x - 2) + 2) - 2)) - 3)^2 - 2(5((1(-2sin(3\u03c0x - 2) + 2) - 1)/(-2(-2sin(3\u03c0x - 2) + 2) - 2)) - 3) - 4 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) = (-2(1(2cos(2\u03c0((-2x + 1)/(2x - 3)) - 1) - 2) + 3) + 1)/(-1(1(2cos(2\u03c0((-2x + 1)/(2x - 3)) - 1) - 2) + 3) - 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": "How many local maxima does the function f(x) = 1|(1|((1(3sin(3\u03c0x - 1) - 3) + 3)/(-2(3sin(3\u03c0x - 1) - 3) - 3))| - 2)| + 2 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) = -5((2(-1|(-3sin(2\u03c0x + 3) + 1)| + 1))/(-2(-1|(-3sin(2\u03c0x + 3) + 1)| + 1) - 3))^2 - 3((2(-1|(-3sin(2\u03c0x + 3) + 1)| + 1))/(-2(-1|(-3sin(2\u03c0x + 3) + 1)| + 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": "How many local maxima does the function f(x) = (-1(-5(-1cos(2\u03c0((-1x - 2)/(-3x - 1)) + 2) - 1) - 1) + 1)/(2(-5(-1cos(2\u03c0((-1x - 2)/(-3x - 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": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -4(5((2(3sin(2\u03c0x + 3) + 3) + 3)/(-1(3sin(2\u03c0x + 3) + 3) - 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": "Determine the count of local maxima for the function f(x) = (1(-2(-3(-1sin(2\u03c0x) - 1) - 4) - 3) - 2)/(3(-2(-3(-1sin(2\u03c0x) - 1) - 4) - 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": "Determine the total count of local extrema points for the function f(x) = (1(-1cos(1\u03c0(-1|(-3x^2 - 5x + 2) + 1| + 2) + 3)) + 1)/(3(-1cos(1\u03c0(-1|(-3x^2 - 5x + 2) + 1| + 2) + 3)) - 1) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "561", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = -2sin(2\u03c0(1|(-5(-5x^2 - 2x - 4) + 5) - 1| - 3) - 3) - 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "235", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -1sin(1\u03c0(-1((-1((1x - 2)/(-2x + 3)) - 3)/(-3((1x - 2)/(-2x + 3)) - 2))^2 + 4((-1((1x - 2)/(-2x + 3)) - 3)/(-3((1x - 2)/(-2x + 3)) - 2))) + 3) + 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "58", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -3cos(2\u03c0(-4(3(2x^2 - 1) - 5)^2 + 2) - 1) 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) = 1|(1(2(3cos(3\u03c0x) - 1)^2 + 5(3cos(3\u03c0x) - 1) + 4) + 2) + 1| - 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 count of local minima for the function f(x) = (-3(-4(-3cos(3\u03c0(5x^2 - 3x - 5) - 3) + 3)^2 + 2(-3cos(3\u03c0(5x^2 - 3x - 5) - 3) + 3) + 5) - 2)/(1(-4(-3cos(3\u03c0(5x^2 - 3x - 5) - 3) + 3)^2 + 2(-3cos(3\u03c0(5x^2 - 3x - 5) - 3) + 3) + 5) - 2) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "357", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -5(3(1sin(3\u03c0(-1x^2 + 5x + 2) - 1) + 3) + 3)^2 - 5(3(1sin(3\u03c0(-1x^2 + 5x + 2) - 1) + 3) + 3) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "528", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 1cos(2\u03c0(1(-5(-3|x - 1| - 1)^2 + 2(-3|x - 1| - 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": "226", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 4((-2(2(-1cos(3\u03c0x - 3) + 3)^2 - 4(-1cos(3\u03c0x - 3) + 3) + 5) - 1)/(1(2(-1cos(3\u03c0x - 3) + 3)^2 - 4(-1cos(3\u03c0x - 3) + 3) + 5) - 2))^2 - 1((-2(2(-1cos(3\u03c0x - 3) + 3)^2 - 4(-1cos(3\u03c0x - 3) + 3) + 5) - 1)/(1(2(-1cos(3\u03c0x - 3) + 3)^2 - 4(-1cos(3\u03c0x - 3) + 3) + 5) - 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": "Find the number of local minimum points for f(x) = -2(-4(1cos(1\u03c0(-1x + 5)) - 2) - 3)^2 - 5(-4(1cos(1\u03c0(-1x + 5)) - 2) - 3) - 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) = 3sin(2\u03c0((-3(3((1x + 2)/(3x + 1))^2 - 1((1x + 2)/(3x + 1)) + 2) - 2)/(1(3((1x + 2)/(3x + 1))^2 - 1((1x + 2)/(3x + 1)) + 2) - 3)) - 1) + 3 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 number of local minimum points for f(x) = (3(-3cos(2\u03c0(2|((2x - 1)/(3x + 3))| + 3) + 3) - 3) + 3)/(2(-3cos(2\u03c0(2|((2x - 1)/(3x + 3))| + 3) + 3) - 3) + 2) where -10 \u2264 x \u2264 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|((3(4(-1sin(2\u03c0x + 3) - 2) - 2) - 1)/(2(4(-1sin(2\u03c0x + 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": "20", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = (3(-3cos(1\u03c0(5(-2x^2 + 4)^2 + 5(-2x^2 + 4) + 2)) - 2) - 1)/(2(-3cos(1\u03c0(5(-2x^2 + 4)^2 + 5(-2x^2 + 4) + 2)) - 2)) 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": "How many local maxima does the function f(x) = 2(1(-3sin(2\u03c0(2|x|) - 3)) + 2) - 4 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": "Find the total number of local minima and maxima for f(x) = 1(2|(-5(2|x + 3| - 1) - 1) - 2| - 3)^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": "How many local extrema (minima and maxima combined) does the function f(x) = 2sin(3\u03c0(4(-1((1x + 1)/(2x - 3)) + 5)^2 + 2(-1((1x + 1)/(2x - 3)) + 5)) + 3) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "219", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 5(-3(3cos(2\u03c0((-3x - 1)/(2x + 2)) + 2) + 1))^2 - 4(-3(3cos(2\u03c0((-3x - 1)/(2x + 2)) + 2) + 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) = 5(-1sin(3\u03c0(1((3x)/(-3x - 3)) - 1) + 2))^2 + 2(-1sin(3\u03c0(1((3x)/(-3x - 3)) - 1) + 2)) + 4 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": "Determine the count of local minima for the function f(x) = -2|(-3sin(2\u03c0(3(5x^2 - 4x + 1) - 5) - 3) - 3) - 2| in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "243", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -2|(3sin(2\u03c0(-1|(-1|x - 2| - 2) + 3| - 1) - 2)) + 3| - 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "43", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 3(1e^(-2(-4(-5x^2 + 2x + 2)^2 - 4(-5x^2 + 2x + 2) + 4)) + 3)^2 - 5(1e^(-2(-4(-5x^2 + 2x + 2)^2 - 4(-5x^2 + 2x + 2) + 4)) + 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 total number of local minima and maxima for f(x) = (3(-2sin(3\u03c0(2((2x)/(3x + 1)) - 4) - 1) - 1) - 2)/(-3(-2sin(3\u03c0(2((2x)/(3x + 1)) - 4) - 1) - 1) + 4) 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": "Find the number of local maximum points for f(x) = 5(-3(-2|(3sin(1\u03c0x) - 3) - 2| + 2)^2 + 4(-2|(3sin(1\u03c0x) - 3) - 2| + 2) - 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": "Determine the count of local maxima for the function f(x) = -2|(1(3(1x^2 - 5x - 1)^2 + 4(1x^2 - 5x - 1) - 3)^2 + 2(3(1x^2 - 5x - 1)^2 + 4(1x^2 - 5x - 1) - 3) + 5) - 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": "Determine the count of local minima for the function f(x) = -2(-2cos(3\u03c0(5(1x - 1)^2 + 4(1x - 1) + 5)) + 1) - 4 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "248", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 1(3sin(3\u03c0(4((3x - 2)/(-2x + 3))^2 + 2((3x - 2)/(-2x + 3)) - 4) + 1) - 1) + 4 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) = -3(-3cos(1\u03c0(1(-3|x - 3| + 1) - 1) - 3) + 1)^2 - 1(-3cos(1\u03c0(1(-3|x - 3| + 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": "121", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -1(1(-3sin(3\u03c0((-3x + 1)/(-1x - 2)) - 3) - 1) - 4)^2 + 1(1(-3sin(3\u03c0((-3x + 1)/(-1x - 2)) - 3) - 1) - 4) 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 extrema (minima and maxima combined) does the function f(x) = 1(2sin(1\u03c0(-5(2|x + 3| - 1))) - 3) + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "201", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = -1|(-1(-1(2|x + 1| + 2) + 2)^2 - 2(-1(2|x + 1| + 2) + 2) + 5) + 1| - 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": "How many local minima does the function f(x) = 2cos(1\u03c0(2|(-1(3|x + 1| + 2)^2 - 4(3|x + 1| + 2) + 4) + 1| + 3) - 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "259", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -5(-1(3sin(1\u03c0(-2|x + 1| + 1) + 1) + 2)^2 - 2(3sin(1\u03c0(-2|x + 1| + 1) + 1) + 2) + 5)^2 + 5(-1(3sin(1\u03c0(-2|x + 1| + 1) + 1) + 2)^2 - 2(3sin(1\u03c0(-2|x + 1| + 1) + 1) + 2) + 5) + 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": "Find the total number of local minima and maxima for f(x) = -4(-3sin(2\u03c0(-4(4x - 4) - 5) - 1) + 3) - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "640", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 1|(3cos(2\u03c0(3(5x - 5)^2 - 5(5x - 5) - 1)) - 3) - 3| in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "404", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 4(2(5(1cos(3\u03c0x - 3) - 1)^2 + 5(1cos(3\u03c0x - 3) - 1) - 5)^2 + 3(5(1cos(3\u03c0x - 3) - 1)^2 + 5(1cos(3\u03c0x - 3) - 1) - 5)) - 2 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": "How many local minima does the function f(x) = (-1(-2|((-1(1sin(3\u03c0x + 3) - 1) + 1)/(1(1sin(3\u03c0x + 3) - 1) + 3)) + 2|) + 1)/(-1(-2|((-1(1sin(3\u03c0x + 3) - 1) + 1)/(1(1sin(3\u03c0x + 3) - 1) + 3)) + 2|) - 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|(5(-2sin(1\u03c0((1x - 2)/(-2x + 3)) - 1) - 2) + 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": "How many local extrema (minima and maxima combined) does the function f(x) = -1|(-5((-1(3sin(3\u03c0x) - 2) + 3)/(-3(3sin(3\u03c0x) - 2) - 1)) - 4) + 3| + 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 maxima does the function f(x) = (-1(-2sin(2\u03c0(-5(3|x + 1| - 3)^2 + 5(3|x + 1| - 3) - 3) - 2) - 1) - 1)/(3(-2sin(2\u03c0(-5(3|x + 1| - 3)^2 + 5(3|x + 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": "163", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -4(-1|((1(2cos(2\u03c0x - 1) + 3) - 1)/(-2(2cos(2\u03c0x - 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": "40", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = (-1(-2cos(3\u03c0(3(-3|x + 1| - 3)^2 - 2(-3|x + 1| - 3)) - 1) - 1) + 2)/(3(-2cos(3\u03c0(3(-3|x + 1| - 3)^2 - 2(-3|x + 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": "221", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -3|(2cos(2\u03c0(3(-1|x - 1| + 1) + 2) - 1) + 3) + 1| + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "121", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -5(2sin(3\u03c0((-1(-2|x + 3|) - 2)/(-2(-2|x + 3|) - 1)) - 3))^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 minima for the function f(x) = -2|(-3cos(2\u03c0((2(2x + 1) - 2)/(2(2x + 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": "10", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -3cos(3\u03c0(-5(3|(1|x - 2|) + 2|)^2 - 5(3|(1|x - 2|) + 2|) - 1) - 2) - 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "183", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -2|(-1sin(1\u03c0(5(-3x - 4)^2 - 5(-3x - 4) + 5)) - 1) + 2| + 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "488", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 3cos(1\u03c0(-5(-5(1x^2 - 1x + 2) + 4)^2 - 5(-5(1x^2 - 1x + 2) + 4) + 1) - 2) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "138", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 5(-2sin(1\u03c0(2|(-1|x - 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": "Find the number of local minimum points for f(x) = -3cos(1\u03c0(3(4(1|x - 2| - 2) - 2)^2 + 1(4(1|x - 2| - 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": "241", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 5(2|(-2(-3sin(2\u03c0x - 2)) - 4) - 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) = 5(-4(4(-3sin(3\u03c0x + 1) + 3)^2 - 3(-3sin(3\u03c0x + 1) + 3) - 1)^2 + 4(4(-3sin(3\u03c0x + 1) + 3)^2 - 3(-3sin(3\u03c0x + 1) + 3) - 1)) + 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "89", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -2((2(-1(3cos(3\u03c0x) - 3)^2 + 4(3cos(3\u03c0x) - 3) + 4) + 1)/(2(-1(3cos(3\u03c0x) - 3)^2 + 4(3cos(3\u03c0x) - 3) + 4) + 2))^2 + 3((2(-1(3cos(3\u03c0x) - 3)^2 + 4(3cos(3\u03c0x) - 3) + 4) + 1)/(2(-1(3cos(3\u03c0x) - 3)^2 + 4(3cos(3\u03c0x) - 3) + 4) + 2)) + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "132", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 1sin(1\u03c0(-3(4(1x - 2)^2 - 4(1x - 2) - 5)) - 2) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "511", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 5(1|(3|(-2sin(2\u03c0x - 1) + 2) - 3| - 3) - 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 maxima does the function f(x) = (3(-3sin(1\u03c0(-2(-3|x - 2| - 2) - 3) + 1) + 1) + 3)/(-2(-3sin(1\u03c0(-2(-3|x - 2| - 2) - 3) + 1) + 1) - 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "233", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = 2(3((-2(-3x^2 + 2x - 2) - 2)/(-3(-3x^2 + 2x - 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": "Determine the count of local maxima for the function f(x) = (-1(1(1e^(2(1x^2 - 1x - 1)) + 2) + 4) + 2)/(-2(1(1e^(2(1x^2 - 1x - 1)) + 2) + 4) - 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(1|((-1(-1x^2 - 3x - 2) + 1)/(-3(-1x^2 - 3x - 2))) - 3| - 2)^2 - 2(1|((-1(-1x^2 - 3x - 2) + 1)/(-3(-1x^2 - 3x - 2))) - 3| - 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": "Find the number of local minimum points for f(x) = 1sin(3\u03c0(3|(-3|(5x^2 + 4x - 5) + 2| + 1) + 3|) + 3) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "222", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = -3|(2|(5(2|x + 2| - 3)^2 - 5) + 1| + 3) - 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) = -2(-3sin(2\u03c0(2(5x + 3)^2 - 3(5x + 3) + 2) + 2) + 1) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "405", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 2(-1(3sin(2\u03c0(-3x^2 + 1) - 2) + 2) + 5) + 5 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "449", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = 5(-1sin(3\u03c0(-2(-1x - 1)^2 + 2(-1x - 1) + 5) - 1) - 2)^2 - 5(-1sin(3\u03c0(-2(-1x - 1)^2 + 2(-1x - 1) + 5) - 1) - 2) + 4 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 count of local minima for the function f(x) = -2(2|(-3cos(2\u03c0(2x^2 - 1x + 1) - 2) + 3) + 2| + 3)^2 - 5(2|(-3cos(2\u03c0(2x^2 - 1x + 1) - 2) + 3) + 2| + 3) - 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "260", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 2(-2e^(1(5(-1x^2 - 1x + 2)^2 - 3(-1x^2 - 1x + 2) + 4)) + 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": "How many local extrema (minima and maxima combined) does the function f(x) = 1(3|(1e^(-2(-1|x - 2| + 3)) + 2) - 3| - 2)^2 + 1(3|(1e^(-2(-1|x - 2| + 3)) + 2) - 3| - 2) + 5 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) = (-3(2cos(3\u03c0(1(-3|x - 1| + 2) - 3)) - 2) - 3)/(-2(2cos(3\u03c0(1(-3|x - 1| + 2) - 3)) - 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 extrema (minima and maxima combined) does the function f(x) = -2sin(1\u03c0(1|(-1(-5x^2 + 3x + 2)^2 - 5(-5x^2 + 3x + 2) - 3) + 2| + 2) + 1) - 1 have 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) = 1e^(-1(-2(-2|(-2x^2 - 5x - 2) + 1| + 3)^2 - 3(-2|(-2x^2 - 5x - 2) + 1| + 3) + 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 total number of local minima and maxima for f(x) = 3cos(2\u03c0(-4(-4(5x^2 + 3x + 1)^2 + 5)^2) - 2) + 3 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": "How many local maxima does the function f(x) = 1(3sin(2\u03c0(3((-3x + 3)/(-3x - 2))^2 - 1((-3x + 3)/(-3x - 2)) + 4) - 3) + 1)^2 + 3(3sin(2\u03c0(3((-3x + 3)/(-3x - 2))^2 - 1((-3x + 3)/(-3x - 2)) + 4) - 3) + 1) - 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": "Determine the count of local minima for the function f(x) = 5(1|(-2sin(2\u03c0(1x^2 + 2x + 4) - 3) + 2) - 2| - 2)^2 - 3(1|(-2sin(2\u03c0(1x^2 + 2x + 4) - 3) + 2) - 2| - 2) - 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "563", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 2sin(1\u03c0(-1((-3(3x))/(2(3x) - 1))) + 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": "How many local minima does the function f(x) = (1(-5(1(-5x^2 + 4x + 2)^2 - 4)^2 - 3) - 3)/(-3(-5(1(-5x^2 + 4x + 2)^2 - 4)^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": "Find the number of local maximum points for f(x) = 3sin(1\u03c0(4(1((-3x - 1)/(-2x - 2)) - 5)^2 - 2(1((-3x - 1)/(-2x - 2)) - 5) - 4)) 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) = 1(-1(-3|(-3sin(3\u03c0x) + 2) + 1| - 3)^2 - 1)^2 - 2(-1(-3|(-3sin(3\u03c0x) + 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": "55", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -1sin(2\u03c0(1(1|(-2x - 1) - 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": "40", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -2((-3(-2sin(2\u03c0(5x^2 - 3x - 1) + 3) + 3) + 2)/(-2(-2sin(2\u03c0(5x^2 - 3x - 1) + 3) + 3) + 3))^2 + 3((-3(-2sin(2\u03c0(5x^2 - 3x - 1) + 3) + 3) + 2)/(-2(-2sin(2\u03c0(5x^2 - 3x - 1) + 3) + 3) + 3)) - 4 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 total number of local minima and maxima for f(x) = 1cos(1\u03c0(2|(2|((2x + 2)/(2x)) + 1| + 3) - 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) = (-3(-1(2|(-2|x| - 2) - 2|) + 2))/(-2(-1(2|(-2|x| - 2) - 2|) + 2)) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "85", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -2(1(-1e^(-1(5x^2 - 1x - 5)) - 2)^2 + 5(-1e^(-1(5x^2 - 1x - 5)) - 2) + 4)^2 - 4(1(-1e^(-1(5x^2 - 1x - 5)) - 2)^2 + 5(-1e^(-1(5x^2 - 1x - 5)) - 2) + 4) - 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 total number of local minima and maxima for f(x) = (2(-3cos(1\u03c0((1((2x + 3)/(3x - 2)) - 3)/(2((2x + 3)/(3x - 2)) - 3)) + 3) + 3) - 3)/(-2(-3cos(1\u03c0((1((2x + 3)/(3x - 2)) - 3)/(2((2x + 3)/(3x - 2)) - 3)) + 3) + 3) - 2) where -10 \u2264 x \u2264 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) = -2((3(1e^(-1(-5x^2 - 5x - 4)) + 1))/(-2(1e^(-1(-5x^2 - 5x - 4)) + 1) - 3)) - 5 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": "How many local minima does the function f(x) = -2|(2(1(-2x + 5)^2 + 5(-2x + 5) - 4)^2 - 3(1(-2x + 5)^2 + 5(-2x + 5) - 4) - 4) + 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 minima does the function f(x) = 1(-3cos(3\u03c0(-3|(-2x^2 - 2x - 2) - 2| - 2) + 2) - 2)^2 - 5(-3cos(3\u03c0(-3|(-2x^2 - 2x - 2) - 2| - 2) + 2) - 2) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "276", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -3(-2(1|(1cos(3\u03c0x + 3) - 1) - 1| - 1) + 1)^2 - 1(-2(1|(1cos(3\u03c0x + 3) - 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": "60", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -2(1sin(1\u03c0((-3(-3|x + 2| + 1) + 3)/(-1(-3|x + 2| + 1) - 2)) + 2) - 3) - 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "62", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 3|(2|(-2cos(1\u03c0(1|x - 3| + 3) + 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": "21", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = (-2(-2cos(3\u03c0((2(1x - 2) + 2)/(-2(1x - 2) - 1)) - 2)) + 2)/(-2(-2cos(3\u03c0((2(1x - 2) + 2)/(-2(1x - 2) - 1)) - 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": "How many local maxima does the function f(x) = (2(2|(1cos(3\u03c0((-2x - 1)/(2x)) + 3) - 2)| - 1) + 1)/(-2(2|(1cos(3\u03c0((-2x - 1)/(2x)) + 3) - 2)| - 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": "Find the number of local maximum points for f(x) = -1|(2(-4(-1|x - 1| + 3)^2 + 2(-1|x - 1| + 3) + 5)^2 + 1(-4(-1|x - 1| + 3)^2 + 2(-1|x - 1| + 3) + 5) + 1) + 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": "How many local maxima does the function f(x) = 2|(1(2|(-4x^2 - 4x - 4) + 3| + 1)^2 - 4(2|(-4x^2 - 4x - 4) + 3| + 1) + 2) - 3| + 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) = (-1(-1(-2|(-3|x + 1| + 3) - 1| - 1) + 5) - 1)/(3(-1(-2|(-3|x + 1| + 3) - 1| - 1) + 5) + 3) 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 number of local maximum points for f(x) = 1(1sin(2\u03c0(1(-3|x + 2| + 3)^2 - 3) - 2) + 1)^2 - 2(1sin(2\u03c0(1(-3|x + 2| + 3)^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": "247", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = (3(-1e^(-2(3(-3x^2 + 1x) - 3)) + 2) - 2)/(1(-1e^(-2(3(-3x^2 + 1x) - 3)) + 2) - 3) 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) = 2|(2cos(1\u03c0(1(-4x^2 + 2x - 5)^2 - 4(-4x^2 + 2x - 5) + 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": "121", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -2cos(3\u03c0(2|(-2|(-3|x + 1| - 1) + 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": "721", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = (-1(-3sin(3\u03c0(-3(-5x) - 2) + 2) - 2) - 1)/(-1(-3sin(3\u03c0(-3(-5x) - 2) + 2) - 2) - 3) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "396", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = (2((-2(4(1sin(2\u03c0x + 1) - 3)^2 + 1(1sin(2\u03c0x + 1) - 3) + 1) + 1)/(-1(4(1sin(2\u03c0x + 1) - 3)^2 + 1(1sin(2\u03c0x + 1) - 3) + 1) - 1)) + 3)/(-3((-2(4(1sin(2\u03c0x + 1) - 3)^2 + 1(1sin(2\u03c0x + 1) - 3) + 1) + 1)/(-1(4(1sin(2\u03c0x + 1) - 3)^2 + 1(1sin(2\u03c0x + 1) - 3) + 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 minima for the function f(x) = -4(3|(1cos(2\u03c0(1|x + 2| - 3) + 2) + 1) - 3| + 2)^2 + 4(3|(1cos(2\u03c0(1|x + 2| - 3) + 2) + 1) - 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": "How many local maxima does the function f(x) = 3|(-2sin(1\u03c0(1(-3x^2 - 4x) - 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": "279", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -3cos(1\u03c0(-2|(1(-1|x + 3| - 1)^2 - 1(-1|x + 3| - 1) - 3) - 1|) - 1) + 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "543", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 5(5(-1(-1sin(2\u03c0x - 2) - 3)^2 + 1(-1sin(2\u03c0x - 2) - 3) - 3)^2 - 1(-1(-1sin(2\u03c0x - 2) - 3)^2 + 1(-1sin(2\u03c0x - 2) - 3) - 3) + 4) - 4 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(-5(1(1cos(3\u03c0x) + 1)^2 - 4(1cos(3\u03c0x) + 1) + 5) + 5)^2 - 4(-5(1(1cos(3\u03c0x) + 1)^2 - 4(1cos(3\u03c0x) + 1) + 5) + 5) - 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 minima for the function f(x) = 2sin(3\u03c0(-4(-3(-2x^2 + 3x + 3)^2 - 3(-2x^2 + 3x + 3) - 4)^2 - 1(-3(-2x^2 + 3x + 3)^2 - 3(-2x^2 + 3x + 3) - 4)) - 1) + 1 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(1(4(4x^2 + 3x) - 4)^2 + 2(4(4x^2 + 3x) - 4) + 4) + 3)/(-1(1(4(4x^2 + 3x) - 4)^2 + 2(4(4x^2 + 3x) - 4) + 4) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "201", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -2|(3|(-1(-2cos(3\u03c0x) + 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": "59", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = 5((-2(1(3x - 3)^2 + 1(3x - 3) - 4) + 1)/(1(1(3x - 3)^2 + 1(3x - 3) - 4) + 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": "Determine the count of local maxima for the function f(x) = 5(-5(1(3sin(3\u03c0x + 1) - 3)^2 - 3(3sin(3\u03c0x + 1) - 3) + 5)^2 - 3(1(3sin(3\u03c0x + 1) - 3)^2 - 3(3sin(3\u03c0x + 1) - 3) + 5) - 3)^2 - 2(-5(1(3sin(3\u03c0x + 1) - 3)^2 - 3(3sin(3\u03c0x + 1) - 3) + 5)^2 - 3(1(3sin(3\u03c0x + 1) - 3)^2 - 3(3sin(3\u03c0x + 1) - 3) + 5) - 3) - 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": "How many local minima does the function f(x) = (-3((-2((-1(2cos(1\u03c0x + 1)) + 2)/(-1(2cos(1\u03c0x + 1)))))/(2((-1(2cos(1\u03c0x + 1)) + 2)/(-1(2cos(1\u03c0x + 1)))) - 1)) - 1)/(-2((-2((-1(2cos(1\u03c0x + 1)) + 2)/(-1(2cos(1\u03c0x + 1)))))/(2((-1(2cos(1\u03c0x + 1)) + 2)/(-1(2cos(1\u03c0x + 1)))) - 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 maxima for the function f(x) = -3(2(-2cos(3\u03c0(-1x^2 + 5x - 1)))^2 + 4(-2cos(3\u03c0(-1x^2 + 5x - 1))) + 5)^2 + 4(2(-2cos(3\u03c0(-1x^2 + 5x - 1)))^2 + 4(-2cos(3\u03c0(-1x^2 + 5x - 1))) + 5) + 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": "Determine the total count of local extrema points for the function f(x) = 1|(1(-2cos(3\u03c0(-2x - 4)) + 3)^2 - 4(-2cos(3\u03c0(-2x - 4)) + 3) - 5) + 1| - 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "360", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = 3(5(2cos(2\u03c0(-3x^2 - 4)) - 2) + 4)^2 - 2(5(2cos(2\u03c0(-3x^2 - 4)) - 2) + 4) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "137", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = (1(-2|(1sin(2\u03c0(-1x^2 + 5x + 5) - 2) + 3) - 1| + 3) - 1)/(1(-2|(1sin(2\u03c0(-1x^2 + 5x + 5) - 2) + 3) - 1| + 3) + 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "427", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -3|(-5(3e^(2(-2|x| - 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) = 2sin(3\u03c0(3((2((1x + 1)/(3x)) + 2)/(2((1x + 1)/(3x)) - 3))^2 + 2((2((1x + 1)/(3x)) + 2)/(2((1x + 1)/(3x)) - 3)) - 5) - 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": "How many local maxima does the function f(x) = -2|(-3sin(3\u03c0(-2|(-1x) + 2| - 2) - 3) - 2) - 3| - 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": "Determine the count of local minima for the function f(x) = -1sin(1\u03c0(5(1(-2|x + 1| - 3) + 4) - 2) + 1) 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 count of local minima for the function f(x) = -1sin(1\u03c0(-3|(1|(1|x + 1| - 3) - 2| - 2) - 2| - 1) + 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": "Find the number of local maximum points for f(x) = -1|((2(1e^(2(-3x - 5)) - 1) + 2)/(2(1e^(2(-3x - 5)) - 1) - 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": "How many local extrema (minima and maxima combined) does the function f(x) = 1(1(1|(-3sin(3\u03c0x + 1) + 1) - 1| + 3) - 1)^2 - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "111", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = -2|(2(-4(-3cos(2\u03c0x - 1) - 2)^2 - 1(-3cos(2\u03c0x - 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": "160", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = (-2(-3sin(3\u03c0(-3(-2x^2 + 3x + 3)^2 - 5(-2x^2 + 3x + 3) + 4) + 1) + 3) - 3)/(-2(-3sin(3\u03c0(-3(-2x^2 + 3x + 3)^2 - 5(-2x^2 + 3x + 3) + 4) + 1) + 3) - 1) 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": "Determine the total count of local extrema points for the function f(x) = 2cos(3\u03c0(-1(-2|(-4x) - 1| - 1) + 2) + 1) + 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "481", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -1(-4(2(2cos(3\u03c0x - 1) + 1) - 1)^2 - 2(2(2cos(3\u03c0x - 1) + 1) - 1) - 4)^2 + 1(-4(2(2cos(3\u03c0x - 1) + 1) - 1)^2 - 2(2(2cos(3\u03c0x - 1) + 1) - 1) - 4) + 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 count of local minima for the function f(x) = -2|(1|(-3(-1x^2 + 1)^2 + 2(-1x^2 + 1) + 2)| + 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": "How many local maxima does the function f(x) = -1cos(1\u03c0(1(1(-1x + 5)^2 + 1(-1x + 5) + 2) + 1) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "130", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 1cos(1\u03c0(-2(-5(-1x + 5) + 3)) - 2) + 3 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": "How many local minima does the function f(x) = 1|(3((-3(-1cos(3\u03c0x + 2) - 2) - 3)/(3(-1cos(3\u03c0x + 2) - 2) - 2)) - 4)| + 3 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(2cos(1\u03c0(-5(5x - 2) - 1) + 3) + 3) - 2)/(3(2cos(1\u03c0(-5(5x - 2) - 1) + 3) + 3) + 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "174", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 1(-3sin(3\u03c0(4(2|x - 3| + 1) - 3) + 1) + 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 extrema (minima and maxima combined) does the function f(x) = 1|(3|(3|(1sin(3\u03c0x + 3) + 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": "60", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = (2(2(1sin(3\u03c0((3x + 1)/(2x - 1)) - 1))^2 - 2(1sin(3\u03c0((3x + 1)/(2x - 1)) - 1))) + 2)/(3(2(1sin(3\u03c0((3x + 1)/(2x - 1)) - 1))^2 - 2(1sin(3\u03c0((3x + 1)/(2x - 1)) - 1))) - 2) 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 count of local maxima for the function f(x) = -3|(-3sin(2\u03c0(3|(2|x - 2| - 2) - 3| - 2) + 3) + 3) + 3| in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "121", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 1cos(3\u03c0(5((1(-2x + 5) + 2)/(-3(-2x + 5) - 1))^2 - 3) - 1) + 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": "How many local extrema (minima and maxima combined) does the function f(x) = 2(1e^(-2(-1(-1|x + 1| + 1)^2 + 2)) + 1)^2 - 4(1e^(-2(-1(-1|x + 1| + 1)^2 + 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) = 2|(-2(2sin(2\u03c0(-3x^2 - 5x - 2)) - 3)^2 - 1(2sin(2\u03c0(-3x^2 - 5x - 2)) - 3) + 5) - 3| - 2 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 total count of local extrema points for the function f(x) = 3|(-3((3(-1cos(3\u03c0x + 1)) + 2)/(2(-1cos(3\u03c0x + 1)) + 3)) - 5) - 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 number of local minimum points for f(x) = -5((2(4(-1cos(3\u03c0x) + 2)^2 - 5(-1cos(3\u03c0x) + 2)) - 3)/(2(4(-1cos(3\u03c0x) + 2)^2 - 5(-1cos(3\u03c0x) + 2)) - 1))^2 - 3((2(4(-1cos(3\u03c0x) + 2)^2 - 5(-1cos(3\u03c0x) + 2)) - 3)/(2(4(-1cos(3\u03c0x) + 2)^2 - 5(-1cos(3\u03c0x) + 2)) - 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": "Find the total number of local minima and maxima for f(x) = -1(-3(1|(-1|x - 1| + 2) + 2| + 1)^2 - 3(1|(-1|x - 1| + 2) + 2| + 1) + 5)^2 - 4(-3(1|(-1|x - 1| + 2) + 2| + 1)^2 - 3(1|(-1|x - 1| + 2) + 2| + 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 total count of local extrema points for the function f(x) = -2(-1(-2(-5x^2 + 5x - 3)^2 - 3(-5x^2 + 5x - 3) - 1)^2 - 4(-2(-5x^2 + 5x - 3)^2 - 3(-5x^2 + 5x - 3) - 1) - 3)^2 - 2(-1(-2(-5x^2 + 5x - 3)^2 - 3(-5x^2 + 5x - 3) - 1)^2 - 4(-2(-5x^2 + 5x - 3)^2 - 3(-5x^2 + 5x - 3) - 1) - 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) = (3(-1sin(2\u03c0(3((-2x - 1)/(-3x)) + 5) + 2)))/(2(-1sin(2\u03c0(3((-2x - 1)/(-3x)) + 5) + 2)) - 1) 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": "Determine the count of local maxima for the function f(x) = 1(3(1(-1cos(3\u03c0x + 2) + 3)^2 + 4(-1cos(3\u03c0x + 2) + 3) + 1) - 4) + 5 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(3sin(2\u03c0(-3|((-1x - 1)/(1x + 3)) - 1| + 1) - 3) + 2)^2 - 3(3sin(2\u03c0(-3|((-1x - 1)/(1x + 3)) - 1| + 1) - 3) + 2) + 2 have in the interval [-10, 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 minimum points for f(x) = 3|(-1cos(2\u03c0(-2|(1x + 5)| - 2)) + 2)| - 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) = -2|(-2|(2sin(1\u03c0(-2|x + 1| + 2) + 2) + 3) + 2| - 1) - 1| + 1 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 maxima does the function f(x) = (-1((-1(-1|((3x + 3)/(-3x + 1)) + 2| - 1))/(-3(-1|((3x + 3)/(-3x + 1)) + 2| - 1))) - 1)/(2((-1(-1|((3x + 3)/(-3x + 1)) + 2| - 1))/(-3(-1|((3x + 3)/(-3x + 1)) + 2| - 1))) - 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "211", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = (1(-3(1|(-2x^2 - 3x - 4) + 3| - 2)^2 + 5(1|(-2x^2 - 3x - 4) + 3| - 2) + 2) - 1)/(-1(-3(1|(-2x^2 - 3x - 4) + 3| - 2)^2 + 5(1|(-2x^2 - 3x - 4) + 3| - 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": "Find the number of local minimum points for f(x) = -3(2cos(1\u03c0(-1(-1x - 3) + 3) + 1)) + 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": "Find the total number of local minima and maxima for f(x) = 1(-5((-1(1sin(2\u03c0x + 2) + 1) + 1)/(2(1sin(2\u03c0x + 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": "80", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -5((2(2sin(1\u03c0(3x^2 + 2) + 2) - 3))/(-1(2sin(1\u03c0(3x^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": "565", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -2(-1(2sin(1\u03c0(-3x + 2) - 1) - 2)^2 - 4(2sin(1\u03c0(-3x + 2) - 1) - 2) - 5)^2 + 4(-1(2sin(1\u03c0(-3x + 2) - 1) - 2)^2 - 4(2sin(1\u03c0(-3x + 2) - 1) - 2) - 5) + 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 count of local maxima for the function f(x) = -3|(-2(4(1|x - 2| - 3)^2 - 3)^2 + 2(4(1|x - 2| - 3)^2 - 3) - 4) - 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": "How many local maxima does the function f(x) = (3((3(2cos(3\u03c0(1x + 3))) - 3)/(-3(2cos(3\u03c0(1x + 3))) - 2)) - 1)/(3((3(2cos(3\u03c0(1x + 3))) - 3)/(-3(2cos(3\u03c0(1x + 3))) - 2)) + 3) 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": "Find the number of local minimum points for f(x) = 2(2|((-2(-2cos(1\u03c0x + 3)) - 1)/(-3(-2cos(1\u03c0x + 3)) - 1)) - 2| - 3)^2 + 2(2|((-2(-2cos(1\u03c0x + 3)) - 1)/(-3(-2cos(1\u03c0x + 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": "48", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -2|(3|(2(1cos(2\u03c0x) + 3)^2 + 5(1cos(2\u03c0x) + 3) - 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": "How many local maxima does the function f(x) = 2((2(1cos(3\u03c0(-2|x + 2| - 1) + 3) - 3) - 2)/(-1(1cos(3\u03c0(-2|x + 2| - 1) + 3) - 3))) + 4 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(-3sin(3\u03c0(4((-2x - 2)/(1x + 3))^2 + 2((-2x - 2)/(1x + 3)) + 2) + 3) - 3) + 3)/(2(-3sin(3\u03c0(4((-2x - 2)/(1x + 3))^2 + 2((-2x - 2)/(1x + 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": "191", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 3cos(1\u03c0(-5((-2(-4x^2 + 3x + 4) + 1)/(1(-4x^2 + 3x + 4) + 1))^2 + 4((-2(-4x^2 + 3x + 4) + 1)/(1(-4x^2 + 3x + 4) + 1)) + 1) + 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": "Find the total number of local minima and maxima for f(x) = -3(1|((-2(2cos(2\u03c0x - 3) + 3))/(-3(2cos(2\u03c0x - 3) + 3) - 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": "Find the number of local minimum points for f(x) = (2(-1(-1(3cos(3\u03c0x - 1) - 2)^2 + 2(3cos(3\u03c0x - 1) - 2) - 1)^2 - 1(-1(3cos(3\u03c0x - 1) - 2)^2 + 2(3cos(3\u03c0x - 1) - 2) - 1)) - 1)/(3(-1(-1(3cos(3\u03c0x - 1) - 2)^2 + 2(3cos(3\u03c0x - 1) - 2) - 1)^2 - 1(-1(3cos(3\u03c0x - 1) - 2)^2 + 2(3cos(3\u03c0x - 1) - 2) - 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 extrema (minima and maxima combined) does the function f(x) = (1(-2(1|(-3sin(2\u03c0x) + 3) - 1| + 1) - 2) + 1)/(1(-2(1|(-3sin(2\u03c0x) + 3) - 1| + 1) - 2) - 3) have in the interval [-10, 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 minimum points for f(x) = (-3(1|((2(-3cos(3\u03c0x) + 2))/(-2(-3cos(3\u03c0x) + 2) - 1)) - 1|) - 3)/(-3(1|((2(-3cos(3\u03c0x) + 2))/(-2(-3cos(3\u03c0x) + 2) - 1)) - 1|) + 2) 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": "Find the number of local minimum points for f(x) = -4(1cos(3\u03c0(5(-1|x + 1| - 2)^2 - 1(-1|x + 1| - 2) - 1) - 3) - 2)^2 + 5(1cos(3\u03c0(5(-1|x + 1| - 2)^2 - 1(-1|x + 1| - 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": "210", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = (-2(-2sin(2\u03c0(-2|(-1x + 5) + 2| - 1) - 1) - 2) + 3)/(-1(-2sin(2\u03c0(-2|(-1x + 5) + 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": "81", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 1cos(3\u03c0((-2(-1|(-2|x|) + 2| + 3) - 3)/(-2(-1|(-2|x|) + 2| + 3) + 1)) + 1) - 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": "Find the number of local minimum points for f(x) = (1(2(3(-1cos(1\u03c0x - 3) + 3)) - 1) - 3)/(-2(2(3(-1cos(1\u03c0x - 3) + 3)) - 1) - 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": "How many local extrema (minima and maxima combined) does the function f(x) = -3(-2(1(-1x^2 + 4x - 5)^2 + 5(-1x^2 + 4x - 5) - 5)^2 - 3(1(-1x^2 + 4x - 5)^2 + 5(-1x^2 + 4x - 5) - 5) - 5)^2 + 5(-2(1(-1x^2 + 4x - 5)^2 + 5(-1x^2 + 4x - 5) - 5)^2 - 3(1(-1x^2 + 4x - 5)^2 + 5(-1x^2 + 4x - 5) - 5) - 5) - 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": "How many local extrema (minima and maxima combined) does the function f(x) = (-2(3|(-3(1cos(1\u03c0x + 3) + 1) + 1) - 1| - 2) + 3)/(2(3|(-3(1cos(1\u03c0x + 3) + 1) + 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": "How many local minima does the function f(x) = 4(-1cos(3\u03c0(2((-3x + 3)/(-1x - 2))^2 - 3((-3x + 3)/(-1x - 2)) - 2)))^2 - 2(-1cos(3\u03c0(2((-3x + 3)/(-1x - 2))^2 - 3((-3x + 3)/(-1x - 2)) - 2))) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "131", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = (2((-1(-2cos(2\u03c0(4x^2 + 5x - 3) - 2) + 2) + 3)/(-1(-2cos(2\u03c0(4x^2 + 5x - 3) - 2) + 2) - 3)) - 3)/(1((-1(-2cos(2\u03c0(4x^2 + 5x - 3) - 2) + 2) + 3)/(-1(-2cos(2\u03c0(4x^2 + 5x - 3) - 2) + 2) - 3))) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "221", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -1(3sin(2\u03c0(5((3x + 2)/(2x - 3)) - 4) + 3) + 2) - 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "55", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -2|(-4(-2cos(1\u03c0(-2x + 4) + 2) - 1) - 1) - 2| where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "76", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = 3|(1cos(1\u03c0(3(3|x|) + 3)) - 2) - 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 count of local minima for the function f(x) = 2(4(-1(-3sin(3\u03c0x - 2) + 2)^2 + 2(-3sin(3\u03c0x - 2) + 2) - 1) - 5)^2 + 4(4(-1(-3sin(3\u03c0x - 2) + 2)^2 + 2(-3sin(3\u03c0x - 2) + 2) - 1) - 5) + 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": "Determine the total count of local extrema points for the function f(x) = (-2(2(2sin(2\u03c0(-1x - 4)) + 2)^2 - 3(2sin(2\u03c0(-1x - 4)) + 2)) - 3)/(-1(2(2sin(2\u03c0(-1x - 4)) + 2)^2 - 3(2sin(2\u03c0(-1x - 4)) + 2)) - 1) 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 minima for the function f(x) = 2(2cos(1\u03c0(1(-2x^2 - 1x + 5) + 1)) - 3) - 4 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "201", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 4(-4(3(-1x^2 + 5x - 5)^2 - 5(-1x^2 + 5x - 5) - 2) - 1)^2 + 4(-4(3(-1x^2 + 5x - 5)^2 - 5(-1x^2 + 5x - 5) - 2) - 1) + 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 extrema (minima and maxima combined) does the function f(x) = 3|(-2(3cos(2\u03c0((-1x - 3)/(-2x + 3)) - 2)))| - 3 have 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 minima for the function f(x) = 5(-2|(-1sin(2\u03c0(2|x| + 1) - 3) + 2)| + 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": "Determine the count of local maxima for the function f(x) = 2((3(-1e^(1(-3x + 1)) - 2) + 2)/(-2(-1e^(1(-3x + 1)) - 2) + 3))^2 + 4 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) = 4(-1(1sin(2\u03c0(-2|x| + 2) - 1) - 3)^2 - 3(1sin(2\u03c0(-2|x| + 2) - 1) - 3) - 3)^2 - 1(-1(1sin(2\u03c0(-2|x| + 2) - 1) - 3)^2 - 3(1sin(2\u03c0(-2|x| + 2) - 1) - 3) - 3) + 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": "Determine the count of local minima for the function f(x) = (-1(2cos(1\u03c0(-1(1|x + 3|) - 5) + 2) - 1))/(1(2cos(1\u03c0(-1(1|x + 3|) - 5) + 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 minimum points for f(x) = 1|(-1|(2|(3x^2 + 1x + 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": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -3cos(1\u03c0(-4(3|(3x^2 - 4x - 5) + 2| + 3) - 2) - 1) - 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "490", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 2sin(2\u03c0(5((1((2x + 3)/(-1x + 3)) - 3)/(-2((2x + 3)/(-1x + 3)) + 1)) + 2) + 3) + 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "82", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -3|(3sin(3\u03c0((2(-3x - 4) - 3)/(-3(-3x - 4))) - 2) - 2) - 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": "How many local extrema (minima and maxima combined) does the function f(x) = -3(-5(-1(1cos(3\u03c0x - 2))^2 + 5(1cos(3\u03c0x - 2)) + 4) + 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": "Find the number of local maximum points for f(x) = -4(-1e^(2(-1|((-3x + 2)/(2x - 3)) - 1| + 3)) + 2)^2 + 4(-1e^(2(-1|((-3x + 2)/(2x - 3)) - 1| + 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 number of local maximum points for f(x) = -1cos(3\u03c0((3((-2(2x^2 + 4x - 1) - 2)/(1(2x^2 + 4x - 1))) - 2)/(2((-2(2x^2 + 4x - 1) - 2)/(1(2x^2 + 4x - 1))) - 3)) - 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": "Find the number of local maximum points for f(x) = -1(2|(-2|(-2sin(1\u03c0x - 1) + 2) - 3| - 1)| + 3)^2 + 3(2|(-2|(-2sin(1\u03c0x - 1) + 2) - 3| - 1)| + 3) 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) = -4(-2|(3sin(1\u03c0(4x^2 + 4x - 2)) + 1) + 1| + 1) + 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "525", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 1sin(1\u03c0(2((-2(4x^2 + 2x + 3) + 3)/(-1(4x^2 + 2x + 3) - 1))^2 + 4) + 3) + 3 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": "Determine the count of local minima for the function f(x) = 2sin(3\u03c0(1(1(-2x^2 - 4x) - 4)^2 - 4) - 3) + 1 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) = 1cos(2\u03c0((-1(-3(3|x + 2| - 2) + 3) - 1)/(2(-3(3|x + 2| - 2) + 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": "How many local extrema (minima and maxima combined) does the function f(x) = -2((2(-3cos(2\u03c0(5x^2 - 1x + 2) + 1) + 2) + 1)/(3(-3cos(2\u03c0(5x^2 - 1x + 2) + 1) + 2))) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "503", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -3|((3((2(2cos(3\u03c0x + 3) - 2) + 1)/(1(2cos(3\u03c0x + 3) - 2))) + 2)/(3((2(2cos(3\u03c0x + 3) - 2) + 1)/(1(2cos(3\u03c0x + 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": "120", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = 1|(-1sin(1\u03c0(-3(2x^2 + 1x + 4)^2 - 4(2x^2 + 1x + 4) - 5) + 2) - 2) + 3| - 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "137", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -2cos(1\u03c0(3|(5((-2x - 1)/(-1x - 3)) + 5) + 3|) - 3) - 3 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 count of local maxima for the function f(x) = 1|(2cos(2\u03c0(1|(2x + 2) + 2| - 1) + 2) + 1) + 2| - 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": "How many local extrema (minima and maxima combined) does the function f(x) = 5(1|(5(-1cos(1\u03c0x - 1) + 1) - 3) + 1| + 1)^2 - 3(1|(5(-1cos(1\u03c0x - 1) + 1) - 3) + 1| + 1) + 4 have in the interval [-10, 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 maxima for the function f(x) = 1|(2sin(2\u03c0((3((2x - 3)/(3x + 1)) - 3)/(-1((2x - 3)/(3x + 1)) - 3)) - 2) + 3) - 3| - 2 in the interval [-10, 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 minima for the function f(x) = -1sin(2\u03c0(-4(3|((-1x - 3)/(-2x - 2)) - 3| + 2) - 4) - 3) 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) = 4((1(-1((-1x)/(-1x - 2))^2 + 1((-1x)/(-1x - 2)) + 4))/(2(-1((-1x)/(-1x - 2))^2 + 1((-1x)/(-1x - 2)) + 4) + 1))^2 - 5((1(-1((-1x)/(-1x - 2))^2 + 1((-1x)/(-1x - 2)) + 4))/(2(-1((-1x)/(-1x - 2))^2 + 1((-1x)/(-1x - 2)) + 4) + 1)) + 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": "How many local extrema (minima and maxima combined) does the function f(x) = 2cos(2\u03c0(2(3|(-2x) - 2| + 1) - 2) + 3) + 2 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": "Find the total number of local minima and maxima for f(x) = 1((-1(-2sin(3\u03c0((2x - 1)/(3x + 2)) + 1) + 2) + 2)/(1(-2sin(3\u03c0((2x - 1)/(3x + 2)) + 1) + 2) - 3)) + 2 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": "Find the number of local maximum points for f(x) = (-2(-3|(1(-2cos(3\u03c0x - 2) + 1)^2 - 4(-2cos(3\u03c0x - 2) + 1) + 3) + 2| - 2) - 1)/(-2(-3|(1(-2cos(3\u03c0x - 2) + 1)^2 - 4(-2cos(3\u03c0x - 2) + 1) + 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": "How many local extrema (minima and maxima combined) does the function f(x) = -1cos(1\u03c0(-5(-1|(-4x^2 + 3x + 5) - 1| + 1)^2 - 1(-1|(-4x^2 + 3x + 5) - 1| + 1) - 3) + 3) 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 number of local minimum points for f(x) = -5(-1(3sin(2\u03c0((1x - 2)/(-2x + 3)) + 3) + 2)^2 - 1(3sin(2\u03c0((1x - 2)/(-2x + 3)) + 3) + 2) + 1)^2 + 1(-1(3sin(2\u03c0((1x - 2)/(-2x + 3)) + 3) + 2)^2 - 1(3sin(2\u03c0((1x - 2)/(-2x + 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": "10", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -2(3cos(2\u03c0(2|(-1x - 1) + 1| - 1) + 1) + 1) 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 maximum points for f(x) = 1|(2cos(3\u03c0((-1(1|x - 2|) - 1)/(1(1|x - 2|))) - 2) + 3) - 3| - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "47", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = 1(-2|((1(3sin(1\u03c0x - 2) - 3) + 1)/(-1(3sin(1\u03c0x - 2) - 3) + 3)) + 2| + 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": "How many local extrema (minima and maxima combined) does the function f(x) = -2sin(1\u03c0(2((-2((3x)/(-3x - 3)) + 3)/(-1((3x)/(-3x - 3)) - 2))^2 + 4((-2((3x)/(-3x - 3)) + 3)/(-1((3x)/(-3x - 3)) - 2)) - 3) - 1) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "172", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 2e^(-1(1(-2(-2|x - 3|)^2 - 2(-2|x - 3|))^2 - 1(-2(-2|x - 3|)^2 - 2(-2|x - 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 count of local minima for the function f(x) = 4(3cos(1\u03c0((-2(1x - 1) + 1)/(-3(1x - 1) - 2)) + 1) - 3)^2 + 5(3cos(1\u03c0((-2(1x - 1) + 1)/(-3(1x - 1) - 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 total count of local extrema points for the function f(x) = -2sin(2\u03c0(3|((1((3x - 2)/(-2x + 3)) + 3)/(-1((3x - 2)/(-2x + 3)) + 2)) + 1|) - 2) + 2 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 count of local minima for the function f(x) = 1sin(3\u03c0(1(2|(-3x^2 - 5x - 1) - 2| + 3) + 3)) + 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": "Find the number of local minimum points for f(x) = 1(-2|(2(-2|x - 1| + 3)^2 - 3(-2|x - 1| + 3) - 5) + 3| + 1)^2 - 4(-2|(2(-2|x - 1| + 3)^2 - 3(-2|x - 1| + 3) - 5) + 3| + 1) + 4 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(-3cos(3\u03c0(5(2x + 1) + 1) - 1) - 1)^2 + 3(-3cos(3\u03c0(5(2x + 1) + 1) - 1) - 1) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "797", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = (-3(2cos(3\u03c0(-5(3x - 3)^2 - 4(3x - 3) - 3) + 1) - 1) - 3)/(1(2cos(3\u03c0(-5(3x - 3)^2 - 4(3x - 3) - 3) + 1) - 1) - 2) in the interval [-10, 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) = 1e^(1(-2(-1(1x + 5)^2 - 3(1x + 5) - 3)^2 - 4(-1(1x + 5)^2 - 3(1x + 5) - 3) + 4)) - 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 total count of local extrema points for the function f(x) = -4((-1(-1|((-2x + 1)/(3x - 2)) + 2| + 1) + 1)/(-2(-1|((-2x + 1)/(3x - 2)) + 2| + 1) - 3))^2 - 4((-1(-1|((-2x + 1)/(3x - 2)) + 2| + 1) + 1)/(-2(-1|((-2x + 1)/(3x - 2)) + 2| + 1) - 3)) - 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) = -2cos(2\u03c0(-1(-1(1x - 2)^2 - 5(1x - 2) - 5) + 1)) + 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "201", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 2cos(2\u03c0((1(-1|((1x + 3)/(-2x - 1)) + 3|) + 2)/(3(-1|((1x + 3)/(-2x - 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": "6", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = (-2(1|(-1cos(2\u03c0(-2x^2 + 5x + 4) - 1) - 3) + 2| - 3) + 3)/(-1(1|(-1cos(2\u03c0(-2x^2 + 5x + 4) - 1) - 3) + 2| - 3)) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "563", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = 4(2|(5(-3sin(3\u03c0x + 3) + 2)^2 - 1(-3sin(3\u03c0x + 3) + 2) + 4) + 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) = -4((-3(1e^(2(3|x + 1| - 1)) + 2) - 3)/(-2(1e^(2(3|x + 1| - 1)) + 2) + 3))^2 - 5((-3(1e^(2(3|x + 1| - 1)) + 2) - 3)/(-2(1e^(2(3|x + 1| - 1)) + 2) + 3)) - 2 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 total number of local minima and maxima for f(x) = (-1((-3(3sin(3\u03c0(1|x - 3| + 3)) + 1))/(2(3sin(3\u03c0(1|x - 3| + 3)) + 1) + 1)) + 3)/(-3((-3(3sin(3\u03c0(1|x - 3| + 3)) + 1))/(2(3sin(3\u03c0(1|x - 3| + 3)) + 1) + 1)) - 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": "Determine the count of local maxima for the function f(x) = -2|(-2|(-4(2cos(1\u03c0x + 1) + 3) - 4) + 2| - 1) - 1| + 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 count of local maxima for the function f(x) = 2|(-1cos(1\u03c0((3(1x^2 + 1x - 4) + 1)/(3(1x^2 + 1x - 4) + 3)) - 2) + 1)| + 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) = 1((-2((3(-3cos(3\u03c0x + 3) - 3) + 3)/(2(-3cos(3\u03c0x + 3) - 3) - 1)) - 1)/(1((3(-3cos(3\u03c0x + 3) - 3) + 3)/(2(-3cos(3\u03c0x + 3) - 3) - 1)) + 3))^2 - 1((-2((3(-3cos(3\u03c0x + 3) - 3) + 3)/(2(-3cos(3\u03c0x + 3) - 3) - 1)) - 1)/(1((3(-3cos(3\u03c0x + 3) - 3) + 3)/(2(-3cos(3\u03c0x + 3) - 3) - 1)) + 3)) - 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": "How many local maxima does the function f(x) = (-1(-2(-2cos(3\u03c0(-3x + 4) + 3) - 3)^2 - 5(-2cos(3\u03c0(-3x + 4) + 3) - 3) - 1) + 3)/(3(-2(-2cos(3\u03c0(-3x + 4) + 3) - 3)^2 - 5(-2cos(3\u03c0(-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": "162", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -2cos(1\u03c0(-2(4(-2|x + 1| - 2) + 3)^2 - 4(4(-2|x + 1| - 2) + 3)) + 2) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "212", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -2(3(-2cos(2\u03c0(-3x^2 + 5x + 3) - 3) + 2)^2 - 1(-2cos(2\u03c0(-3x^2 + 5x + 3) - 3) + 2) + 4) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "193", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = (3((2(4(-3e^(-2x))^2 - 2(-3e^(-2x)) - 1) - 2)/(1(4(-3e^(-2x))^2 - 2(-3e^(-2x)) - 1) - 2)) + 2)/(1((2(4(-3e^(-2x))^2 - 2(-3e^(-2x)) - 1) - 2)/(1(4(-3e^(-2x))^2 - 2(-3e^(-2x)) - 1) - 2)) - 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) = 2cos(1\u03c0((-2((-2(-1x - 1))/(3(-1x - 1) - 2)) + 1)/(1((-2(-1x - 1))/(3(-1x - 1) - 2))))) - 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 minimum points for f(x) = 1|(1((2(2cos(1\u03c0x - 1) + 3) + 1)/(3(2cos(1\u03c0x - 1) + 3) - 1))^2 - 5((2(2cos(1\u03c0x - 1) + 3) + 1)/(3(2cos(1\u03c0x - 1) + 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": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 3|(-2cos(3\u03c0(-1(-1x + 1)^2 - 1(-1x + 1) + 4)) + 2) - 1| + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "490", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = (-3(2sin(3\u03c0((-3(-3|x + 3| - 1) + 1)/(-2(-3|x + 3| - 1) - 1))) - 2) - 1)/(-2(2sin(3\u03c0((-3(-3|x + 3| - 1) + 1)/(-2(-3|x + 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": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -1((-2(2|(3sin(3\u03c0x) - 2) + 3| + 3))/(-2(2|(3sin(3\u03c0x) - 2) + 3| + 3) - 2))^2 + 3((-2(2|(3sin(3\u03c0x) - 2) + 3| + 3))/(-2(2|(3sin(3\u03c0x) - 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": "119", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 3cos(1\u03c0(-1|(-3((-1x + 1)/(-2x + 3))^2 - 5((-1x + 1)/(-2x + 3)) + 1) + 2| + 3) + 2) + 2 in the interval [-10, 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) = 3(2|(-1cos(3\u03c0(3x + 2) - 2)) - 3| - 2) + 5 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 number of local minimum points for f(x) = 2(-5(-1(-1cos(3\u03c0x + 2) - 2) - 2)^2 + 5(-1(-1cos(3\u03c0x + 2) - 2) - 2) - 4)^2 + 1(-5(-1(-1cos(3\u03c0x + 2) - 2) - 2)^2 + 5(-1(-1cos(3\u03c0x + 2) - 2) - 2) - 4) - 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": "How many local maxima does the function f(x) = -2(-2cos(3\u03c0(1|(-3|x + 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": "90", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = (1(2cos(1\u03c0((-3(5x^2 - 2))/(3(5x^2 - 2) - 2)) - 3) + 3) + 3)/(1(2cos(1\u03c0((-3(5x^2 - 2))/(3(5x^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": "9", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -3|(-1|(-3cos(1\u03c0((-3x - 2)/(-2x + 3)) + 1) - 3) - 3|) - 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 minima does the function f(x) = (2((2(-1(2sin(3\u03c0x) - 1)^2 + 4(2sin(3\u03c0x) - 1) - 4))/(-3(-1(2sin(3\u03c0x) - 1)^2 + 4(2sin(3\u03c0x) - 1) - 4) + 1)) - 2)/(1((2(-1(2sin(3\u03c0x) - 1)^2 + 4(2sin(3\u03c0x) - 1) - 4))/(-3(-1(2sin(3\u03c0x) - 1)^2 + 4(2sin(3\u03c0x) - 1) - 4) + 1)) + 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": "Find the number of local minimum points for f(x) = -2(1|(3sin(3\u03c0(-4x^2 + 3x + 5) - 1) - 3) + 1| - 2)^2 + 1(1|(3sin(3\u03c0(-4x^2 + 3x + 5) - 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": "112", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 2|(3(3|(2|x|) - 2| - 3)^2 - 4(3|(2|x|) - 2| - 3) - 4) + 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) = -3(-1(2|(-2sin(1\u03c0x) - 2)| - 3) - 4) - 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) = 3((-2(3sin(1\u03c0(3|x - 1|) - 1) - 1))/(3(3sin(1\u03c0(3|x - 1|) - 1) - 1) + 2)) + 3 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": "Determine the count of local minima for the function f(x) = 3|(2(-4(1sin(3\u03c0x - 3) - 3)^2 + 5(1sin(3\u03c0x - 3) - 3))^2 - 5(-4(1sin(3\u03c0x - 3) - 3)^2 + 5(1sin(3\u03c0x - 3) - 3)) + 4) + 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 count of local maxima for the function f(x) = 1((2(-1cos(3\u03c0(-5x + 2) + 3) - 2) + 3)/(1(-1cos(3\u03c0(-5x + 2) + 3) - 2) + 1))^2 + 5((2(-1cos(3\u03c0(-5x + 2) + 3) - 2) + 3)/(1(-1cos(3\u03c0(-5x + 2) + 3) - 2) + 1)) - 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "244", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -1cos(3\u03c0(-3((2((-2x)/(2x - 3)) - 3)/(2((-2x)/(2x - 3)))) - 2) + 2) - 2 in the interval [-10, 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) = (-1(-1|(3cos(1\u03c0((1x - 2)/(2x + 1)) + 3) + 3) - 3| - 3))/(2(-1|(3cos(1\u03c0((1x - 2)/(2x + 1)) + 3) + 3) - 3| - 3) - 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": "How many local maxima does the function f(x) = 3|((2(3sin(3\u03c0(-5x^2 - 5x + 5)) + 1) - 3)/(-3(3sin(3\u03c0(-5x^2 - 5x + 5)) + 1) - 3)) - 3| have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "322", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = (-1(-1(-2|(3sin(1\u03c0x - 3) - 3) - 1| + 2) - 4) + 2)/(1(-1(-2|(3sin(1\u03c0x - 3) - 3) - 1| + 2) - 4) - 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": "Find the number of local minimum points for f(x) = (-3(-2cos(3\u03c0(-3((3x + 1)/(2x + 2))^2 - 5((3x + 1)/(2x + 2))) - 1) - 1))/(2(-2cos(3\u03c0(-3((3x + 1)/(2x + 2))^2 - 5((3x + 1)/(2x + 2))) - 1) - 1) + 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": "How many local extrema (minima and maxima combined) does the function f(x) = (2(-3sin(3\u03c0(-3((3x + 3)/(-1x + 2))) + 3) - 3) + 3)/(2(-3sin(3\u03c0(-3((3x + 3)/(-1x + 2))) + 3) - 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": "How many local minima does the function f(x) = 2cos(1\u03c0(-3((-2(-4x - 2) - 2)/(-1(-4x - 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": "32", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -1|(1e^(-1(3(1x - 1)^2 - 5(1x - 1) - 4)) - 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": "Find the total number of local minima and maxima for f(x) = -5(1(1(2|x - 2| - 3)^2 + 2(2|x - 2| - 3) - 2)^2 + 3(1(2|x - 2| - 3)^2 + 2(2|x - 2| - 3) - 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": "Determine the count of local minima for the function f(x) = 2|(-3sin(2\u03c0(5(2|x + 1| - 1) - 3) + 2) + 3) + 1| - 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "201", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 2|(1|((-2(3cos(1\u03c0x + 2) + 2) - 1)/(-2(3cos(1\u03c0x + 2) + 2) - 2))|) + 2| + 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": "Determine the total count of local extrema points for the function f(x) = 2|(1(2|(-3x^2 + 3x + 1) + 2| - 2) - 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": "Find the number of local minimum points for f(x) = -1|(-2(-5(1sin(1\u03c0x - 1) + 3)^2 - 4(1sin(1\u03c0x - 1) + 3)) + 1) + 3| - 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) = (1(-2cos(1\u03c0((1((-2x + 2)/(-2x - 1)) - 2)/(3((-2x + 2)/(-2x - 1)))) + 3)) - 3)/(-3(-2cos(1\u03c0((1((-2x + 2)/(-2x - 1)) - 2)/(3((-2x + 2)/(-2x - 1)))) + 3)) + 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": "How many local minima does the function f(x) = 1cos(3\u03c0(3(4((-2x)/(-2x + 3))^2 + 3((-2x)/(-2x + 3)) + 2) - 5) + 3) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "98", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -2(-1(-5(3|x + 3| - 3)^2 - 3(3|x + 3| - 3) - 1)^2 + 4(-5(3|x + 3| - 3)^2 - 3(3|x + 3| - 3) - 1) + 5)^2 - 4(-1(-5(3|x + 3| - 3)^2 - 3(3|x + 3| - 3) - 1)^2 + 4(-5(3|x + 3| - 3)^2 - 3(3|x + 3| - 3) - 1) + 5) - 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(-2cos(3\u03c0(1(-5x)^2 - 5(-5x) + 3) + 2)) + 2)/(-2(-2cos(3\u03c0(1(-5x)^2 - 5(-5x) + 3) + 2)) + 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "431", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 5(5(-2(2|x + 2|)^2 + 1(2|x + 2|) + 2)^2 + 2(-2(2|x + 2|)^2 + 1(2|x + 2|) + 2) - 1)^2 + 1(5(-2(2|x + 2|)^2 + 1(2|x + 2|) + 2)^2 + 2(-2(2|x + 2|)^2 + 1(2|x + 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": "How many local extrema (minima and maxima combined) does the function f(x) = (2(3((3(-2cos(1\u03c0x + 1) - 2) + 3)/(-2(-2cos(1\u03c0x + 1) - 2) + 3)) - 4) - 2)/(-2(3((3(-2cos(1\u03c0x + 1) - 2) + 3)/(-2(-2cos(1\u03c0x + 1) - 2) + 3)) - 4) + 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(4(-1|(5x^2 - 2x - 2) - 1| + 2)^2 - 3(-1|(5x^2 - 2x - 2) - 1| + 2) - 5)^2 - 3(4(-1|(5x^2 - 2x - 2) - 1| + 2)^2 - 3(-1|(5x^2 - 2x - 2) - 1| + 2) - 5) - 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 maxima does the function f(x) = (-2(1sin(3\u03c0(2((3x + 1)/(-2x - 2))^2 - 3) + 1) - 2) - 2)/(-3(1sin(3\u03c0(2((3x + 1)/(-2x - 2))^2 - 3) + 1) - 2) + 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 count of local maxima for the function f(x) = -1|((-3(2sin(2\u03c0(3|x - 2| + 1) + 2) - 3) - 1)/(-2(2sin(2\u03c0(3|x - 2| + 1) + 2) - 3))) - 2| + 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 maxima does the function f(x) = -2|(-3sin(3\u03c0(2|(2x^2 - 4x - 2) - 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": "260", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -4(2sin(3\u03c0((-3((2x + 3)/(2x - 1)) - 3)/(1((2x + 3)/(2x - 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) = 5(5(-1sin(1\u03c0(1x + 1) + 1) - 3)^2 - 3(-1sin(1\u03c0(1x + 1) + 1) - 3) + 2) + 5 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(2sin(2\u03c0(-3|(-4x - 1) - 3| + 1) + 2) + 1)^2 - 5 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "328", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -3|(2((3(-1|x + 3| + 2) - 2)/(-3(-1|x + 3| + 2) - 2))^2 - 5((3(-1|x + 3| + 2) - 2)/(-3(-1|x + 3| + 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": "7", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -5(-1(-3cos(1\u03c0(5x^2 + 5x + 5) + 2) + 2)^2 - 5(-3cos(1\u03c0(5x^2 + 5x + 5) + 2) + 2) - 2)^2 - 4(-1(-3cos(1\u03c0(5x^2 + 5x + 5) + 2) + 2)^2 - 5(-3cos(1\u03c0(5x^2 + 5x + 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": "146", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 3|(1cos(1\u03c0(-2|(-1x + 2) + 3| - 3) + 3) - 3) - 3| + 1 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 total count of local extrema points for the function f(x) = 1|(3(-3sin(2\u03c0((-3x)/(1x + 3)) - 2)) - 5) + 3| + 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "118", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = 1(2sin(2\u03c0(3((1x)/(-2x - 1)) + 3))) + 4 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": "Find the total number of local minima and maxima for f(x) = 2sin(2\u03c0((3(4(-1x^2 + 5x - 2)^2 + 1(-1x^2 + 5x - 2) - 3) + 3)/(1(4(-1x^2 + 5x - 2)^2 + 1(-1x^2 + 5x - 2) - 3) + 3)) + 3) - 2 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 maxima for the function f(x) = 3(4(5(-3cos(2\u03c0x - 3) - 3) - 1) - 2)^2 + 3(4(5(-3cos(2\u03c0x - 3) - 3) - 1) - 2) - 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": "How many local extrema (minima and maxima combined) does the function f(x) = -1sin(1\u03c0(5((2(-3x^2 + 5x + 5) - 3)/(2(-3x^2 + 5x + 5) + 3)) + 5) + 3) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "47", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 2(1((-1(3sin(1\u03c0x + 1) + 2))/(2(3sin(1\u03c0x + 1) + 2) + 3))^2 + 4((-1(3sin(1\u03c0x + 1) + 2))/(2(3sin(1\u03c0x + 1) + 2) + 3)) + 5)^2 + 5(1((-1(3sin(1\u03c0x + 1) + 2))/(2(3sin(1\u03c0x + 1) + 2) + 3))^2 + 4((-1(3sin(1\u03c0x + 1) + 2))/(2(3sin(1\u03c0x + 1) + 2) + 3)) + 5) + 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": "Find the number of local maximum points for f(x) = (-3(-1(2cos(3\u03c0(2x^2 + 4x + 5)) - 2) + 5) + 1)/(1(-1(2cos(3\u03c0(2x^2 + 4x + 5)) - 2) + 5) + 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "212", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -5(3(5(1|x - 3| - 2)^2 + 1(1|x - 3| - 2) - 1)^2 + 3(5(1|x - 3| - 2)^2 + 1(1|x - 3| - 2) - 1) - 3)^2 + 3(3(5(1|x - 3| - 2)^2 + 1(1|x - 3| - 2) - 1)^2 + 3(5(1|x - 3| - 2)^2 + 1(1|x - 3| - 2) - 1) - 3) + 4 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) = 1(1|(3|((-1x - 1)/(2x - 1)) - 1|) - 1| - 3)^2 - 5(1|(3|((-1x - 1)/(2x - 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": "4", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -2|((-1(-4(-2cos(2\u03c0x - 3) + 1) + 1) + 2)/(-3(-4(-2cos(2\u03c0x - 3) + 1) + 1) + 4)) - 2| - 1 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) = 3e^(-2(-1(-1|(3x^2 - 3x - 4) + 3|)^2 + 1(-1|(3x^2 - 3x - 4) + 3|) + 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 total number of local minima and maxima for f(x) = 1|((2(-2(1cos(3\u03c0x + 1) + 1) + 4) - 1)/(1(-2(1cos(3\u03c0x + 1) + 1) + 4))) + 1| + 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": "How many local minima does the function f(x) = 3cos(2\u03c0(4(-3|((-3x)/(2x + 2)) + 2| + 3)^2 + 3(-3|((-3x)/(2x + 2)) + 2| + 3) + 3) - 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "104", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = (1(-5(-5(-1|x + 1| + 1)^2 + 1(-1|x + 1| + 1) + 2)^2 - 5(-5(-1|x + 1| + 1)^2 + 1(-1|x + 1| + 1) + 2) - 5) + 2)/(2(-5(-5(-1|x + 1| + 1)^2 + 1(-1|x + 1| + 1) + 2)^2 - 5(-5(-1|x + 1| + 1)^2 + 1(-1|x + 1| + 1) + 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": "How many local extrema (minima and maxima combined) does the function f(x) = -2|(2|(-5(1sin(3\u03c0x - 1) - 2) - 5) - 2|) - 3| - 2 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 total number of local minima and maxima for f(x) = -1|(-3|(-1(2cos(2\u03c0x) - 2)^2 + 1(2cos(2\u03c0x) - 2) - 5) + 3| - 2) - 2| - 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": "How many local maxima does the function f(x) = -4(-3((2(-2sin(2\u03c0x) - 2))/(3(-2sin(2\u03c0x) - 2) - 1))^2 + 5((2(-2sin(2\u03c0x) - 2))/(3(-2sin(2\u03c0x) - 2) - 1)) + 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": "Determine the count of local minima for the function f(x) = 1sin(1\u03c0(1|(3((2x + 3)/(2x)) - 1) + 3| + 3) - 1) - 1 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 maximum points for f(x) = 4(-1sin(3\u03c0(1|(-3x^2 + 3x + 2) - 1| + 2) + 2)) + 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "262", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 3(1|(3(-2|x + 2| + 3)^2 + 5(-2|x + 2| + 3) - 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": "Determine the count of local maxima for the function f(x) = -3sin(1\u03c0(2|(-5(-2x^2 - 3x - 5)^2 - 4(-2x^2 - 3x - 5) + 3)|) - 3) + 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": "How many local maxima does the function f(x) = 1cos(3\u03c0(4((3(-3|x| + 1) + 1)/(-1(-3|x| + 1) + 3))^2 + 2((3(-3|x| + 1) + 1)/(-1(-3|x| + 1) + 3)) - 5) - 3) - 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 total number of local minima and maxima for f(x) = 1|(1(-2|(-3x^2 - 5x - 4)| + 2)^2 + 5(-2|(-3x^2 - 5x - 4)| + 2) + 3) - 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": "Determine the count of local maxima for the function f(x) = 2cos(2\u03c0(1(-4((3x + 1)/(-1x - 2))^2 + 2((3x + 1)/(-1x - 2)))^2 - 4(-4((3x + 1)/(-1x - 2))^2 + 2((3x + 1)/(-1x - 2))) + 2) + 2) - 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "206", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -1(2|(1cos(3\u03c0(-4x - 4) + 3) + 3) - 1| - 2)^2 - 4(2|(1cos(3\u03c0(-4x - 4) + 3) + 3) - 1| - 2) + 4 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 total number of local minima and maxima for f(x) = 2((2(-3sin(3\u03c0(4x^2 - 5x - 5)) - 2) - 1)/(1(-3sin(3\u03c0(4x^2 - 5x - 5)) - 2) - 3))^2 - 3((2(-3sin(3\u03c0(4x^2 - 5x - 5)) - 2) - 1)/(1(-3sin(3\u03c0(4x^2 - 5x - 5)) - 2) - 3)) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "457", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = (-2((3(-4(-2sin(1\u03c0x - 2))^2 + 1(-2sin(1\u03c0x - 2)) + 3) + 3)/(-1(-4(-2sin(1\u03c0x - 2))^2 + 1(-2sin(1\u03c0x - 2)) + 3) - 3)) - 3)/(3((3(-4(-2sin(1\u03c0x - 2))^2 + 1(-2sin(1\u03c0x - 2)) + 3) + 3)/(-1(-4(-2sin(1\u03c0x - 2))^2 + 1(-2sin(1\u03c0x - 2)) + 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": "Determine the total count of local extrema points for the function f(x) = -2sin(2\u03c0(-4(2((-3x + 1)/(-2x + 3))^2 - 4((-3x + 1)/(-2x + 3)) + 5)) - 3) + 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "116", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = (2(1cos(1\u03c0(5(1x - 2)^2 - 3(1x - 2) - 4) + 3) + 3) - 1)/(1(1cos(1\u03c0(5(1x - 2)^2 - 3(1x - 2) - 4) + 3) + 3) + 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "501", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 2cos(2\u03c0((-2(-5(3x + 1)^2 + 1(3x + 1) + 2) + 1)/(1(-5(3x + 1)^2 + 1(3x + 1) + 2) - 2)) - 1) + 1 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 total number of local minima and maxima for f(x) = 2|(2sin(3\u03c0((-1(-2x - 3) + 3)/(2(-2x - 3) + 2)) - 1)) - 1| - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "47", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -3sin(1\u03c0(-5(-2(1|x - 2| + 1) - 1)^2 - 2(-2(1|x - 2| + 1) - 1) + 4) - 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": "Find the number of local maximum points for f(x) = -1cos(3\u03c0(-3|(-1|(-3|x + 3| + 1) - 2| + 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": "270", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -3(-2cos(2\u03c0((3(-3x^2 + 5x) - 3)/(-3(-3x^2 + 5x))) - 1) - 1)^2 + 1(-2cos(2\u03c0((3(-3x^2 + 5x) - 3)/(-3(-3x^2 + 5x))) - 1) - 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) = -1sin(3\u03c0(2|(4(-1|x - 3| - 2)^2 - 5(-1|x - 3| - 2) - 1) + 1|) + 1) + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "261", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -5(-2cos(3\u03c0(-4((1x - 1)/(1x - 2))^2 - 1((1x - 1)/(1x - 2)) + 2) + 1) - 2)^2 + 2(-2cos(3\u03c0(-4((1x - 1)/(1x - 2))^2 - 1((1x - 1)/(1x - 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": "93", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -3sin(2\u03c0(2|(5(1x^2 - 3x - 4) + 4) - 2| - 2) + 1) + 3 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 maximum points for f(x) = (-3(-1(-2sin(3\u03c0(1|x - 1|) - 1) - 1)^2 - 5(-2sin(3\u03c0(1|x - 1|) - 1) - 1) + 5) + 1)/(-2(-1(-2sin(3\u03c0(1|x - 1|) - 1) - 1)^2 - 5(-2sin(3\u03c0(1|x - 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": "90", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -1sin(1\u03c0(5((2((1x - 1)/(1x - 2)) + 3)/(-2((1x - 1)/(1x - 2)) - 2))^2 - 3((2((1x - 1)/(1x - 2)) + 3)/(-2((1x - 1)/(1x - 2)) - 2)) - 5) - 1) - 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 total count of local extrema points for the function f(x) = (2((-3(1e^(-1((-3x)/(-1x + 2))) + 2) + 2)/(-2(1e^(-1((-3x)/(-1x + 2))) + 2) + 3)) + 2)/(-3((-3(1e^(-1((-3x)/(-1x + 2))) + 2) + 2)/(-2(1e^(-1((-3x)/(-1x + 2))) + 2) + 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": "Determine the total count of local extrema points for the function f(x) = -1(-1(-2sin(3\u03c0(-2|x - 3| - 2)))^2 - 4(-2sin(3\u03c0(-2|x - 3| - 2))) - 2) - 5 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 minimum points for f(x) = 3|(3cos(1\u03c0(-5(-1x^2 + 1x - 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 number of local maximum points for f(x) = -2|(-5(2cos(3\u03c0(-3x + 4) - 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": "90", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = (3(-2(3(2|x + 3| - 1)^2 - 2(2|x + 3| - 1) - 2)^2 - 1(3(2|x + 3| - 1)^2 - 2(2|x + 3| - 1) - 2) - 2) - 3)/(3(-2(3(2|x + 3| - 1)^2 - 2(2|x + 3| - 1) - 2)^2 - 1(3(2|x + 3| - 1)^2 - 2(2|x + 3| - 1) - 2) - 2) + 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": "Determine the count of local minima for the function f(x) = -4((3(4(-3sin(3\u03c0x + 2) - 3)) + 1)/(-1(4(-3sin(3\u03c0x + 2) - 3)) + 2))^2 - 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": "Find the total number of local minima and maxima for f(x) = (-1((3(-2(1cos(2\u03c0x - 2) - 3)^2 - 5(1cos(2\u03c0x - 2) - 3) + 2) - 1)/(-2(-2(1cos(2\u03c0x - 2) - 3)^2 - 5(1cos(2\u03c0x - 2) - 3) + 2) - 2)) + 3)/(2((3(-2(1cos(2\u03c0x - 2) - 3)^2 - 5(1cos(2\u03c0x - 2) - 3) + 2) - 1)/(-2(-2(1cos(2\u03c0x - 2) - 3)^2 - 5(1cos(2\u03c0x - 2) - 3) + 2) - 2)) + 1) 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": "Find the total number of local minima and maxima for f(x) = 3cos(1\u03c0(1|(5(5x - 1) + 3) + 2| - 2)) + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "500", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -3(-2cos(3\u03c0(-1|(-4x - 4) - 2| + 1) - 1) - 1)^2 - 2(-2cos(3\u03c0(-1|(-4x - 4) - 2| + 1) - 1) - 1) 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": "Determine the count of local maxima for the function f(x) = 5(-3((-2(3cos(3\u03c0x + 2) + 2) - 3)/(-1(3cos(3\u03c0x + 2) + 2) + 2)) + 5) - 5 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(-2cos(3\u03c0((1(-4x^2 - 2x + 1) - 1)/(-1(-4x^2 - 2x + 1) + 2)) + 3))^2 - 5(-2cos(3\u03c0((1(-4x^2 - 2x + 1) - 1)/(-1(-4x^2 - 2x + 1) + 2)) + 3)) + 4 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 minima does the function f(x) = (2(-3(5(1x + 5)^2 - 2(1x + 5) - 2)^2 - 3(5(1x + 5)^2 - 2(1x + 5) - 2) - 3) + 2)/(3(-3(5(1x + 5)^2 - 2(1x + 5) - 2)^2 - 3(5(1x + 5)^2 - 2(1x + 5) - 2) - 3) + 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "79", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -4(-2cos(2\u03c0(-5(3x + 2) + 3) + 1))^2 + 3(-2cos(2\u03c0(-5(3x + 2) + 3) + 1)) - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "793", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 2e^(-1(4((-2(4x^2 - 1x - 1) - 1)/(1(4x^2 - 1x - 1) + 2))^2 - 3((-2(4x^2 - 1x - 1) - 1)/(1(4x^2 - 1x - 1) + 2)) + 5)) - 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) = 1e^(-1(-2(-1(2|x - 3|) - 4) - 5)) + 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) = -3cos(3\u03c0((1(5(-4x^2 - 4x + 4)^2) - 3)/(1(5(-4x^2 - 4x + 4)^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": "How many local maxima does the function f(x) = -1((-2(-2|(2cos(3\u03c0x) - 1) - 3| + 2) + 2)/(2(-2|(2cos(3\u03c0x) - 1) - 3| + 2) + 1))^2 - 2((-2(-2|(2cos(3\u03c0x) - 1) - 3| + 2) + 2)/(2(-2|(2cos(3\u03c0x) - 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": "30", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -2cos(3\u03c0(2(-1(1x - 1)^2 + 4(1x - 1) + 5) - 1) - 3) - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "537", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = (1(3cos(3\u03c0(1|(1x + 3) - 3| + 1) + 3) - 1))/(-1(3cos(3\u03c0(1|(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": "30", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = 3(-1sin(3\u03c0(-2|(3x + 1) - 1| + 2) + 2) + 3) + 5 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "181", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = (1(-1|(1(-2cos(2\u03c0x + 2) + 2))| + 3) - 2)/(3(-1|(1(-2cos(2\u03c0x + 2) + 2))| + 3) + 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": "How many local minima does the function f(x) = 3sin(1\u03c0(-2|((-2((1x)/(3x - 1)) - 2)/(2((1x)/(3x - 1)) + 1)) - 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 extrema (minima and maxima combined) does the function f(x) = 3((-3(1(1sin(2\u03c0x - 2) - 1)^2 + 1(1sin(2\u03c0x - 2) - 1) - 2) - 3)/(-2(1(1sin(2\u03c0x - 2) - 1)^2 + 1(1sin(2\u03c0x - 2) - 1) - 2) + 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 number of local minimum points for f(x) = 5(5(3sin(3\u03c0((1x + 3)/(-1x)) - 3) - 2)^2 - 4(3sin(3\u03c0((1x + 3)/(-1x)) - 3) - 2) + 5) + 2 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": "Determine the count of local maxima for the function f(x) = -1(-2cos(3\u03c0((3(-1x - 2) - 1)/(-3(-1x - 2) - 2)) + 3) + 3)^2 - 3(-2cos(3\u03c0((3(-1x - 2) - 1)/(-3(-1x - 2) - 2)) + 3) + 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": "How many local minima does the function f(x) = -1|(-2sin(1\u03c0((-3(-1|x| + 1) - 2)/(-2(-1|x| + 1) - 3)) - 2) - 2)| 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 extrema (minima and maxima combined) does the function f(x) = -3(3cos(2\u03c0(2|(-3|x + 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": "239", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = (-2(-4(-2cos(1\u03c0((-2x + 3)/(-2x - 3)) - 3) - 3) + 3) - 2)/(2(-4(-2cos(1\u03c0((-2x + 3)/(-2x - 3)) - 3) - 3) + 3) - 1) 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 minima does the function f(x) = 1(-1|(-2|(-1|x - 3| - 1) + 2| - 3)| + 2)^2 + 4(-1|(-2|(-1|x - 3| - 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": "7", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = -2(5(1sin(2\u03c0(-5x - 3) - 1) + 3)^2 + 4(1sin(2\u03c0(-5x - 3) - 1) + 3) + 1)^2 + 1(5(1sin(2\u03c0(-5x - 3) - 1) + 3)^2 + 4(1sin(2\u03c0(-5x - 3) - 1) + 3) + 1) - 2 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 count of local maxima for the function f(x) = 3(-3e^(1(-3|(5x - 3)|)) + 1)^2 - 5(-3e^(1(-3|(5x - 3)|)) + 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 minima does the function f(x) = 2(3(-3cos(2\u03c0((3x + 3)/(2x - 3)) - 2) + 1) + 2)^2 + 5(3(-3cos(2\u03c0((3x + 3)/(2x - 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": "35", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -3|(-2cos(1\u03c0(-2|((2x)/(3x - 2)) + 3| - 2) - 1) + 2) + 3| - 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": "Find the total number of local minima and maxima for f(x) = 2sin(1\u03c0(-4((-2(-3x^2 + 3x) + 1)/(-1(-3x^2 + 3x) + 3))^2 - 5((-2(-3x^2 + 3x) + 1)/(-1(-3x^2 + 3x) + 3))) - 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": "Find the total number of local minima and maxima for f(x) = 1((1(-2e^(2(-1x^2 + 1x + 4)) + 3) - 3)/(-3(-2e^(2(-1x^2 + 1x + 4)) + 3)))^2 + 3((1(-2e^(2(-1x^2 + 1x + 4)) + 3) - 3)/(-3(-2e^(2(-1x^2 + 1x + 4)) + 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 count of local minima for the function f(x) = -4(-3(1sin(3\u03c0((-3x + 2)/(1x + 3)) - 2) - 1)^2 + 2(1sin(3\u03c0((-3x + 2)/(1x + 3)) - 2) - 1) + 4)^2 + 3(-3(1sin(3\u03c0((-3x + 2)/(1x + 3)) - 2) - 1)^2 + 2(1sin(3\u03c0((-3x + 2)/(1x + 3)) - 2) - 1) + 4) + 2 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 maxima does the function f(x) = -5(3|(5(-3cos(3\u03c0x - 3))) - 1| - 2)^2 + 5(3|(5(-3cos(3\u03c0x - 3))) - 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": "Find the number of local minimum points for f(x) = 4(2cos(2\u03c0(-5((2x)/(2x + 2)) + 2) - 2) + 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": "Determine the total count of local extrema points for the function f(x) = -5(1|(-4(1x^2 + 4x - 1)^2 + 2(1x^2 + 4x - 1) + 4)|) + 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) = 3(-2|(-1cos(1\u03c0(-1x - 1) + 3) + 1) - 2| + 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) = 1cos(1\u03c0((-2(-1(-3x^2 - 1x) - 4) + 2)/(3(-1(-3x^2 - 1x) - 4) + 3)) - 3) + 2 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 maxima for the function f(x) = -1(-1(-1cos(2\u03c0(-1x^2 + 2x + 2)) - 2)^2 - 3) + 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "189", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 4(2cos(2\u03c0(4(-3x + 4)^2 + 4(-3x + 4) - 1) - 1) - 3)^2 + 4(2cos(2\u03c0(4(-3x + 4)^2 + 4(-3x + 4) - 1) - 1) - 3) + 4 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": "Find the number of local maximum points for f(x) = 1sin(3\u03c0(-4(5((2x + 1)/(1x + 2)) + 5)^2 - 3(5((2x + 1)/(1x + 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": "247", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 1cos(1\u03c0(-1|(-1(-1x^2 - 4)^2 - 2(-1x^2 - 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": "215", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = 4((1(-2sin(3\u03c0(3|x + 3| + 1)) + 3) - 3)/(-1(-2sin(3\u03c0(3|x + 3| + 1)) + 3) - 1))^2 - 5((1(-2sin(3\u03c0(3|x + 3| + 1)) + 3) - 3)/(-1(-2sin(3\u03c0(3|x + 3| + 1)) + 3) - 1)) - 5 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "181", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 3|(-2(1sin(2\u03c0(-1|x + 1| - 2)) + 1) - 2) - 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": "Determine the count of local minima for the function f(x) = -5((2((-1(-1sin(1\u03c0x + 2) + 3) - 1)/(-3(-1sin(1\u03c0x + 2) + 3) - 2)))/(-3((-1(-1sin(1\u03c0x + 2) + 3) - 1)/(-3(-1sin(1\u03c0x + 2) + 3) - 2)) + 1)) + 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": "Find the total number of local minima and maxima for f(x) = -1e^(2(1(-2(-1x^2 - 3x - 1)^2 + 2(-1x^2 - 3x - 1) - 2) - 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 maxima for the function f(x) = -1|(1(-3(-2sin(2\u03c0x - 2) - 1)^2 + 3(-2sin(2\u03c0x - 2) - 1) - 4) - 1) + 3| + 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": "How many local minima does the function f(x) = 1(3(5(4x^2 + 2x)^2 - 2(4x^2 + 2x))^2 + 5(5(4x^2 + 2x)^2 - 2(4x^2 + 2x)) - 1)^2 - 1(3(5(4x^2 + 2x)^2 - 2(4x^2 + 2x))^2 + 5(5(4x^2 + 2x)^2 - 2(4x^2 + 2x)) - 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) = -2sin(3\u03c0(-2(-3(-2x^2 - 5x - 1)^2 + 2(-2x^2 - 5x - 1) + 1) + 1) + 3) - 3 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 number of local minimum points for f(x) = -2|(-2(4(3x^2 + 4x - 2))^2 - 5(4(3x^2 + 4x - 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) = -4(2e^(2((-3(-1x^2 + 3x + 5) - 3)/(1(-1x^2 + 3x + 5)))) - 1)^2 + 5(2e^(2((-3(-1x^2 + 3x + 5) - 3)/(1(-1x^2 + 3x + 5)))) - 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": "How many local extrema (minima and maxima combined) does the function f(x) = -4((-2(-1(-2|x - 2|)^2 + 4(-2|x - 2|) + 1) - 2)/(-2(-1(-2|x - 2|)^2 + 4(-2|x - 2|) + 1) - 1))^2 + 2((-2(-1(-2|x - 2|)^2 + 4(-2|x - 2|) + 1) - 2)/(-2(-1(-2|x - 2|)^2 + 4(-2|x - 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": "How many local minima does the function f(x) = -5(-5((2(-5x^2 - 3x + 3) + 2)/(2(-5x^2 - 3x + 3) - 1))^2 - 3((2(-5x^2 - 3x + 3) + 2)/(2(-5x^2 - 3x + 3) - 1)) - 5) + 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) = 1sin(2\u03c0(2((3(-3x) + 1)/(-3(-3x) - 3)) - 2) - 3) - 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": "Find the total number of local minima and maxima for f(x) = 3sin(1\u03c0((-3(3|(-1x + 1) + 3|) + 1)/(-2(3|(-1x + 1) + 3|) + 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": "Find the number of local maximum points for f(x) = -1sin(3\u03c0(2|((3(-1|x - 1| + 1) - 3)/(-2(-1|x - 1| + 1) + 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": "8", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 2(1(-1cos(3\u03c0(-2x^2 - 2) - 1) + 1) - 1)^2 - 5(1(-1cos(3\u03c0(-2x^2 - 2) - 1) + 1) - 1) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "449", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = 2cos(2\u03c0(5((1(2x^2 - 4x - 4) - 3)/(-1(2x^2 - 4x - 4) - 3))^2 + 4((1(2x^2 - 4x - 4) - 3)/(-1(2x^2 - 4x - 4) - 3)) + 3) + 2) - 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 number of local minimum points for f(x) = 2sin(1\u03c0(5(-3|(1|x - 2| - 1) - 1| - 3)^2 + 1(-3|(1|x - 2| - 1) - 1| - 3) - 4) + 3) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "236", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -5(-1cos(2\u03c0(-2((-3x)/(1x - 2)) - 5)) - 3)^2 - 4(-1cos(2\u03c0(-2((-3x)/(1x - 2)) - 5)) - 3) - 3 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": "Determine the total count of local extrema points for the function f(x) = -3cos(2\u03c0(5(-2(2|x - 2| - 2)^2 - 3(2|x - 2| - 2) + 4) + 1) - 3) - 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "450", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -3(1((2(-3cos(3\u03c0x) + 3) - 1)/(2(-3cos(3\u03c0x) + 3) + 3)) - 3)^2 - 1(1((2(-3cos(3\u03c0x) + 3) - 1)/(2(-3cos(3\u03c0x) + 3) + 3)) - 3) - 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 total number of local minima and maxima for f(x) = 3(-2(2cos(3\u03c0(-4x - 4) + 1)) + 3)^2 - 4(-2(2cos(3\u03c0(-4x - 4) + 1)) + 3) + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "480", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -3|((3(-2sin(3\u03c0((-2x - 3)/(3x + 2)) + 3)) + 2)/(1(-2sin(3\u03c0((-2x - 3)/(3x + 2)) + 3)))) - 3| + 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = (1(2|((1(3x^2 - 1x - 4) + 2)/(-1(3x^2 - 1x - 4) + 3))| + 3) - 1)/(3(2|((1(3x^2 - 1x - 4) + 2)/(-1(3x^2 - 1x - 4) + 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": "How many local minima does the function f(x) = 2((-2(-4(-2sin(2\u03c0x + 1) - 2)^2 - 5(-2sin(2\u03c0x + 1) - 2) + 2) + 1)/(1(-4(-2sin(2\u03c0x + 1) - 2)^2 - 5(-2sin(2\u03c0x + 1) - 2) + 2) + 2))^2 + 3((-2(-4(-2sin(2\u03c0x + 1) - 2)^2 - 5(-2sin(2\u03c0x + 1) - 2) + 2) + 1)/(1(-4(-2sin(2\u03c0x + 1) - 2)^2 - 5(-2sin(2\u03c0x + 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": "119", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = (3((2(-3((3x - 1)/(-2x - 3))^2 + 5((3x - 1)/(-2x - 3)) - 1) + 3)/(-1(-3((3x - 1)/(-2x - 3))^2 + 5((3x - 1)/(-2x - 3)) - 1) - 2)) + 3)/(-2((2(-3((3x - 1)/(-2x - 3))^2 + 5((3x - 1)/(-2x - 3)) - 1) + 3)/(-1(-3((3x - 1)/(-2x - 3))^2 + 5((3x - 1)/(-2x - 3)) - 1) - 2)) - 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "146", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = (2(3|(3sin(2\u03c0(1x^2 + 4x + 5) + 1) - 1)| - 1) - 3)/(2(3|(3sin(2\u03c0(1x^2 + 4x + 5) + 1) - 1)| - 1) + 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "534", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 1cos(1\u03c0(2|(-4(2|x - 2| - 2)^2 - 5) + 3| + 3)) - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "499", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 3(-2(-1sin(1\u03c0((3x + 2)/(1x + 3)) - 1) + 3)^2 - 4(-1sin(1\u03c0((3x + 2)/(1x + 3)) - 1) + 3) + 4)^2 - 2(-2(-1sin(1\u03c0((3x + 2)/(1x + 3)) - 1) + 3)^2 - 4(-1sin(1\u03c0((3x + 2)/(1x + 3)) - 1) + 3) + 4) + 4 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": "Find the number of local maximum points for f(x) = -2((1(3e^(-2(-3x + 3))) + 3)/(-3(3e^(-2(-3x + 3))) - 2))^2 + 4((1(3e^(-2(-3x + 3))) + 3)/(-3(3e^(-2(-3x + 3))) - 2)) 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": "Find the number of local minimum points for f(x) = -3|((-1(3cos(3\u03c0(1x^2 + 5x - 5) + 3) + 1) - 2)/(2(3cos(3\u03c0(1x^2 + 5x - 5) + 3) + 1))) + 2| - 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": "Find the number of local minimum points for f(x) = 3cos(2\u03c0(-1|(1|(1x^2 + 1x + 5)| - 2) - 1| + 1) - 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "200", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = 1(4(1(-1x^2 - 2x + 3)^2 + 3(-1x^2 - 2x + 3) + 2) - 5)^2 + 5(4(1(-1x^2 - 2x + 3)^2 + 3(-1x^2 - 2x + 3) + 2) - 5) - 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": "Find the number of local maximum points for f(x) = -2|(-1(3|(2cos(1\u03c0x - 1) + 1)|)^2 - 5(3|(2cos(1\u03c0x - 1) + 1)|)) - 2| + 2 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 number of local maximum points for f(x) = -3sin(2\u03c0(-4(4(5x^2 + 2x + 1)^2 - 4(5x^2 + 2x + 1) + 2)^2 + 1(4(5x^2 + 2x + 1)^2 - 4(5x^2 + 2x + 1) + 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": "How many local extrema (minima and maxima combined) does the function f(x) = 4(1|(-1(1cos(3\u03c0x - 2) - 3)^2 - 4(1cos(3\u03c0x - 2) - 3) + 1) + 3| - 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 extrema (minima and maxima combined) does the function f(x) = -3|((-2(2e^(1(-3|x + 1| - 2)) - 1) - 3)/(-2(2e^(1(-3|x + 1| - 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": "How many local minima does the function f(x) = (-1((2(1cos(1\u03c0(-1x^2 - 5x - 1) - 2) - 2) - 2)/(-1(1cos(1\u03c0(-1x^2 - 5x - 1) - 2) - 2) - 1)) + 3)/(-3((2(1cos(1\u03c0(-1x^2 - 5x - 1) - 2) - 2) - 2)/(-1(1cos(1\u03c0(-1x^2 - 5x - 1) - 2) - 2) - 1)) + 4) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "104", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 2((3(-5(-1x^2 + 4x + 1) - 3))/(2(-5(-1x^2 + 4x + 1) - 3)))^2 + 1((3(-5(-1x^2 + 4x + 1) - 3))/(2(-5(-1x^2 + 4x + 1) - 3))) + 5 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 extrema (minima and maxima combined) does the function f(x) = (3(1(1|(-3sin(1\u03c0x + 1) - 3) - 3| + 1)) + 1)/(1(1(1|(-3sin(1\u03c0x + 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": "20", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -3|((-1(-1(-2sin(1\u03c0x)) + 4) - 1)/(-2(-1(-2sin(1\u03c0x)) + 4) - 3))| - 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 number of local maximum points for f(x) = (-3(2(-2|(1e^(-2x) + 1) + 2|)^2 - 4(-2|(1e^(-2x) + 1) + 2|) - 2))/(-1(2(-2|(1e^(-2x) + 1) + 2|)^2 - 4(-2|(1e^(-2x) + 1) + 2|) - 2) - 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) = -3(1(5(-2cos(3\u03c0x + 3) + 1)^2 + 1(-2cos(3\u03c0x + 3) + 1) - 1) - 4) - 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": "How many local maxima does the function f(x) = -2(-1cos(1\u03c0(5(1|x - 1| - 2)^2 + 3(1|x - 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": "244", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -2((1(-2(-3cos(2\u03c0x - 3) - 1)^2 - 3(-3cos(2\u03c0x - 3) - 1) - 4) + 2)/(-3(-2(-3cos(2\u03c0x - 3) - 1)^2 - 3(-3cos(2\u03c0x - 3) - 1) - 4) - 1)) + 5 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 extrema (minima and maxima combined) does the function f(x) = -1|((1((-2(3cos(3\u03c0x - 2) - 2) + 3)/(-2(3cos(3\u03c0x - 2) - 2) + 1)) + 1)/(1((-2(3cos(3\u03c0x - 2) - 2) + 3)/(-2(3cos(3\u03c0x - 2) - 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": "132", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = 5(1((-3(-2cos(2\u03c0x + 3) - 2) + 2)/(1(-2cos(2\u03c0x + 3) - 2)))^2 + 2((-3(-2cos(2\u03c0x + 3) - 2) + 2)/(1(-2cos(2\u03c0x + 3) - 2))) - 3)^2 + 4(1((-3(-2cos(2\u03c0x + 3) - 2) + 2)/(1(-2cos(2\u03c0x + 3) - 2)))^2 + 2((-3(-2cos(2\u03c0x + 3) - 2) + 2)/(1(-2cos(2\u03c0x + 3) - 2))) - 3) - 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": "Find the total number of local minima and maxima for f(x) = (-3((-2(-3(-3e^(2x))^2 + 3(-3e^(2x)) - 3) - 2)/(3(-3(-3e^(2x))^2 + 3(-3e^(2x)) - 3) - 1)) + 3)/(-3((-2(-3(-3e^(2x))^2 + 3(-3e^(2x)) - 3) - 2)/(3(-3(-3e^(2x))^2 + 3(-3e^(2x)) - 3) - 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": "Find the number of local maximum points for f(x) = (2(-3|(-2sin(3\u03c0(-1x^2 + 4x + 4) - 3) + 3) - 1| + 2))/(-1(-3|(-2sin(3\u03c0(-1x^2 + 4x + 4) - 3) + 3) - 1| + 2) + 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "81", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = (-2(1(3sin(1\u03c0(-1|x - 3| - 1) + 1) - 1) - 2) - 3)/(1(1(3sin(1\u03c0(-1|x - 3| - 1) + 1) - 1) - 2) + 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 minima does the function f(x) = 4((-1((3(1cos(2\u03c0x)) - 3)/(-1(1cos(2\u03c0x)) + 3)) + 1)/(-1((3(1cos(2\u03c0x)) - 3)/(-1(1cos(2\u03c0x)) + 3)) - 2))^2 - 5((-1((3(1cos(2\u03c0x)) - 3)/(-1(1cos(2\u03c0x)) + 3)) + 1)/(-1((3(1cos(2\u03c0x)) - 3)/(-1(1cos(2\u03c0x)) + 3)) - 2)) - 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(3sin(2\u03c0(2x^2 - 1x - 1) - 3) + 3)^2 - 3(3sin(2\u03c0(2x^2 - 1x - 1) - 3) + 3) - 2) + 1| have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "405", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 1sin(1\u03c0(2(-5((2x)/(2x - 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": "50", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 3(-5(-1(-3x^2 + 1x + 4) - 3)^2 - 2(-1(-3x^2 + 1x + 4) - 3) + 4)^2 + 5(-5(-1(-3x^2 + 1x + 4) - 3)^2 - 2(-1(-3x^2 + 1x + 4) - 3) + 4) + 5 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(3cos(3\u03c0(-3|x + 1| - 1) + 1))^2 - 5(3cos(3\u03c0(-3|x + 1| - 1) + 1)) + 1) - 2)/(-3(2(3cos(3\u03c0(-3|x + 1| - 1) + 1))^2 - 5(3cos(3\u03c0(-3|x + 1| - 1) + 1)) + 1) + 1) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "181", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = 1cos(3\u03c0(-5(-5(1x^2 + 5x - 1) + 2)^2 - 2(-5(1x^2 + 5x - 1) + 2) - 5) + 1) - 3 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 maxima does the function f(x) = -1|(-1(1cos(1\u03c0((1x - 2)/(1x)) + 2) + 3)^2 - 1(1cos(1\u03c0((1x - 2)/(1x)) + 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": "18", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = 1|(-4(2((1x - 2)/(2x + 2))^2 + 5((1x - 2)/(2x + 2)) - 1)^2 - 4(2((1x - 2)/(2x + 2))^2 + 5((1x - 2)/(2x + 2)) - 1) + 1) + 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) = (-2((3(1sin(3\u03c0(-4x^2 - 2) + 2) - 2) + 1)/(-3(1sin(3\u03c0(-4x^2 - 2) + 2) - 2) - 2)))/(-3((3(1sin(3\u03c0(-4x^2 - 2) + 2) - 2) + 1)/(-3(1sin(3\u03c0(-4x^2 - 2) + 2) - 2) - 2)) - 3) have 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 maximum points for f(x) = -1cos(1\u03c0(5(2(3x + 4)^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": "224", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = (1(4(-1(1e^(-2x) + 1) + 3)^2 + 1(-1(1e^(-2x) + 1) + 3) - 3) + 3)/(3(4(-1(1e^(-2x) + 1) + 3)^2 + 1(-1(1e^(-2x) + 1) + 3) - 3) + 1) 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) = -2((-2(2cos(2\u03c0(-5x - 5) - 2) + 2) - 3)/(1(2cos(2\u03c0(-5x - 5) - 2) + 2) - 3))^2 + 1((-2(2cos(2\u03c0(-5x - 5) - 2) + 2) - 3)/(1(2cos(2\u03c0(-5x - 5) - 2) + 2) - 3)) - 4 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 total number of local minima and maxima for f(x) = (1(-2|(-1(-1cos(3\u03c0x + 1) - 3) + 2)| + 2))/(3(-2|(-1(-1cos(3\u03c0x + 1) - 3) + 2)| + 2) - 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": "Find the number of local maximum points for f(x) = 5(-1(-2|(-3sin(3\u03c0x - 3) + 3) - 2| + 1)^2 + 2(-2|(-3sin(3\u03c0x - 3) + 3) - 2| + 1) - 2)^2 - 3(-1(-2|(-3sin(3\u03c0x - 3) + 3) - 2| + 1)^2 + 2(-2|(-3sin(3\u03c0x - 3) + 3) - 2| + 1) - 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": "Find the number of local minimum points for f(x) = -1((-1(3cos(1\u03c0(-1x^2 - 5x + 4) + 1) + 3) + 1)/(-3(3cos(1\u03c0(-1x^2 - 5x + 4) + 1) + 3) - 1))^2 - 4((-1(3cos(1\u03c0(-1x^2 - 5x + 4) + 1) + 3) + 1)/(-3(3cos(1\u03c0(-1x^2 - 5x + 4) + 1) + 3) - 1)) 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 minima does the function f(x) = 3(-5((1(-2sin(1\u03c0x - 3) - 2))/(-1(-2sin(1\u03c0x - 3) - 2) - 1)) + 3)^2 - 5(-5((1(-2sin(1\u03c0x - 3) - 2))/(-1(-2sin(1\u03c0x - 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": "50", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -5(-1|(-1(2cos(1\u03c0x))^2 - 1)| + 2)^2 + 3(-1|(-1(2cos(1\u03c0x))^2 - 1)| + 2) + 5 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": "How many local minima does the function f(x) = 2|(1sin(2\u03c0(-1|((-2x + 3)/(1x + 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": "31", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = (-1(-1|(-2sin(1\u03c0(-5x^2 + 4x + 3) + 3)) - 3|) + 2)/(-1(-1|(-2sin(1\u03c0(-5x^2 + 4x + 3) + 3)) - 3|) - 1) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "499", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = 3((-3(3(2sin(2\u03c0x - 1) - 2) - 4) + 1)/(-3(3(2sin(2\u03c0x - 1) - 2) - 4) + 2)) - 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 total number of local minima and maxima for f(x) = (1((-3(-5(2|x|)^2 - 2(2|x|) + 1) + 3)/(-1(-5(2|x|)^2 - 2(2|x|) + 1) - 1)))/(-3((-3(-5(2|x|)^2 - 2(2|x|) + 1) + 3)/(-1(-5(2|x|)^2 - 2(2|x|) + 1) - 1))) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "330", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = (-2(1cos(1\u03c0(3(1x^2 - 5x) + 2) - 1) - 2) - 1)/(-1(1cos(1\u03c0(3(1x^2 - 5x) + 2) - 1) - 2) - 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "533", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = (3(-1cos(1\u03c0((3(-2x^2 + 2x + 2) + 2)/(-3(-2x^2 + 2x + 2) + 1)) + 3) - 3) + 2)/(-3(-1cos(1\u03c0((3(-2x^2 + 2x + 2) + 2)/(-3(-2x^2 + 2x + 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": "25", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 1(-3(-3(-3sin(1\u03c0x + 3) + 1)^2 - 2)^2 + 1(-3(-3sin(1\u03c0x + 3) + 1)^2 - 2) + 2)^2 + 4(-3(-3(-3sin(1\u03c0x + 3) + 1)^2 - 2)^2 + 1(-3(-3sin(1\u03c0x + 3) + 1)^2 - 2) + 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 total count of local extrema points for the function f(x) = -2sin(2\u03c0(-1(-2((-3x)/(1x - 2))^2 - 3((-3x)/(1x - 2)) + 3)^2 - 1(-2((-3x)/(1x - 2))^2 - 3((-3x)/(1x - 2)) + 3) - 3)) + 2 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 extrema (minima and maxima combined) does the function f(x) = (3(2sin(1\u03c0(1|(-3|x - 2| + 3) + 2| - 2) - 2) + 3))/(2(2sin(1\u03c0(1|(-3|x - 2| + 3) + 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": "63", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -5((2(1(-2x^2 - 2x - 4)^2 + 3(-2x^2 - 2x - 4) - 5) - 1)/(2(1(-2x^2 - 2x - 4)^2 + 3(-2x^2 - 2x - 4) - 5)))^2 + 2((2(1(-2x^2 - 2x - 4)^2 + 3(-2x^2 - 2x - 4) - 5) - 1)/(2(1(-2x^2 - 2x - 4)^2 + 3(-2x^2 - 2x - 4) - 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": "Find the total number of local minima and maxima for f(x) = (3(5(1|(2e^(-2x) - 2) + 3| + 2)^2 + 1(1|(2e^(-2x) - 2) + 3| + 2) + 2) + 3)/(-1(5(1|(2e^(-2x) - 2) + 3| + 2)^2 + 1(1|(2e^(-2x) - 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": "46", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -1((2(1((-1x + 1)/(2x + 1))^2 - 5((-1x + 1)/(2x + 1)) + 4) + 1)/(-1(1((-1x + 1)/(2x + 1))^2 - 5((-1x + 1)/(2x + 1)) + 4) + 3))^2 - 1((2(1((-1x + 1)/(2x + 1))^2 - 5((-1x + 1)/(2x + 1)) + 4) + 1)/(-1(1((-1x + 1)/(2x + 1))^2 - 5((-1x + 1)/(2x + 1)) + 4) + 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 maxima does the function f(x) = 3((1((-2(1sin(1\u03c0x + 3) + 2) - 1)/(2(1sin(1\u03c0x + 3) + 2) + 2)) + 2)/(-2((-2(1sin(1\u03c0x + 3) + 2) - 1)/(2(1sin(1\u03c0x + 3) + 2) + 2)) + 3)) + 3 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) = -4(3(-1(-3sin(2\u03c0x + 2) + 1)^2 - 4(-3sin(2\u03c0x + 2) + 1) + 1)^2 - 5(-1(-3sin(2\u03c0x + 2) + 1)^2 - 4(-3sin(2\u03c0x + 2) + 1) + 1) + 1)^2 - 2(3(-1(-3sin(2\u03c0x + 2) + 1)^2 - 4(-3sin(2\u03c0x + 2) + 1) + 1)^2 - 5(-1(-3sin(2\u03c0x + 2) + 1)^2 - 4(-3sin(2\u03c0x + 2) + 1) + 1) + 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": "Find the number of local maximum points for f(x) = (-3(-1(-3(3e^(2x)) - 1)^2 + 3(-3(3e^(2x)) - 1) - 1) - 2)/(-1(-1(-3(3e^(2x)) - 1)^2 + 3(-3(3e^(2x)) - 1) - 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": "Determine the total count of local extrema points for the function f(x) = 5(-3cos(3\u03c0(2|((-2x - 1)/(3x + 3)) + 1| + 1) - 1)) + 5 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) = (-3(3|(3sin(1\u03c0(1x + 4)) - 2) + 1| - 2) - 2)/(-3(3|(3sin(1\u03c0(1x + 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": "16", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 2|((1(2|((1x + 1)/(-1x - 3)) + 1| - 3))/(2(2|((1x + 1)/(-1x - 3)) + 1| - 3) - 1)) - 1| + 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 total count of local extrema points for the function f(x) = -3((-2(3cos(2\u03c0(1x) + 1) - 1))/(-2(3cos(2\u03c0(1x) + 1) - 1) - 2))^2 + 2((-2(3cos(2\u03c0(1x) + 1) - 1))/(-2(3cos(2\u03c0(1x) + 1) - 1) - 2)) - 3 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) = (3(1(-2cos(3\u03c0(-1x) + 1) - 1)^2 - 3(-2cos(3\u03c0(-1x) + 1) - 1) + 1) + 1)/(-2(1(-2cos(3\u03c0(-1x) + 1) - 1)^2 - 3(-2cos(3\u03c0(-1x) + 1) - 1) + 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) = -2|(3(-2e^(2(3x^2 + 3x - 4)) + 2)^2 + 3(-2e^(2(3x^2 + 3x - 4)) + 2) + 5) - 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": "Find the number of local minimum points for f(x) = -3|(-2cos(1\u03c0(5(3x^2 + 5x + 1)^2 - 1(3x^2 + 5x + 1) + 4) + 2) - 1)| where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "179", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = 2|((3(2(1x^2 - 5x + 2)^2 - 2(1x^2 - 5x + 2) - 4) - 2)/(3(2(1x^2 - 5x + 2)^2 - 2(1x^2 - 5x + 2) - 4) + 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": "How many local maxima does the function f(x) = 1((-3(3(3sin(1\u03c0x - 2)) + 2) - 1)/(2(3(3sin(1\u03c0x - 2)) + 2) + 3)) + 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": "Determine the count of local minima for the function f(x) = 2cos(1\u03c0(5(-1(-3|x + 2| + 3) - 1)^2 + 2(-1(-3|x + 2| + 3) - 1) + 1) + 2) + 1 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 total number of local minima and maxima for f(x) = 2sin(1\u03c0((2(-5(5x) + 4) + 2)/(1(-5(5x) + 4))) - 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": "Determine the count of local minima for the function f(x) = -2(1sin(3\u03c0(-1(5x - 2) + 4) - 3) - 3) + 2 in the interval [-10, 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(2|(1cos(1\u03c0(-4x^2 + 2x + 2) - 1) - 2) + 1| - 1))/(-3(2|(1cos(1\u03c0(-4x^2 + 2x + 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": "353", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = (2(1cos(1\u03c0(5(5x^2 + 1x + 4)^2) + 2) - 2))/(3(1cos(1\u03c0(5(5x^2 + 1x + 4)^2) + 2) - 2) - 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "188", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = 3|((2(-1|(-3sin(1\u03c0x + 2) + 3) + 1| - 3) + 2)/(-2(-1|(-3sin(1\u03c0x + 2) + 3) + 1| - 3) + 3)) + 1| + 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": "Find the number of local maximum points for f(x) = 3(4(-3cos(2\u03c0(-3x^2 - 4) + 2) + 3)^2 + 2(-3cos(2\u03c0(-3x^2 - 4) + 2) + 3) + 3) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "174", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = (2(2(1sin(2\u03c0(-1x - 5) - 1) - 2) + 2))/(-2(2(1sin(2\u03c0(-1x - 5) - 1) - 2) + 2) + 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": "Find the number of local maximum points for f(x) = -2sin(1\u03c0(-5(-5((-2x + 2)/(2x - 1)) + 1) - 5) - 3) - 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": "How many local minima does the function f(x) = (2(3sin(3\u03c0(-3|(-3x^2 - 1x - 5) + 1| - 2) - 2) - 2) - 2)/(-3(3sin(3\u03c0(-3|(-3x^2 - 1x - 5) + 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": "200", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -3sin(1\u03c0(-2(-1((3x - 2)/(-1x + 2)) - 2) + 4) - 2) + 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 total number of local minima and maxima for f(x) = 2|(5(-1(2|x - 3| + 1)^2 + 1(2|x - 3| + 1) + 2)^2 + 5(-1(2|x - 3| + 1)^2 + 1(2|x - 3| + 1) + 2) + 2) - 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 total number of local minima and maxima for f(x) = 1(-3cos(2\u03c0(-1|(1|x - 1| + 2) - 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": "41", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = (3(4(1sin(3\u03c0(-4x^2 + 1x - 2) - 1) + 2) - 5) + 3)/(-3(4(1sin(3\u03c0(-4x^2 + 1x - 2) - 1) + 2) - 5) - 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "476", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -1cos(3\u03c0(-2((-3(-4x - 5) + 3)/(2(-4x - 5) + 1))^2 - 5((-3(-4x - 5) + 3)/(2(-4x - 5) + 1)) - 4) - 3) - 3 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": "Determine the total count of local extrema points for the function f(x) = -3|(3(-3|(-1x^2 + 5x - 3) + 2| + 1)^2 + 1(-3|(-1x^2 + 5x - 3) + 2| + 1) + 1)| + 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": "Determine the total count of local extrema points for the function f(x) = (-3(-2cos(3\u03c0(3|((-3x + 2)/(-2x)) - 1| - 3)) - 3) - 1)/(3(-2cos(3\u03c0(3|((-3x + 2)/(-2x)) - 1| - 3)) - 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": "Determine the count of local maxima for the function f(x) = 2cos(1\u03c0(-2|((-1(-4x^2 + 4x + 5) + 3)/(3(-4x^2 + 4x + 5) - 2)) + 1|) - 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": "Find the total number of local minima and maxima for f(x) = 2cos(1\u03c0(-3(5(3x + 2)^2 - 1(3x + 2)) + 2) + 3) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "417", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = 3(-1sin(2\u03c0(1(-2|x + 1| - 3)^2 + 4(-2|x + 1| - 3) + 5) - 3)) - 1 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 count of local minima for the function f(x) = 2|(-4(3(3sin(1\u03c0x - 1) - 3) + 2)^2 - 5(3(3sin(1\u03c0x - 1) - 3) + 2) - 5) - 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": "Find the total number of local minima and maxima for f(x) = -3((-1(-2sin(2\u03c0(-2|x + 2| + 1) - 3) + 1))/(-1(-2sin(2\u03c0(-2|x + 2| + 1) - 3) + 1) + 3)) + 3 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": "Determine the total count of local extrema points for the function f(x) = -4((-2(1|(4x + 2) + 2| - 3) + 1)/(-3(1|(4x + 2) + 2| - 3) + 4))^2 - 5((-2(1|(4x + 2) + 2| - 3) + 1)/(-3(1|(4x + 2) + 2| - 3) + 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": "Find the number of local maximum points for f(x) = -2|(-1(4((3x)/(1x))^2 + 5((3x)/(1x)) - 5)) - 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": "Determine the count of local maxima for the function f(x) = 2cos(1\u03c0((-2(2((1x)/(-1x - 2))^2 - 1((1x)/(-1x - 2))) - 3)/(1(2((1x)/(-1x - 2))^2 - 1((1x)/(-1x - 2))) - 2)) - 2) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "74", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = 2cos(3\u03c0((2(-1((-2x + 2)/(-3x + 1)) - 2) + 1)/(1(-1((-2x + 2)/(-3x + 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": "Find the number of local minimum points for f(x) = -1cos(3\u03c0((3(-1|(-1|x + 3| + 2) + 1| - 2))/(1(-1|(-1|x + 3| + 2) + 1| - 2) - 3)) - 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": "Determine the count of local maxima for the function f(x) = -3(-2((-1(-3cos(1\u03c0x - 1) - 2))/(-3(-3cos(1\u03c0x - 1) - 2) - 2))^2 - 2((-1(-3cos(1\u03c0x - 1) - 2))/(-3(-3cos(1\u03c0x - 1) - 2) - 2)) + 5)^2 + 4(-2((-1(-3cos(1\u03c0x - 1) - 2))/(-3(-3cos(1\u03c0x - 1) - 2) - 2))^2 - 2((-1(-3cos(1\u03c0x - 1) - 2))/(-3(-3cos(1\u03c0x - 1) - 2) - 2)) + 5) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "45", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 1|(-2cos(3\u03c0(3|((3x - 3)/(-2x - 3)) + 2| + 1) - 3) - 1) - 3| + 3 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": "How many local minima does the function f(x) = 1sin(1\u03c0((2((-3(5x + 4) - 3)/(1(5x + 4) - 2)) - 2)/(-2((-3(5x + 4) - 3)/(1(5x + 4) - 2)) - 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": "Determine the count of local minima for the function f(x) = -2sin(1\u03c0(-4(2|(-3x + 4) + 1|) + 1) + 3) - 1 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 total number of local minima and maxima for f(x) = 2(-1sin(2\u03c0(1|((2x + 2)/(2x + 3)) - 3| - 3)) - 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": "Determine the count of local minima for the function f(x) = 3(1cos(3\u03c0(-3(-2x^2 - 4x - 2) - 1) + 2) + 2) + 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "247", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -1(1|((-2(-3sin(2\u03c0x + 2) + 1) + 3)/(2(-3sin(2\u03c0x + 2) + 1))) - 1| - 3)^2 + 3(1|((-2(-3sin(2\u03c0x + 2) + 1) + 3)/(2(-3sin(2\u03c0x + 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": "170", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = 3|((2((3(-1cos(2\u03c0x + 1) - 1) - 3)/(-2(-1cos(2\u03c0x + 1) - 1) + 3)) - 3)/(3((3(-1cos(2\u03c0x + 1) - 1) - 3)/(-2(-1cos(2\u03c0x + 1) - 1) + 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": "Determine the count of local minima for the function f(x) = -4(-1(-1sin(3\u03c0(3|x + 2| - 2) - 3) + 1))^2 + 1(-1(-1sin(3\u03c0(3|x + 2| - 2) - 3) + 1)) + 2 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) = -1(-1sin(1\u03c0(-1(2|x - 2| + 1) + 3)) + 3) + 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": "Find the number of local maximum points for f(x) = 2cos(1\u03c0(3(-3|(2x^2 - 4x + 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": "242", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = (3(-3|(-2|(5x^2 - 2x - 3)| + 3) - 2| - 1) - 3)/(-1(-3|(-2|(5x^2 - 2x - 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": "5", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = (-1(3(1cos(2\u03c0(4x) + 2) - 2)^2 - 2) - 2)/(-2(3(1cos(2\u03c0(4x) + 2) - 2)^2 - 2) + 1) 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 minimum points for f(x) = 2|(-5((3(2cos(1\u03c0x - 3)) + 2)/(1(2cos(1\u03c0x - 3)) + 1)) - 4) + 1| + 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": "Determine the count of local minima for the function f(x) = (-1((-1(-3(-5x^2 - 2x - 5) + 3) - 2)/(-2(-3(-5x^2 - 2x - 5) + 3) + 3)))/(3((-1(-3(-5x^2 - 2x - 5) + 3) - 2)/(-2(-3(-5x^2 - 2x - 5) + 3) + 3))) 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 maximum points for f(x) = (-2(3cos(3\u03c0(-3((3x + 2)/(2x - 3))^2 - 3) - 1) - 1) - 2)/(-3(3cos(3\u03c0(-3((3x + 2)/(2x - 3))^2 - 3) - 1) - 1) + 4) 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 maxima does the function f(x) = 2|(1sin(3\u03c0(3|(5x + 2) - 3| - 2) + 3) - 2)| have in the interval [-10, 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) = -1sin(3\u03c0(-2((-1(-3x - 2) + 2)/(-1(-3x - 2)))^2 + 5((-1(-3x - 2) + 2)/(-1(-3x - 2))) - 5) + 2) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "25", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 1cos(1\u03c0(2(3|(-1|x| - 3) + 3| - 1) + 5) - 3) - 1 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 minimum points for f(x) = 2sin(1\u03c0(1|((-3(1x - 5) + 1)/(-3(1x - 5) - 2)) - 1| + 1) + 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": "Determine the total count of local extrema points for the function f(x) = -3|(3e^(-2(1(1x^2 + 5x - 2)^2 + 4(1x^2 + 5x - 2) - 2)) - 3) + 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": "Determine the count of local minima for the function f(x) = 4(1cos(3\u03c0(-3(3|x + 1| - 2)^2 + 3(3|x + 1| - 2) + 5) + 2) + 1)^2 - 5(1cos(3\u03c0(-3(3|x + 1| - 2)^2 + 3(3|x + 1| - 2) + 5) + 2) + 1) + 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "108", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -3cos(3\u03c0(1(-3((-1x + 1)/(2x)) + 1)^2 + 1(-3((-1x + 1)/(2x)) + 1) - 1) + 3) - 2 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) = -2cos(3\u03c0(1(-4(-3|x - 3|) + 1)^2 + 3(-4(-3|x - 3|) + 1) + 4) - 3) + 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "322", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -2|((1(3(1sin(3\u03c0x + 2) - 2) + 2) + 3)/(1(3(1sin(3\u03c0x + 2) - 2) + 2) + 2)) - 2| - 2 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 maxima for the function f(x) = 1(1(3sin(2\u03c0(-5x - 3) + 3) - 2) + 5)^2 - 3(1(3sin(2\u03c0(-5x - 3) + 3) - 2) + 5) - 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "200", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = -1(-2(2cos(2\u03c0(-1|x| + 2) + 3) + 1) + 5)^2 + 3(-2(2cos(2\u03c0(-1|x| + 2) + 3) + 1) + 5) - 2 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 total count of local extrema points for the function f(x) = -2sin(2\u03c0(-3(4(-2|x - 2| - 1)^2 - 5(-2|x - 2| - 1) - 1)^2 + 1(4(-2|x - 2| - 1)^2 - 5(-2|x - 2| - 1) - 1)) + 3) - 1 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 maximum points for f(x) = -1|(-4(2sin(1\u03c0((1x + 3)/(-1x)) + 1) + 1)^2 - 4(2sin(1\u03c0((1x + 3)/(-1x)) + 1) + 1)) - 1| - 3 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 count of local maxima for the function f(x) = -2sin(1\u03c0((-1(-3|(1x + 4) - 3| - 1) + 2)/(2(-3|(1x + 4) - 3| - 1) + 3)) - 1) - 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": "Find the number of local minimum points for f(x) = (1(-1|(-2(1|x - 1| - 3)^2 - 1(1|x - 1| - 3) + 5) + 3| - 2) - 1)/(1(-1|(-2(1|x - 1| - 3)^2 - 1(1|x - 1| - 3) + 5) + 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 extrema (minima and maxima combined) does the function f(x) = -3sin(3\u03c0(1((-2((1x + 3)/(2x + 3)) - 1)/(2((1x + 3)/(2x + 3)) + 2)) + 5) + 2) + 2 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": "How many local minima does the function f(x) = 3sin(3\u03c0(1|(3|(5x - 4) - 2|) + 3| + 2)) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "449", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 2e^(1(4((-3(-2x^2 + 1x + 4))/(2(-2x^2 + 1x + 4) + 1))^2 - 1((-3(-2x^2 + 1x + 4))/(2(-2x^2 + 1x + 4) + 1)) + 5)) - 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) = 3(-2cos(2\u03c0(-5(2|x - 2| - 3)^2 + 2(2|x - 2| - 3) - 5) - 2) - 1)^2 - 5 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "236", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -3(1|(3(-2sin(2\u03c0x - 3) - 2) + 3) - 3| - 3) - 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 total number of local minima and maxima for f(x) = (-2(1((1(2x^2 - 5x - 1))/(1(2x^2 - 5x - 1) + 1))^2 + 4((1(2x^2 - 5x - 1))/(1(2x^2 - 5x - 1) + 1)) + 3) - 2)/(-1(1((1(2x^2 - 5x - 1))/(1(2x^2 - 5x - 1) + 1))^2 + 4((1(2x^2 - 5x - 1))/(1(2x^2 - 5x - 1) + 1)) + 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": "Find the total number of local minima and maxima for f(x) = 5((3(1cos(1\u03c0(-4x) + 2) - 2) + 2)/(1(1cos(1\u03c0(-4x) + 2) - 2) - 3)) + 5 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": "Find the number of local maximum points for f(x) = -4(2|(-1cos(1\u03c0(-1x^2 - 4x - 5)) + 2) + 2| + 1) - 4 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": "How many local extrema (minima and maxima combined) does the function f(x) = -5(1sin(2\u03c0((3(1x - 4) + 3)/(-2(1x - 4) - 3)) + 1) - 3)^2 - 1(1sin(2\u03c0((3(1x - 4) + 3)/(-2(1x - 4) - 3)) + 1) - 3) + 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": "Determine the total count of local extrema points for the function f(x) = -2cos(2\u03c0(2|(-2|(2x + 1) + 3| + 3) + 2| + 2) + 3) - 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "319", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -1|(1(-2cos(3\u03c0(-4x - 2)) - 2)^2 + 2(-2cos(3\u03c0(-4x - 2)) - 2) - 5) + 3| have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "186", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 5(3(1sin(2\u03c0(-3x - 2) - 3) - 3) - 4)^2 - 1(3(1sin(2\u03c0(-3x - 2) - 3) - 3) - 4) - 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": "How many local extrema (minima and maxima combined) does the function f(x) = (1((-1(1sin(3\u03c0(1x^2 - 1x - 5) - 1) - 3))/(-1(1sin(3\u03c0(1x^2 - 1x - 5) - 1) - 3) - 2)) + 1)/(1((-1(1sin(3\u03c0(1x^2 - 1x - 5) - 1) - 3))/(-1(1sin(3\u03c0(1x^2 - 1x - 5) - 1) - 3) - 2)) + 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "564", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 1|(2|((3(5x^2 - 3x - 1) - 1)/(-3(5x^2 - 3x - 1) + 2)) - 1| - 3) - 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": "Determine the count of local minima for the function f(x) = -2|(-3(2|(-1sin(3\u03c0x - 1) - 2) - 1| + 1)^2 - 5(2|(-1sin(3\u03c0x - 1) - 2) - 1| + 1) + 5) + 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": "Determine the total count of local extrema points for the function f(x) = (-1((2(-2sin(2\u03c0(3|x - 1| + 3) - 2) - 1) + 2)/(3(-2sin(2\u03c0(3|x - 1| + 3) - 2) - 1) - 2)) - 3)/(2((2(-2sin(2\u03c0(3|x - 1| + 3) - 2) - 1) + 2)/(3(-2sin(2\u03c0(3|x - 1| + 3) - 2) - 1) - 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": "How many local minima does the function f(x) = -2(1cos(1\u03c0(3(-1x + 5) + 3) - 2) - 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": "Find the number of local maximum points for f(x) = 2|(1(1(3sin(3\u03c0x) - 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": "120", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = 2|(-2|(-5(1|x| - 2)^2 - 2(1|x| - 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": "7", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = 3|((3(-5(-3sin(2\u03c0x + 2) + 3)^2 + 2(-3sin(2\u03c0x + 2) + 3) - 2) - 3)/(1(-5(-3sin(2\u03c0x + 2) + 3)^2 + 2(-3sin(2\u03c0x + 2) + 3) - 2))) + 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": "How many local minima does the function f(x) = 2sin(2\u03c0(3(1|(2|x + 3| + 3)| - 1)^2 - 3(1|(2|x + 3| + 3)| - 1) - 2) + 2) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "255", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = (-2(2(-3e^(-1(-4x + 3)) + 2)^2 - 1(-3e^(-1(-4x + 3)) + 2) + 1) - 1)/(2(2(-3e^(-1(-4x + 3)) + 2)^2 - 1(-3e^(-1(-4x + 3)) + 2) + 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": "How many local extrema (minima and maxima combined) does the function f(x) = -1((-3(-1(-2cos(2\u03c0x) - 1) - 3) - 2)/(-1(-1(-2cos(2\u03c0x) - 1) - 3) + 2)) - 1 have in the interval [-10, 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) = (3(1(-1(2e^(-1x) + 3)^2 + 3(2e^(-1x) + 3) + 5)^2 + 1(-1(2e^(-1x) + 3)^2 + 3(2e^(-1x) + 3) + 5) - 1) + 3)/(2(1(-1(2e^(-1x) + 3)^2 + 3(2e^(-1x) + 3) + 5)^2 + 1(-1(2e^(-1x) + 3)^2 + 3(2e^(-1x) + 3) + 5) - 1) - 1) 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) = 1|(-1sin(2\u03c0(3(-5x^2 - 3x)^2 - 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": "73", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -1cos(1\u03c0(1(3(2|x + 3| - 2)^2 - 4(2|x + 3| - 2) - 1) - 2) + 2) + 1 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 total number of local minima and maxima for f(x) = -3|(2|(-5(2sin(1\u03c0x + 3) + 3) + 4) + 3| - 2) - 1| - 1 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": "Find the total number of local minima and maxima for f(x) = -1cos(1\u03c0(-1|(-2((2x)/(-3x - 2)) - 4) - 2| - 1) + 3) - 3 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": "Find the number of local minimum points for f(x) = 1(-3sin(3\u03c0(-4((-1x - 3)/(2x + 1))^2 + 5((-1x - 3)/(2x + 1)) - 4) + 2))^2 + 5(-3sin(3\u03c0(-4((-1x - 3)/(2x + 1))^2 + 5((-1x - 3)/(2x + 1)) - 4) + 2)) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "54", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = 1|((1(-1(1sin(2\u03c0x + 2) - 2) - 2))/(-3(-1(1sin(2\u03c0x + 2) - 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": "80", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -3e^(-1(-5(1((2x - 2)/(2x + 1))^2 - 5((2x - 2)/(2x + 1)) + 1)^2 - 1(1((2x - 2)/(2x + 1))^2 - 5((2x - 2)/(2x + 1)) + 1) + 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 count of local maxima for the function f(x) = -1((-3(4(-1cos(2\u03c0x + 3))) + 2)/(1(4(-1cos(2\u03c0x + 3))) - 3))^2 - 4((-3(4(-1cos(2\u03c0x + 3))) + 2)/(1(4(-1cos(2\u03c0x + 3))) - 3)) + 5 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "79", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 4((-1(-1(-2cos(3\u03c0x - 2) + 1) + 1) + 2)/(-3(-1(-2cos(3\u03c0x - 2) + 1) + 1) + 4))^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": "Determine the count of local maxima for the function f(x) = -2(-2cos(1\u03c0(-4(3x - 5) + 3) - 2) - 1)^2 - 5(-2cos(1\u03c0(-4(3x - 5) + 3) - 2) - 1) + 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "240", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = -3|((-2(1|(1cos(2\u03c0x + 3) + 1) + 2| - 3) - 1)/(2(1|(1cos(2\u03c0x + 3) + 1) + 2| - 3) - 1))| - 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "78", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = (-2(1(3cos(3\u03c0((3x + 2)/(2x - 3)) + 1))^2 - 1(3cos(3\u03c0((3x + 2)/(2x - 3)) + 1))) - 1)/(1(1(3cos(3\u03c0((3x + 2)/(2x - 3)) + 1))^2 - 1(3cos(3\u03c0((3x + 2)/(2x - 3)) + 1)))) where -10 \u2264 x \u2264 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) = -2(-5(1cos(3\u03c0(1|x|)) - 2)^2 - 5(1cos(3\u03c0(1|x|)) - 2) + 4)^2 + 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": "Determine the total count of local extrema points for the function f(x) = 1|(-3|(-1(-4x^2)^2 - 1(-4x^2) + 1) + 1| - 2) + 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": "How many local maxima does the function f(x) = 1(-5(-3(2sin(3\u03c0x + 2) + 2)^2 + 3(2sin(3\u03c0x + 2) + 2))^2 - 3(-3(2sin(3\u03c0x + 2) + 2)^2 + 3(2sin(3\u03c0x + 2) + 2)) - 4) + 5 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 maxima does the function f(x) = -3((3(-1(-3cos(1\u03c0x + 1) + 2)^2 - 1(-3cos(1\u03c0x + 1) + 2) - 4) - 1)/(1(-1(-3cos(1\u03c0x + 1) + 2)^2 - 1(-3cos(1\u03c0x + 1) + 2) - 4) + 3))^2 - 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 minima does the function f(x) = 5(2|(1|(3cos(1\u03c0x + 3) - 1) + 1| - 2) + 3| + 3)^2 - 1(2|(1|(3cos(1\u03c0x + 3) - 1) + 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": "16", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 1(2(-1(1cos(1\u03c0x - 2) - 1)^2 + 5(1cos(1\u03c0x - 2) - 1) + 5)^2 - 1(-1(1cos(1\u03c0x - 2) - 1)^2 + 5(1cos(1\u03c0x - 2) - 1) + 5) - 4)^2 + 3(2(-1(1cos(1\u03c0x - 2) - 1)^2 + 5(1cos(1\u03c0x - 2) - 1) + 5)^2 - 1(-1(1cos(1\u03c0x - 2) - 1)^2 + 5(1cos(1\u03c0x - 2) - 1) + 5) - 4) 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": "Find the number of local maximum points for f(x) = 2|((3(-3|(-2sin(2\u03c0x - 3)) + 1|) + 1)/(-2(-3|(-2sin(2\u03c0x - 3)) + 1|) - 1))| + 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": "Find the number of local maximum points for f(x) = (-3((3(3sin(2\u03c0(-2x - 2) + 3) - 3) - 2)/(1(3sin(2\u03c0(-2x - 2) + 3) - 3) - 3)) - 1)/(-2((3(3sin(2\u03c0(-2x - 2) + 3) - 3) - 2)/(1(3sin(2\u03c0(-2x - 2) + 3) - 3) - 3)) - 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": "Find the total number of local minima and maxima for f(x) = 2|(-4(3|(2|x + 2| - 2) - 3| - 2)^2 - 1(3|(2|x + 2| - 2) - 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": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 1(5(3sin(2\u03c0(1x + 1)) - 1)^2 + 5(3sin(2\u03c0(1x + 1)) - 1) - 1)^2 - 2 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 total count of local extrema points for the function f(x) = 2|(2e^(2(2|(-2x^2 + 3x + 5) - 1| - 3)) - 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) = -1(2(-3sin(1\u03c0(3x^2 - 2x + 1) - 3) + 1) + 1) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "283", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 2|(-3|(-1cos(3\u03c0(3x^2 - 2x + 2) + 1) - 1)|)| + 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "529", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 2(-1|(2sin(2\u03c0(1x - 1) + 3)) - 1|) - 1 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) = 2cos(2\u03c0(-3|((1(4x^2 + 5x - 5) + 3)/(3(4x^2 + 5x - 5) + 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": "28", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -1cos(3\u03c0((1(3(2|x + 3| - 3)^2 - 4(2|x + 3| - 3)) + 1)/(-3(3(2|x + 3| - 3)^2 - 4(2|x + 3| - 3)) - 2))) 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": "How many local extrema (minima and maxima combined) does the function f(x) = (3(2|(-2(-2x^2 - 4x + 4)^2 + 5(-2x^2 - 4x + 4) + 1) + 2| + 3) - 1)/(-2(2|(-2(-2x^2 - 4x + 4)^2 + 5(-2x^2 - 4x + 4) + 1) + 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 count of local minima for the function f(x) = -2((-2(-1sin(2\u03c0((1x + 2)/(1x)) + 1) - 3) + 3)/(3(-1sin(2\u03c0((1x + 2)/(1x)) + 1) - 3) + 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 number of local maximum points for f(x) = (-2(2(-2(2cos(3\u03c0x + 2) + 3)^2 - 4(2cos(3\u03c0x + 2) + 3) + 5)^2 - 2(-2(2cos(3\u03c0x + 2) + 3)^2 - 4(2cos(3\u03c0x + 2) + 3) + 5) - 5) - 2)/(-2(2(-2(2cos(3\u03c0x + 2) + 3)^2 - 4(2cos(3\u03c0x + 2) + 3) + 5)^2 - 2(-2(2cos(3\u03c0x + 2) + 3)^2 - 4(2cos(3\u03c0x + 2) + 3) + 5) - 5) - 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": "Determine the total count of local extrema points for the function f(x) = -1|(-1|(5(-3x^2 - 3x + 1)^2 + 4(-3x^2 - 3x + 1) - 2) - 1| - 1) - 2| - 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 minima for the function f(x) = -5(3sin(2\u03c0(1(-1x - 1) - 5) + 3) + 2)^2 + 1(3sin(2\u03c0(1(-1x - 1) - 5) + 3) + 2) + 4 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) = -3cos(1\u03c0(5((1(-4x^2 - 5x - 3))/(-1(-4x^2 - 5x - 3) - 1))^2 - 4((1(-4x^2 - 5x - 3))/(-1(-4x^2 - 5x - 3) - 1)) - 3) + 2) - 2 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) = 2|(2(-1(-1sin(2\u03c0x - 3)) + 3)^2 + 4(-1(-1sin(2\u03c0x - 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": "40", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 3(3(-5(-5x^2 - 2x + 1) + 2)^2 - 1)^2 - 2(3(-5(-5x^2 - 2x + 1) + 2)^2 - 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": "How many local maxima does the function f(x) = (-3((-3((1(-3sin(2\u03c0x + 2) + 2) - 1)/(1(-3sin(2\u03c0x + 2) + 2) + 2)) + 1)/(2((1(-3sin(2\u03c0x + 2) + 2) - 1)/(1(-3sin(2\u03c0x + 2) + 2) + 2)))) - 3)/(-1((-3((1(-3sin(2\u03c0x + 2) + 2) - 1)/(1(-3sin(2\u03c0x + 2) + 2) + 2)) + 1)/(2((1(-3sin(2\u03c0x + 2) + 2) - 1)/(1(-3sin(2\u03c0x + 2) + 2) + 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 minima does the function f(x) = -3sin(3\u03c0(2|((2(1|x - 2| - 3) - 1)/(-2(1|x - 2| - 3) - 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": "52", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -1(-3|(2sin(2\u03c0(-5x^2 + 4x - 4) + 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": "502", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 1|(-2cos(1\u03c0(2(-1x^2 - 4x - 1)) + 2) - 3) + 1| - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "206", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = (2(5((2(-2cos(1\u03c0x + 1) + 1) - 2)/(3(-2cos(1\u03c0x + 1) + 1) + 3))^2 + 4) + 2)/(2(5((2(-2cos(1\u03c0x + 1) + 1) - 2)/(3(-2cos(1\u03c0x + 1) + 1) + 3))^2 + 4) + 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": "How many local maxima does the function f(x) = -1e^(1(-3(5(2x^2 + 1x - 4)^2 - 1(2x^2 + 1x - 4) - 1)^2 + 2(5(2x^2 + 1x - 4)^2 - 1(2x^2 + 1x - 4) - 1) + 3)) - 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) = (2(3sin(2\u03c0(-3(-1|x + 3| + 3)^2 - 3(-1|x + 3| + 3) - 1) - 1) - 3) + 1)/(1(3sin(2\u03c0(-3(-1|x + 3| + 3)^2 - 3(-1|x + 3| + 3) - 1) - 1) - 3)) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "436", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -1cos(1\u03c0(5(4(1x - 5) - 1) - 5) - 2) + 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "200", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -1(5(-2(-2|x|)^2 - 3(-2|x|) + 3)^2 + 5(-2(-2|x|)^2 - 3(-2|x|) + 3) - 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": "Find the number of local minimum points for f(x) = 1(1cos(3\u03c0(-5(-3|x + 1| - 2)^2 + 4)) + 1) + 4 where -10 \u2264 x \u2264 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 minima for the function f(x) = -3|(-3|(-3cos(3\u03c0(1x^2 - 5x + 3) + 3) + 1) + 3| - 3) + 1| + 3 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 total number of local minima and maxima for f(x) = -2(5(-3sin(2\u03c0((-2x + 1)/(1x - 2)) + 3))^2 - 4(-3sin(2\u03c0((-2x + 1)/(1x - 2)) + 3)) + 1)^2 + 3(5(-3sin(2\u03c0((-2x + 1)/(1x - 2)) + 3))^2 - 4(-3sin(2\u03c0((-2x + 1)/(1x - 2)) + 3)) + 1) + 3 where -10 \u2264 x \u2264 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 minimum points for f(x) = (-2(-2cos(1\u03c0(2(5x + 5)^2 - 2(5x + 5) + 4) + 2) - 3) - 1)/(1(-2cos(1\u03c0(2(5x + 5)^2 - 2(5x + 5) + 4) + 2) - 3) + 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "227", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -1cos(3\u03c0((-3(5(3x + 2) - 3) + 3)/(-3(5(3x + 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": "5", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = 3(-3(3cos(1\u03c0((2x + 1)/(3x - 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": "8", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -3sin(3\u03c0(-5((1(-3|x - 3| + 3) + 2)/(-3(-3|x - 3| + 3) - 1))) + 2) - 2 where -10 \u2264 x \u2264 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) = -1cos(1\u03c0(-2|(3(2x - 5)) - 1| + 2) + 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 extrema (minima and maxima combined) does the function f(x) = (2(3(3cos(1\u03c0(-4x + 5) - 3) - 3)^2 + 4(3cos(1\u03c0(-4x + 5) - 3) - 3) + 1) - 1)/(-1(3(3cos(1\u03c0(-4x + 5) - 3) - 3)^2 + 4(3cos(1\u03c0(-4x + 5) - 3) - 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": "How many local extrema (minima and maxima combined) does the function f(x) = 1((-1(-1sin(2\u03c0(-2|x + 3| - 1) - 3) + 3) - 1)/(3(-1sin(2\u03c0(-2|x + 3| - 1) - 3) + 3) + 1))^2 + 2((-1(-1sin(2\u03c0(-2|x + 3| - 1) - 3) + 3) - 1)/(3(-1sin(2\u03c0(-2|x + 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": "81", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = (1(2|(-1sin(1\u03c0(1x^2 + 5x + 1) + 2)) + 3| + 2))/(2(2|(-1sin(1\u03c0(1x^2 + 5x + 1) + 2)) + 3| + 2) + 3) 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": "Find the number of local maximum points for f(x) = 3|(2(-1(3cos(2\u03c0x + 2) - 2) + 3)^2 - 3(-1(3cos(2\u03c0x + 2) - 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": "80", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = 5(1((3(3|x - 1| - 2))/(2(3|x - 1| - 2) + 3))^2 + 3((3(3|x - 1| - 2))/(2(3|x - 1| - 2) + 3)) + 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": "Find the total number of local minima and maxima for f(x) = (1(-2|(1sin(2\u03c0((3x - 3)/(3x))) - 3) + 1| - 1) + 2)/(-3(-2|(1sin(2\u03c0((3x - 3)/(3x))) - 3) + 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 extrema (minima and maxima combined) does the function f(x) = -2cos(1\u03c0((-1(4((-1x - 1)/(-1x - 2))^2 + 5((-1x - 1)/(-1x - 2)) - 5) - 3)/(1(4((-1x - 1)/(-1x - 2))^2 + 5((-1x - 1)/(-1x - 2)) - 5) - 2)) - 3) + 2 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 extrema (minima and maxima combined) does the function f(x) = 1|(-1(-1sin(3\u03c0(-2|x - 3| + 1) - 1) + 3)^2 + 4(-1sin(3\u03c0(-2|x - 3| + 1) - 1) + 3) + 5) + 3| - 2 have 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) = (3(4(2sin(2\u03c0(1|x - 3| - 1) + 3) + 1) - 5) + 2)/(2(4(2sin(2\u03c0(1|x - 3| - 1) + 3) + 1) - 5) + 2) 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) = (-2(-5(2e^(-1(2|x + 3| + 2)) + 3) - 3))/(-1(-5(2e^(-1(2|x + 3| + 2)) + 3) - 3) + 3) 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 maxima does the function f(x) = 3|(5(2cos(2\u03c0(3|x + 1| - 1) + 1) + 2) - 5) - 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": "Determine the total count of local extrema points for the function f(x) = -1|(1|(-1(3cos(1\u03c0x + 2)) - 3) - 2| + 2) + 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": "How many local extrema (minima and maxima combined) does the function f(x) = -3(3sin(2\u03c0(-1|(1|x + 3| + 1) - 2| + 1) + 2) - 2) + 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": "Determine the count of local minima for the function f(x) = -5(2|(-1sin(1\u03c0(-1|x + 2| - 2) - 2) + 2) - 1| - 2)^2 - 2(2|(-1sin(1\u03c0(-1|x + 2| - 2) - 2) + 2) - 1| - 2) + 5 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -2(2cos(3\u03c0(1(1x^2 + 1x + 4)^2 + 3(1x^2 + 1x + 4) + 2) - 1) - 3)^2 - 2(2cos(3\u03c0(1(1x^2 + 1x + 4)^2 + 3(1x^2 + 1x + 4) + 2) - 1) - 3) - 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "127", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -1cos(1\u03c0(-4((1((2x + 1)/(3x)) + 1)/(2((2x + 1)/(3x))))^2 - 2((1((2x + 1)/(3x)) + 1)/(2((2x + 1)/(3x)))) - 4) + 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": "Find the total number of local minima and maxima for f(x) = (3(2(-1sin(2\u03c0((-3x + 2)/(-1x + 3))) - 2)^2 - 1(-1sin(2\u03c0((-3x + 2)/(-1x + 3))) - 2)) + 3)/(2(2(-1sin(2\u03c0((-3x + 2)/(-1x + 3))) - 2)^2 - 1(-1sin(2\u03c0((-3x + 2)/(-1x + 3))) - 2)) - 3) 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 total number of local minima and maxima for f(x) = (1(4((-2(-3sin(3\u03c0x - 3) + 2) + 2)/(3(-3sin(3\u03c0x - 3) + 2) + 1))^2 + 5((-2(-3sin(3\u03c0x - 3) + 2) + 2)/(3(-3sin(3\u03c0x - 3) + 2) + 1)) + 2) + 3)/(3(4((-2(-3sin(3\u03c0x - 3) + 2) + 2)/(3(-3sin(3\u03c0x - 3) + 2) + 1))^2 + 5((-2(-3sin(3\u03c0x - 3) + 2) + 2)/(3(-3sin(3\u03c0x - 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": "120", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 4(-1(1sin(2\u03c0(2|x| - 2) + 2) - 2)^2 + 2(1sin(2\u03c0(2|x| - 2) + 2) - 2)) - 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 1|(-3|(1(-1|x - 2|)^2 + 5(-1|x - 2|) + 3)|) + 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) = (2(2cos(2\u03c0(3|(2|x - 2| - 3) - 2| + 3) - 3) + 2) + 3)/(-2(2cos(2\u03c0(3|(2|x - 2| - 3) - 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": "143", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = (-1(-2cos(1\u03c0((-1(4x^2 + 2x - 3) + 1)/(2(4x^2 + 2x - 3) - 3)) - 2) - 2))/(-2(-2cos(1\u03c0((-1(4x^2 + 2x - 3) + 1)/(2(4x^2 + 2x - 3) - 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 maxima does the function f(x) = 4(-3(3|(1cos(2\u03c0x + 3))| - 3)^2 - 4(3|(1cos(2\u03c0x + 3))| - 3) + 3)^2 - 2(-3(3|(1cos(2\u03c0x + 3))| - 3)^2 - 4(3|(1cos(2\u03c0x + 3))| - 3) + 3) + 5 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) = 2cos(3\u03c0((-1(4(-5x - 2) - 2) - 1)/(1(4(-5x - 2) - 2) - 3))) - 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 total count of local extrema points for the function f(x) = 1sin(1\u03c0(-5(-3((-3x)/(-3x - 2)) + 1) - 5) - 2) + 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "71", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = 1(1(-3(-1cos(3\u03c0x + 1) - 1)^2 - 1(-1cos(3\u03c0x + 1) - 1) + 2)^2 - 5(-3(-1cos(3\u03c0x + 1) - 1)^2 - 1(-1cos(3\u03c0x + 1) - 1) + 2) + 4)^2 - 5(1(-3(-1cos(3\u03c0x + 1) - 1)^2 - 1(-1cos(3\u03c0x + 1) - 1) + 2)^2 - 5(-3(-1cos(3\u03c0x + 1) - 1)^2 - 1(-1cos(3\u03c0x + 1) - 1) + 2) + 4) + 5 where -10 \u2264 x \u2264 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((2(-1sin(1\u03c0(3x + 5) - 1) + 2) - 1)/(-3(-1sin(1\u03c0(3x + 5) - 1) + 2) + 4)) - 5 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) = 3|(-1(-1(2cos(3\u03c0x - 2) - 3)^2 - 4(2cos(3\u03c0x - 2) - 3) + 1)^2 - 4(-1(2cos(3\u03c0x - 2) - 3)^2 - 4(2cos(3\u03c0x - 2) - 3) + 1)) - 2| - 2 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": "Determine the count of local minima for the function f(x) = -3|(1|(-1(1cos(3\u03c0x - 3) - 1) + 4) + 3| + 1) + 2| + 3 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 minima for the function f(x) = -1|((-1(-1(-3x^2 + 5x + 1) - 3) + 1)/(-1(-1(-3x^2 + 5x + 1) - 3) - 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|(1cos(3\u03c0((3(1x + 2) + 3)/(2(1x + 2) + 1)))) + 1| - 1 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 total count of local extrema points for the function f(x) = 2|(-2|(-5(-2x - 1)^2 - 4(-2x - 1) + 4) - 2| + 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 total number of local minima and maxima for f(x) = 1((3(-1e^(1(1x^2 + 1x - 4)) + 1) + 1)/(-1(-1e^(1(1x^2 + 1x - 4)) + 1) + 2)) + 1 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": "How many local maxima does the function f(x) = (-2(-3(5(-2cos(2\u03c0x + 1) + 2)) + 2) + 1)/(2(-3(5(-2cos(2\u03c0x + 1) + 2)) + 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 total number of local minima and maxima for f(x) = 1|(-3(-3sin(3\u03c0(3|x + 1|) - 3)) + 5) + 2| + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "363", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 2|(-1|(-1sin(1\u03c0(1x + 4) - 2) + 3) - 2| + 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": "Find the number of local minimum points for f(x) = -2cos(3\u03c0(5(1|((-2x - 1)/(3x + 1))| + 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) = -3(-3((2(2cos(3\u03c0x)) - 2)/(-2(2cos(3\u03c0x)) - 2))^2 + 4((2(2cos(3\u03c0x)) - 2)/(-2(2cos(3\u03c0x)) - 2)) - 4) - 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": "How many local maxima does the function f(x) = -2sin(2\u03c0(-2|((-2(-2|x - 2| + 1) + 3)/(3(-2|x - 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": "28", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = -1(2cos(3\u03c0(3|(2|x + 1| - 3) + 3| + 1) - 2) - 3)^2 + 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "180", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -1(-4(3e^(-1(-2x^2 + 5)) - 2)^2 - 3(3e^(-1(-2x^2 + 5)) - 2) - 1)^2 - 5(-4(3e^(-1(-2x^2 + 5)) - 2)^2 - 3(3e^(-1(-2x^2 + 5)) - 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": "Find the number of local maximum points for f(x) = 1|(-2(2sin(2\u03c0(-1|x - 3| + 1)) - 3) - 2) - 3| + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "76", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -3(-3|(-1(-3cos(1\u03c0x) - 2) - 3) - 3| - 3)^2 - 5(-3|(-1(-3cos(1\u03c0x) - 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": "9", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 2|(2|(-2sin(2\u03c0(-3|x| - 2) + 3) + 2) + 3| - 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": "Find the number of local maximum points for f(x) = 2sin(2\u03c0(-2|(1((3x - 1)/(1x)) - 5) + 1| + 1) - 3) + 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": "Determine the total count of local extrema points for the function f(x) = -2|((3((-2(2sin(2\u03c0x + 2) + 1) + 3)/(2(2sin(2\u03c0x + 2) + 1) - 1)) - 2)/(-2((-2(2sin(2\u03c0x + 2) + 1) + 3)/(2(2sin(2\u03c0x + 2) + 1) - 1)) + 3)) + 3| 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|(-3cos(1\u03c0(2((-1x - 1)/(-2x + 1))^2 + 2((-1x - 1)/(-2x + 1)) + 1) - 1) - 1) + 1| - 3 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": "How many local extrema (minima and maxima combined) does the function f(x) = (-3(1(-3e^(-1(1x^2 - 3x + 3)) + 2) - 4))/(1(1(-3e^(-1(1x^2 - 3x + 3)) + 2) - 4)) 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": "Find the total number of local minima and maxima for f(x) = -2((1((2(1|x + 1| - 2))/(1(1|x + 1| - 2) - 2)) + 3)/(3((2(1|x + 1| - 2))/(1(1|x + 1| - 2) - 2)) + 3))^2 + 2((1((2(1|x + 1| - 2))/(1(1|x + 1| - 2) - 2)) + 3)/(3((2(1|x + 1| - 2))/(1(1|x + 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": "4", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -2|(1(1(2sin(3\u03c0x - 1) - 1)^2 + 5(2sin(3\u03c0x - 1) - 1) + 1)^2 - 5(1(2sin(3\u03c0x - 1) - 1)^2 + 5(2sin(3\u03c0x - 1) - 1) + 1) - 5) + 3| + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "297", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -2|(2(5(2cos(1\u03c0x + 1) - 1) + 5)^2 - 5(5(2cos(1\u03c0x + 1) - 1) + 5) + 4) + 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": "Find the number of local maximum points for f(x) = 1|(-1cos(3\u03c0(-1(-3|x + 2|)^2 - 5(-3|x + 2|) - 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": "488", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = -3|(3(3sin(2\u03c0(-4x + 3) - 3) + 2)^2 + 4(3sin(2\u03c0(-4x + 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": "384", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = (1(2sin(3\u03c0(-1(-1|x| - 1) + 1) - 3) - 3) + 3)/(1(2sin(3\u03c0(-1(-1|x| - 1) + 1) - 3) - 3) - 2) 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 total number of local minima and maxima for f(x) = -3((-3(2(-1sin(3\u03c0x + 2) + 3) + 2) - 3)/(-2(2(-1sin(3\u03c0x + 2) + 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": "60", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -2sin(3\u03c0((2((-2(1|x + 2| + 3))/(-2(1|x + 2| + 3) + 1)))/(2((-2(1|x + 2| + 3))/(-2(1|x + 2| + 3) + 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": "Determine the count of local minima for the function f(x) = 1cos(3\u03c0((2(-1(-1x + 3)^2 + 4(-1x + 3) - 3) + 2)/(2(-1(-1x + 3)^2 + 4(-1x + 3) - 3)))) + 3 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 total count of local extrema points for the function f(x) = (-1(2sin(2\u03c0(-3((1x - 2)/(-3x - 2)) + 1) - 1) - 2))/(-2(2sin(2\u03c0(-3((1x - 2)/(-3x - 2)) + 1) - 1) - 2) - 2) 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) = -1(-1cos(1\u03c0(-4(-2x)^2 + 1(-2x) + 3) + 2) - 2)^2 + 2(-1cos(1\u03c0(-4(-2x)^2 + 1(-2x) + 3) + 2) - 2) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "262", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -1|(1|(-1(2|x + 2| - 2)^2 - 3(2|x + 2| - 2) - 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": "7", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -2(-2(-1|(5x^2 - 3x - 3) - 3| + 1)^2 - 4(-1|(5x^2 - 3x - 3) - 3| + 1) - 5)^2 - 2(-2(-1|(5x^2 - 3x - 3) - 3| + 1)^2 - 4(-1|(5x^2 - 3x - 3) - 3| + 1) - 5) + 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 count of local maxima for the function f(x) = (-2(-2sin(1\u03c0(2(-1x^2 - 5x - 2)^2 - 5(-1x^2 - 5x - 2) - 1) - 2) + 3) + 2)/(-3(-2sin(1\u03c0(2(-1x^2 - 5x - 2)^2 - 5(-1x^2 - 5x - 2) - 1) - 2) + 3) + 2) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "324", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = (-2(2cos(3\u03c0(-1(2|x| - 3)^2 + 4(2|x| - 3) + 4)) - 2) + 1)/(1(2cos(3\u03c0(-1(2|x| - 3)^2 + 4(2|x| - 3) + 4)) - 2)) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "541", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = (-1(-2e^(2(1|(4x) + 1| - 3)) + 1) - 1)/(3(-2e^(2(1|(4x) + 1| - 3)) + 1) + 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "48", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -4(-5((-3(-1sin(3\u03c0x - 2) + 1))/(2(-1sin(3\u03c0x - 2) + 1)))^2 - 4((-3(-1sin(3\u03c0x - 2) + 1))/(2(-1sin(3\u03c0x - 2) + 1))) + 4)^2 - 5(-5((-3(-1sin(3\u03c0x - 2) + 1))/(2(-1sin(3\u03c0x - 2) + 1)))^2 - 4((-3(-1sin(3\u03c0x - 2) + 1))/(2(-1sin(3\u03c0x - 2) + 1))) + 4) + 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "220", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = -1|((-1(-1(3sin(3\u03c0x + 2) - 2) - 2) + 3)/(3(-1(3sin(3\u03c0x + 2) - 2) - 2) - 2)) + 1| + 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) = (-3((3(1(-4x^2 + 5x) - 5) - 2)/(1(1(-4x^2 + 5x) - 5))) - 3)/(1((3(1(-4x^2 + 5x) - 5) - 2)/(1(1(-4x^2 + 5x) - 5))) + 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "391", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 3|(1|(3|(-1sin(3\u03c0x - 3) + 3) + 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": "30", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 2sin(3\u03c0(3(3(1x - 4)^2 - 4(1x - 4))^2 - 5(3(1x - 4)^2 - 4(1x - 4)) + 1) + 3) - 3 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": "Find the number of local maximum points for f(x) = 4(4((1(-3sin(2\u03c0x - 1) - 3) - 3)/(2(-3sin(2\u03c0x - 1) - 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 maxima does the function f(x) = 1(-4((1(-1cos(3\u03c0x) - 1) - 3)/(2(-1cos(3\u03c0x) - 1) - 3)) - 3)^2 - 3(-4((1(-1cos(3\u03c0x) - 1) - 3)/(2(-1cos(3\u03c0x) - 1) - 3)) - 3) - 5 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 maxima does the function f(x) = 5(-3cos(3\u03c0(-3(1x^2 + 5x - 4) - 4)) - 3) - 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "235", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -4(-1(3sin(3\u03c0(4x + 1) - 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": "480", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -1cos(2\u03c0(3(3|(1x - 1) + 3| + 2) - 5) + 2) + 3 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(1e^(1(-2(-5x + 3) - 1)) + 1)^2 + 1(1e^(1(-2(-5x + 3) - 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": "How many local minima does the function f(x) = 2(-3cos(2\u03c0(5(-3|x + 1| - 2)^2 + 4(-3|x + 1| - 2) + 5) + 1) - 1)^2 + 5(-3cos(2\u03c0(5(-3|x + 1| - 2)^2 + 4(-3|x + 1| - 2) + 5) + 1) - 1) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "96", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -3((1(-1cos(3\u03c0((1x + 2)/(-2x)) + 2)) - 1)/(1(-1cos(3\u03c0((1x + 2)/(-2x)) + 2)) - 3)) + 5 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 total number of local minima and maxima for f(x) = (2((-2((-3(2x^2 + 5x - 5))/(-1(2x^2 + 5x - 5))) + 3)/(2((-3(2x^2 + 5x - 5))/(-1(2x^2 + 5x - 5))) + 3)) - 1)/(-3((-2((-3(2x^2 + 5x - 5))/(-1(2x^2 + 5x - 5))) + 3)/(2((-3(2x^2 + 5x - 5))/(-1(2x^2 + 5x - 5))) + 3)) - 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "184", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -2sin(3\u03c0(-2|(-1(-1|x| - 3)^2 - 1(-1|x| - 3) + 5) + 2| - 2) + 2) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "547", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = 2(-5(3sin(1\u03c0(-4x^2 - 1x + 5) - 1) + 3) + 3)^2 + 3(-5(3sin(1\u03c0(-4x^2 - 1x + 5) - 1) + 3) + 3) - 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "170", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = 3|(1|(-3sin(1\u03c0(3x^2 - 4x + 5) + 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": "258", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -3|((-3(-2cos(1\u03c0(-1x - 1) + 2) + 3) - 3)/(3(-2cos(1\u03c0(-1x - 1) + 2) + 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": "Find the number of local minimum points for f(x) = -1(2cos(1\u03c0(-4(4x^2 + 2x - 5)^2 - 5(4x^2 + 2x - 5) - 5) + 3) + 2) - 2 where -10 \u2264 x \u2264 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) = -2(4(1sin(1\u03c0((1x - 2)/(2x - 1))) - 1)^2 - 5(1sin(1\u03c0((1x - 2)/(2x - 1))) - 1) - 2)^2 - 4(4(1sin(1\u03c0((1x - 2)/(2x - 1))) - 1)^2 - 5(1sin(1\u03c0((1x - 2)/(2x - 1))) - 1) - 2) - 3 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": "Determine the count of local maxima for the function f(x) = 1cos(3\u03c0(-3|(5(3|x| - 1) + 3) + 3| + 2) - 1) - 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "352", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -3sin(1\u03c0(-3|(-1|(3|x| - 3) - 3| - 3) + 3| - 3) + 1) - 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": "Find the total number of local minima and maxima for f(x) = -5(1cos(3\u03c0((-1(1x - 1) + 3)/(-3(1x - 1) - 1)) - 3) - 3)^2 + 3(1cos(3\u03c0((-1(1x - 1) + 3)/(-3(1x - 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": "38", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = (-2(-2|(-3|(-1cos(2\u03c0x) - 2) - 1| + 2) + 3| + 3) + 3)/(-2(-2|(-3|(-1cos(2\u03c0x) - 2) - 1| + 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": "How many local maxima does the function f(x) = 2(-1(-2|(2cos(1\u03c0x + 2) + 2) + 1| - 3) + 2)^2 - 3(-1(-2|(2cos(1\u03c0x + 2) + 2) + 1| - 3) + 2) + 4 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) = -3|(-3(-1cos(2\u03c0(-2x + 3) + 1) - 2) + 4) + 2| 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) = -5(1cos(1\u03c0(1(2x + 5)^2 + 2(2x + 5) + 3) + 3) - 1)^2 + 5 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "302", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -3cos(2\u03c0(1(3(-5x + 1) + 2) + 2) - 3) + 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "300", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 1(-2sin(2\u03c0(-4(-4x^2 - 2x + 4) - 3)) - 1) + 5 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "488", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = (3(-3|((3(-3sin(2\u03c0x + 2) + 1) - 3)/(-2(-3sin(2\u03c0x + 2) + 1) + 3)) - 2| + 3))/(3(-3|((3(-3sin(2\u03c0x + 2) + 1) - 3)/(-2(-3sin(2\u03c0x + 2) + 1) + 3)) - 2| + 3) + 2) have 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 maxima does the function f(x) = 2(1cos(3\u03c0(1|(-5x + 2) + 2| + 3) + 2) - 1)^2 + 3(1cos(3\u03c0(1|(-5x + 2) + 2| + 3) + 2) - 1) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "300", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -2|(2|(4(-1x^2 + 1x + 4)^2 - 5(-1x^2 + 1x + 4) - 4) + 1| - 2) - 3| + 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": "Determine the count of local maxima for the function f(x) = 1((2(-3cos(3\u03c0(-2|x + 3| + 1)) + 2) + 3)/(3(-3cos(3\u03c0(-2|x + 3| + 1)) + 2) + 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": "How many local extrema (minima and maxima combined) does the function f(x) = 1((1(1(-2|x - 3|)^2 + 2(-2|x - 3|) - 1) + 2)/(3(1(-2|x - 3|)^2 + 2(-2|x - 3|) - 1) - 2))^2 - 1((1(1(-2|x - 3|)^2 + 2(-2|x - 3|) - 1) + 2)/(3(1(-2|x - 3|)^2 + 2(-2|x - 3|) - 1) - 2)) - 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": "Find the total number of local minima and maxima for f(x) = (-1(1|(-1|(-1sin(3\u03c0x - 2) + 3) + 1| - 1) + 1| + 3))/(3(1|(-1|(-1sin(3\u03c0x - 2) + 3) + 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": "60", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = (-3(1|((-3(2sin(2\u03c0x) + 1) + 1)/(3(2sin(2\u03c0x) + 1) + 3)) + 1| + 3) - 1)/(3(1|((-3(2sin(2\u03c0x) + 1) + 1)/(3(2sin(2\u03c0x) + 1) + 3)) + 1| + 3) + 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": "Determine the count of local maxima for the function f(x) = 5(-3(-1sin(2\u03c0(-2x + 4) + 1) - 3)^2 - 5(-1sin(2\u03c0(-2x + 4) + 1) - 3) + 5) - 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": "Find the number of local maximum points for f(x) = 4(-2|(1|(1sin(3\u03c0x - 2) - 2) + 1| - 3) - 2|)^2 - 5(-2|(1|(1sin(3\u03c0x - 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": "30", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = (2(-2|(-5(1sin(2\u03c0x - 2) - 2)^2 - 2(1sin(2\u03c0x - 2) - 2) + 2) + 2|) + 1)/(3(-2|(-5(1sin(2\u03c0x - 2) - 2)^2 - 2(1sin(2\u03c0x - 2) - 2) + 2) + 2|) - 1) 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": "Determine the count of local minima for the function f(x) = (-1(-1|(3(2sin(3\u03c0x - 1))^2 - 2(2sin(3\u03c0x - 1)) - 5) - 3| - 1) + 1)/(1(-1|(3(2sin(3\u03c0x - 1))^2 - 2(2sin(3\u03c0x - 1)) - 5) - 3| - 1) + 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": "Determine the total count of local extrema points for the function f(x) = -1|(3(3cos(3\u03c0(-2x^2 - 2x) - 1) - 3)^2 - 4(3cos(3\u03c0(-2x^2 - 2x) - 1) - 3) + 5) + 2| - 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "453", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -2(3|(4(-3x^2 + 2x + 5) - 5) + 1| - 2)^2 - 2(3|(4(-3x^2 + 2x + 5) - 5) + 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": "How many local extrema (minima and maxima combined) does the function f(x) = 3sin(1\u03c0(-1|(-2(-1|x + 1| + 3)^2 + 2(-1|x + 1| + 3) - 4)| - 2) - 3) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "259", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = (-2(3cos(1\u03c0(1(-2|x|)^2 + 1) - 2) - 2))/(-3(3cos(1\u03c0(1(-2|x|)^2 + 1) - 2) - 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": "How many local extrema (minima and maxima combined) does the function f(x) = 2|((-3(1(-1cos(2\u03c0x - 1) - 2)^2 + 2(-1cos(2\u03c0x - 1) - 2) - 3) + 2)/(-2(1(-1cos(2\u03c0x - 1) - 2)^2 + 2(-1cos(2\u03c0x - 1) - 2) - 3)))| + 2 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": "Determine the count of local minima for the function f(x) = 5(-2(-1cos(1\u03c0(-3x - 2) + 1) + 3)^2 - 2(-1cos(1\u03c0(-3x - 2) + 1) + 3) - 5) 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) = -1|(-2|(-4(1cos(3\u03c0x + 2) - 1)^2 + 4(1cos(3\u03c0x + 2) - 1) - 5) - 2| - 3) + 3| + 3 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(-1(1|((3x - 1)/(-3x - 3)) + 2| - 2)^2 + 1(1|((3x - 1)/(-3x - 3)) + 2| - 2))^2 - 2(-1(1|((3x - 1)/(-3x - 3)) + 2| - 2)^2 + 1(1|((3x - 1)/(-3x - 3)) + 2| - 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) = (-1(4((2(2cos(2\u03c0x - 2)) + 3)/(-3(2cos(2\u03c0x - 2)) - 3)) + 3) - 3)/(1(4((2(2cos(2\u03c0x - 2)) + 3)/(-3(2cos(2\u03c0x - 2)) - 3)) + 3) - 2) 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) = (-3(2sin(3\u03c0((-1((2x + 3)/(3x + 1)))/(1((2x + 3)/(3x + 1)) - 3))) - 1) - 1)/(1(2sin(3\u03c0((-1((2x + 3)/(3x + 1)))/(1((2x + 3)/(3x + 1)) - 3))) - 1) - 3) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 5(1(-1(-3cos(3\u03c0x + 1) + 2)^2 - 1(-3cos(3\u03c0x + 1) + 2) - 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": "Determine the count of local minima for the function f(x) = -1|(4(1(-5x^2 + 5x + 2)^2 - 5) - 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|(4(-3(-2sin(3\u03c0x) + 1)^2 - 4(-2sin(3\u03c0x) + 1) - 4)) + 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 extrema (minima and maxima combined) does the function f(x) = 4((1(1(2sin(3\u03c0x - 3) - 2)^2 + 2(2sin(3\u03c0x - 3) - 2) - 4) - 3)/(1(1(2sin(3\u03c0x - 3) - 2)^2 + 2(2sin(3\u03c0x - 3) - 2) - 4))) + 4 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": "Find the total number of local minima and maxima for f(x) = -2(5(-2|(-4x^2 - 3x + 3)| + 1) + 4)^2 - 1(5(-2|(-4x^2 - 3x + 3)| + 1) + 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": "How many local minima does the function f(x) = 4((1(-1cos(2\u03c0(3x + 3) - 3)) + 3)/(-1(-1cos(2\u03c0(3x + 3) - 3)) - 2))^2 + 5((1(-1cos(2\u03c0(3x + 3) - 3)) + 3)/(-1(-1cos(2\u03c0(3x + 3) - 3)) - 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": "How many local minima does the function f(x) = -3cos(3\u03c0(1|(-2|(1x - 4) - 1| - 1) - 2| + 3) + 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": "How many local maxima does the function f(x) = 1(4(-3(-1sin(3\u03c0x + 3) - 3)^2 + 3(-1sin(3\u03c0x + 3) - 3))^2 - 4(-3(-1sin(3\u03c0x + 3) - 3)^2 + 3(-1sin(3\u03c0x + 3) - 3))) 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) = -3sin(2\u03c0(1|((1(2|x + 1| - 2) + 1)/(1(2|x + 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": "43", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 3(-3|(1cos(3\u03c0(-1x^2 - 3x - 4) - 3) - 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": "549", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = 4(-3|((3(-2x - 5) - 1)/(3(-2x - 5) - 2)) - 2| + 2)^2 + 2(-3|((3(-2x - 5) - 1)/(3(-2x - 5) - 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": "Determine the count of local minima for the function f(x) = -2|(1cos(3\u03c0(1(-1|x + 1| - 3)^2 + 5(-1|x + 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": "298", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = (1(5(3|(2cos(1\u03c0x - 1) - 3)| + 3)^2 - 5(3|(2cos(1\u03c0x - 1) - 3)| + 3) + 2) - 3)/(2(5(3|(2cos(1\u03c0x - 1) - 3)| + 3)^2 - 5(3|(2cos(1\u03c0x - 1) - 3)| + 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": "Find the total number of local minima and maxima for f(x) = (3(1(-2|(-1e^(-2x) + 2) - 3| + 3)^2 - 2(-2|(-1e^(-2x) + 2) - 3| + 3) + 1) - 1)/(2(1(-2|(-1e^(-2x) + 2) - 3| + 3)^2 - 2(-2|(-1e^(-2x) + 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": "59", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 3cos(3\u03c0(-3(-2(2x^2 - 3x - 3) - 1)^2 + 1(-2(2x^2 - 3x - 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": "66", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = -1(-5(-3|(-5x^2 - 2x + 3) - 1| + 3)^2 - 2(-3|(-5x^2 - 2x + 3) - 1| + 3) + 1) + 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": "Determine the total count of local extrema points for the function f(x) = 2((-2(-3(3sin(1\u03c0x - 2) + 2)^2 - 5(3sin(1\u03c0x - 2) + 2) - 1) + 2)/(-1(-3(3sin(1\u03c0x - 2) + 2)^2 - 5(3sin(1\u03c0x - 2) + 2) - 1) + 2)) - 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": "How many local extrema (minima and maxima combined) does the function f(x) = (-3(-1cos(2\u03c0(-4(-3|x| - 1)^2 - 5(-3|x| - 1) - 5) - 3) - 3) + 2)/(-1(-1cos(2\u03c0(-4(-3|x| - 1)^2 - 5(-3|x| - 1) - 5) - 3) - 3) - 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "363", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = 2|((-2(2|(1cos(2\u03c0x - 2) - 3)| + 3) + 2)/(2(2|(1cos(2\u03c0x - 2) - 3)| + 3) - 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": "Determine the count of local minima for the function f(x) = 2sin(2\u03c0(-4(4((3x - 1)/(1x))^2 - 2((3x - 1)/(1x)) + 4) + 3) - 2) + 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "125", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 2|(-1(2|(-3x^2 - 5x + 2) + 3| + 3)^2 + 2(2|(-3x^2 - 5x + 2) + 3| + 3) + 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) = -3|((1(2(3cos(3\u03c0x + 1) + 1)^2 + 5(3cos(3\u03c0x + 1) + 1) - 1) + 3)/(3(2(3cos(3\u03c0x + 1) + 1)^2 + 5(3cos(3\u03c0x + 1) + 1) - 1) + 2)) - 3| - 2 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) = -2sin(1\u03c0(3|(-4(-1x^2 - 4x + 5)^2 - 4(-1x^2 - 4x + 5) + 4) + 3| + 2)) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "153", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -1(1(-1|(1x^2 - 4x + 3) - 3| + 3)^2 - 2(-1|(1x^2 - 4x + 3) - 3| + 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": "Determine the total count of local extrema points for the function f(x) = 5(-2(1|(1sin(1\u03c0x + 3) - 1) + 3| + 2) + 5)^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": "Find the number of local minimum points for f(x) = 2cos(2\u03c0(4((2(-5x + 2) + 2)/(1(-5x + 2) - 3)) + 5) + 3) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "44", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = (3(1((1(1x^2 - 2))/(-3(1x^2 - 2) - 3))^2 - 5((1(1x^2 - 2))/(-3(1x^2 - 2) - 3)) + 4) + 1)/(3(1((1(1x^2 - 2))/(-3(1x^2 - 2) - 3))^2 - 5((1(1x^2 - 2))/(-3(1x^2 - 2) - 3)) + 4) + 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 total number of local minima and maxima for f(x) = (2(2|(-2(-2|x| + 2)^2 - 4(-2|x| + 2) + 2) - 3| - 1) + 2)/(3(2|(-2(-2|x| + 2)^2 - 4(-2|x| + 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": "How many local minima does the function f(x) = 5(-2e^(1(-3(2|x + 1| - 3)^2 - 2(2|x + 1| - 3) + 4)) + 3)^2 - 3(-2e^(1(-3(2|x + 1| - 3)^2 - 2(2|x + 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": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 1sin(3\u03c0(1|((3(-2|x - 2| + 3) - 2)/(1(-2|x - 2| + 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": "68", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = (1(-1sin(3\u03c0(-2|(-1|x + 3| - 1) - 2| + 2) + 1)) + 2)/(3(-1sin(3\u03c0(-2|(-1|x + 3| - 1) - 2| + 2) + 1))) have 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 total count of local extrema points for the function f(x) = 1cos(3\u03c0(2(-3(3x^2 - 5) + 5)^2 + 5(-3(3x^2 - 5) + 5)) + 3) + 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "118", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 2(1(-2(3sin(1\u03c0x - 2) - 2) - 4)^2 - 4)^2 + 2 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": "How many local extrema (minima and maxima combined) does the function f(x) = 2|(-1sin(1\u03c0(-1|(1x^2 - 5x + 4) + 3|) - 2) + 3) + 1| - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "215", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = -5(3(-1|(1cos(3\u03c0x + 3)) + 1| + 2)) + 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 maxima does the function f(x) = 1(-1cos(2\u03c0((-2(4x^2 + 2x - 3))/(1(4x^2 + 2x - 3) + 2)) - 2) + 1)^2 - 4 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": "Determine the count of local maxima for the function f(x) = 1|(-4(-2(2sin(1\u03c0x - 1) + 1)^2 + 4(2sin(1\u03c0x - 1) + 1) - 1)^2 + 1(-2(2sin(1\u03c0x - 1) + 1)^2 + 4(2sin(1\u03c0x - 1) + 1) - 1) + 1) + 3| in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "100", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -3(-5(-2(3x^2 + 4x)^2 + 2(3x^2 + 4x) + 2) - 4)^2 - 1(-5(-2(3x^2 + 4x)^2 + 2(3x^2 + 4x) + 2) - 4) + 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) = (-2(-3cos(1\u03c0((1(-1|x| + 3) - 2)/(-1(-1|x| + 3) + 3)) + 2) + 2))/(-2(-3cos(1\u03c0((1(-1|x| + 3) - 2)/(-1(-1|x| + 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": "12", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 3|(1(-3cos(1\u03c0(-4x^2 - 3x - 2) + 1) + 3)^2 + 5(-3cos(1\u03c0(-4x^2 - 3x - 2) + 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": "245", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -5((-3(3|(-3x)|) - 3)/(1(3|(-3x)|) + 1))^2 + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "139", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 5(3(-1sin(2\u03c0(5x + 2) - 2))^2 + 2(-1sin(2\u03c0(5x + 2) - 2)) - 4) + 5 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|(-3(3sin(1\u03c0(-3|x| + 2) - 2) + 3)^2 + 5(3sin(1\u03c0(-3|x| + 2) - 2) + 3) - 5) - 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 total number of local minima and maxima for f(x) = 2|(-4(3|(-3|x + 1| + 3) - 2| - 1)^2 + 2(3|(-3|x + 1| + 3) - 2| - 1) + 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": "Determine the count of local maxima for the function f(x) = 2|(4(1(2cos(1\u03c0x + 2) - 2)^2 + 1(2cos(1\u03c0x + 2) - 2) + 1)^2 + 1(1(2cos(1\u03c0x + 2) - 2)^2 + 1(2cos(1\u03c0x + 2) - 2) + 1) - 2) + 2| + 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 maxima for the function f(x) = 1cos(1\u03c0(-2((2(-1|x + 3| + 3) + 1)/(-2(-1|x + 3| + 3) + 3)) - 3) + 3) + 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = (2(-5(3|(-1x^2 - 5x - 1) + 2| - 3)^2 + 4(3|(-1x^2 - 5x - 1) + 2| - 3) - 5) - 3)/(2(-5(3|(-1x^2 - 5x - 1) + 2| - 3)^2 + 4(3|(-1x^2 - 5x - 1) + 2| - 3) - 5) + 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) = -4((-1(-1sin(2\u03c0((1x + 2)/(3x - 1)) + 2) - 3) + 3)/(-2(-1sin(2\u03c0((1x + 2)/(3x - 1)) + 2) - 3) - 3))^2 + 1((-1(-1sin(2\u03c0((1x + 2)/(3x - 1)) + 2) - 3) + 3)/(-2(-1sin(2\u03c0((1x + 2)/(3x - 1)) + 2) - 3) - 3)) + 5 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 number of local maximum points for f(x) = 1|((-1(1|(2cos(1\u03c0x - 1) - 3)| - 2) + 3)/(-3(1|(2cos(1\u03c0x - 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": "40", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -1(-3(-3|(1sin(2\u03c0x + 2) - 2) + 3| + 1)^2 - 3(-3|(1sin(2\u03c0x + 2) - 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": "40", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = (-1(1cos(1\u03c0(2(-2|x - 1| + 3) - 5) - 2) + 3) - 2)/(1(1cos(1\u03c0(2(-2|x - 1| + 3) - 5) - 2) + 3) + 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": "How many local maxima does the function f(x) = -3(-2cos(1\u03c0(1|(-3x^2 + 1x + 1) - 3| + 3) + 3) + 3)^2 + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "337", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -5((2(-1|(-2cos(1\u03c0x - 1) - 3) - 1| + 2))/(-3(-1|(-2cos(1\u03c0x - 1) - 3) - 1| + 2) + 1))^2 + 1((2(-1|(-2cos(1\u03c0x - 1) - 3) - 1| + 2))/(-3(-1|(-2cos(1\u03c0x - 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": "10", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = (-1(5(1sin(1\u03c0(-1x^2 + 2x + 1) + 3) - 2)^2 - 2(1sin(1\u03c0(-1x^2 + 2x + 1) + 3) - 2) + 2) + 2)/(1(5(1sin(1\u03c0(-1x^2 + 2x + 1) + 3) - 2)^2 - 2(1sin(1\u03c0(-1x^2 + 2x + 1) + 3) - 2) + 2) + 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "203", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -2sin(3\u03c0(-3|((3(-2x^2 - 4x + 3) - 1)/(-2(-2x^2 - 4x + 3) - 3)) - 2| - 2) - 3) - 1 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": "Determine the total count of local extrema points for the function f(x) = -3|((-2(-1sin(1\u03c0(5x - 4) + 1) + 1) - 3)/(-2(-1sin(1\u03c0(5x - 4) + 1) + 1))) + 2| - 2 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) = -2sin(1\u03c0((2((2(5x + 4) + 3)/(2(5x + 4) - 3)) + 3)/(-1((2(5x + 4) + 3)/(2(5x + 4) - 3)) + 3)) - 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": "Determine the count of local minima for the function f(x) = -4(-1(-1|(-3cos(2\u03c0x - 3) - 1) - 2|)^2 + 1(-1|(-3cos(2\u03c0x - 3) - 1) - 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": "How many local extrema (minima and maxima combined) does the function f(x) = 5((2(2sin(2\u03c0((1x - 2)/(-2x + 3)) - 2) + 2) - 2)/(-1(2sin(2\u03c0((1x - 2)/(-2x + 3)) - 2) + 2) - 2)) - 5 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 total number of local minima and maxima for f(x) = -3|(-3(3cos(3\u03c0((-3x + 3)/(2x + 3)) + 1)) + 4) + 2| - 1 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": "Determine the count of local minima for the function f(x) = -1cos(2\u03c0((2((-1(-4x^2 + 4x + 3) + 3)/(-3(-4x^2 + 4x + 3) - 3)) - 1)/(-3((-1(-4x^2 + 4x + 3) + 3)/(-3(-4x^2 + 4x + 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": "Determine the total count of local extrema points for the function f(x) = 2|(2(-2|(1x + 2) + 2| + 3)^2 + 3(-2|(1x + 2) + 2| + 3) - 1) - 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) = -3|(3((-2(-2x^2 - 3x + 3) + 1)/(-3(-2x^2 - 3x + 3) - 3))^2 - 2((-2(-2x^2 - 3x + 3) + 1)/(-3(-2x^2 - 3x + 3) - 3)) - 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": "Find the total number of local minima and maxima for f(x) = (-1(-3sin(3\u03c0(3(-2|x - 3|) - 5) + 1) - 3) - 3)/(-2(-3sin(3\u03c0(3(-2|x - 3|) - 5) + 1) - 3) - 1) 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((-3(2cos(3\u03c0(-2x + 3) - 3) + 1) - 3)/(-3(2cos(3\u03c0(-2x + 3) - 3) + 1) + 4)) 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((2(-5(-3cos(2\u03c0x + 3))^2 - 3(-3cos(2\u03c0x + 3)) - 3) - 2)/(1(-5(-3cos(2\u03c0x + 3))^2 - 3(-3cos(2\u03c0x + 3)) - 3) - 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": "Find the total number of local minima and maxima for f(x) = 2|(3(-3|(-2cos(3\u03c0x - 2) + 1) - 1| + 2)^2 + 1(-3|(-2cos(3\u03c0x - 2) + 1) - 1| + 2) + 5) + 2| + 3 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": "Determine the count of local minima for the function f(x) = -5(2cos(1\u03c0(-3(-5x^2 + 1x + 5)^2 - 5(-5x^2 + 1x + 5) - 4) - 2) - 1) - 4 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "89", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = (1(-2|(-2sin(2\u03c0(-1x) - 2)) - 3| + 3) + 1)/(-1(-2|(-2sin(2\u03c0(-1x) - 2)) - 3| + 3) - 2) 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": "Find the number of local maximum points for f(x) = 2|(-2|(-1cos(2\u03c0(1|x - 1| + 1)) + 2) + 1| - 2) - 1| + 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(-3cos(1\u03c0(-3|(-4x^2 - 1x + 2) + 1| + 1) - 3) - 2)^2 - 3(-3cos(1\u03c0(-3|(-4x^2 - 1x + 2) + 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": "450", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 1|(1sin(2\u03c0(3(2x - 3) + 4) + 3) + 3) + 2| + 2 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": "Determine the count of local minima for the function f(x) = 2(-2sin(2\u03c0(3(2|x - 2| + 1) - 1) - 3) + 3)^2 + 4(-2sin(2\u03c0(3(2|x - 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": "121", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 2|(1cos(3\u03c0(1|(-4x) + 1| - 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": "120", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 3sin(3\u03c0(-3(-3(-3x + 1) + 5)^2 + 1(-3(-3x + 1) + 5) - 1) - 1) - 3 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": "How many local maxima does the function f(x) = (-1((-1(4(-3cos(3\u03c0x - 1) + 3)^2 + 5(-3cos(3\u03c0x - 1) + 3) - 2))/(-1(4(-3cos(3\u03c0x - 1) + 3)^2 + 5(-3cos(3\u03c0x - 1) + 3) - 2) - 2)) - 2)/(3((-1(4(-3cos(3\u03c0x - 1) + 3)^2 + 5(-3cos(3\u03c0x - 1) + 3) - 2))/(-1(4(-3cos(3\u03c0x - 1) + 3)^2 + 5(-3cos(3\u03c0x - 1) + 3) - 2) - 2)) - 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": "Find the number of local maximum points for f(x) = 1|((1(-1e^(2(3|x + 2| + 3)) - 1) + 2)/(3(-1e^(2(3|x + 2| + 3)) - 1) + 3)) + 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": "How many local minima does the function f(x) = -3|(-1|((-2(-2|x + 3| + 3) + 2)/(1(-2|x + 3| + 3))) + 3|) + 3| + 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 maxima for the function f(x) = -1cos(2\u03c0(-3|(5(-2|x + 2| + 3) - 2) - 1| + 3) - 1) - 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "399", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 3sin(1\u03c0(1|(-1((1x - 2)/(1x))^2 - 2((1x - 2)/(1x)) - 5) - 1| + 2) - 2) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "62", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -1|(-2|(-1sin(3\u03c0((-1x + 2)/(1x)) + 3) - 3) + 2|) + 3| where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "69", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -2((-2(3cos(3\u03c0(-1x^2 - 1x - 1))) - 3)/(1(3cos(3\u03c0(-1x^2 - 1x - 1))) + 1))^2 - 1((-2(3cos(3\u03c0(-1x^2 - 1x - 1))) - 3)/(1(3cos(3\u03c0(-1x^2 - 1x - 1))) + 1)) + 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "530", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 4(1cos(1\u03c0(-1(-1x + 3)^2 + 3(-1x + 3) + 3) + 1) + 2)^2 - 1(1cos(1\u03c0(-1(-1x + 3)^2 + 3(-1x + 3) + 3) + 1) + 2) + 4 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": "Determine the total count of local extrema points for the function f(x) = -1sin(2\u03c0(2|(-1(-4x^2 - 3)^2 - 3(-4x^2 - 3) + 3) - 1| - 1)) - 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "174", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -3(2cos(2\u03c0((-2(-4x^2 + 1x - 4) + 2)/(-1(-4x^2 + 1x - 4) - 3)) + 1) + 1)^2 + 5(2cos(2\u03c0((-2(-4x^2 + 1x - 4) + 2)/(-1(-4x^2 + 1x - 4) - 3)) + 1) + 1) - 4 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) = -2|(-4(2|(1|x + 1| + 1) - 2| - 2)^2 + 4(2|(1|x + 1| + 1) - 2| - 2) + 1) + 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": "How many local extrema (minima and maxima combined) does the function f(x) = -3(1(3cos(3\u03c0(-3x) + 2) - 3) - 1)^2 - 2(1(3cos(3\u03c0(-3x) + 2) - 3) - 1) - 5 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": "How many local minima does the function f(x) = 4(-1|(1cos(2\u03c0((2x + 2)/(-1x)) + 1) + 2) + 2| + 3) + 3 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 number of local maximum points for f(x) = -2cos(3\u03c0(-3(-1|((-2x + 3)/(2x - 1)) + 3| - 2)^2 - 1(-1|((-2x + 3)/(2x - 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": "79", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = 1((-3((1(-1sin(2\u03c0x + 2) + 2) - 1)/(-1(-1sin(2\u03c0x + 2) + 2) + 2)) + 2)/(-2((1(-1sin(2\u03c0x + 2) + 2) - 1)/(-1(-1sin(2\u03c0x + 2) + 2) + 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": "Determine the count of local minima for the function f(x) = 3|(3|((-2(3cos(2\u03c0x - 2) + 1) - 2)/(2(3cos(2\u03c0x - 2) + 1) + 3))| - 3) - 1| + 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "152", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -3(1cos(3\u03c0(5(-5x - 2) - 2) - 3) - 3)^2 - 5(1cos(3\u03c0(5(-5x - 2) - 2) - 3) - 3) + 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "249", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 2(1(4(-3cos(2\u03c0x + 2) - 3)^2 + 5(-3cos(2\u03c0x + 2) - 3) - 5)^2 + 5(4(-3cos(2\u03c0x + 2) - 3)^2 + 5(-3cos(2\u03c0x + 2) - 3) - 5)) - 1 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) = 3(-1cos(2\u03c0(1(1|x - 3| - 2)^2 + 1(1|x - 3| - 2) - 3)) + 3)^2 - 5(-1cos(2\u03c0(1(1|x - 3| - 2)^2 + 1(1|x - 3| - 2) - 3)) + 3) + 5 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "335", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -1sin(3\u03c0(-1|(-2(-5x + 2)^2 + 3(-5x + 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": "221", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 2((1(-3cos(1\u03c0(1|x - 1| - 1) - 3) + 1) - 1)/(1(-3cos(1\u03c0(1|x - 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": "11", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -3(-1sin(3\u03c0(2|(-1x - 3) - 1| + 2) + 3) + 2)^2 + 5 have 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 total number of local minima and maxima for f(x) = 3sin(2\u03c0(5(1|((-1x - 2)/(2x + 3)) - 2| - 2)^2 + 4(1|((-1x - 2)/(2x + 3)) - 2| - 2) + 5) + 2) - 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": "How many local maxima does the function f(x) = -3(-1sin(3\u03c0(1(3x + 2)^2 - 1(3x + 2) - 5) + 1) + 3) - 2 have 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 count of local minima for the function f(x) = 3|(-2(-1(1sin(3\u03c0x - 1) - 3))^2 + 2(-1(1sin(3\u03c0x - 1) - 3))) + 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 extrema (minima and maxima combined) does the function f(x) = -4((1((2(3|x + 1| - 2))/(2(3|x + 1| - 2) + 3)) + 1)/(-3((2(3|x + 1| - 2))/(2(3|x + 1| - 2) + 3)) + 2))^2 + 3((1((2(3|x + 1| - 2))/(2(3|x + 1| - 2) + 3)) + 1)/(-3((2(3|x + 1| - 2))/(2(3|x + 1| - 2) + 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 number of local maximum points for f(x) = 2(-1(-3cos(2\u03c0(-2x^2 + 3x))) + 1) - 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "288", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 1((3(1e^(-1(4x^2 + 3x - 2)) - 3) + 1)/(-2(1e^(-1(4x^2 + 3x - 2)) - 3) - 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((3(3cos(2\u03c0(-1x) + 2)) + 1)/(2(3cos(2\u03c0(-1x) + 2)) - 1))^2 - 2((3(3cos(2\u03c0(-1x) + 2)) + 1)/(2(3cos(2\u03c0(-1x) + 2)) - 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": "Determine the count of local minima for the function f(x) = (2(5(-3sin(3\u03c0(2x^2 - 4x + 1) + 1) + 2)^2 + 1(-3sin(3\u03c0(2x^2 - 4x + 1) + 1) + 2) - 3) + 2)/(1(5(-3sin(3\u03c0(2x^2 - 4x + 1) + 1) + 2)^2 + 1(-3sin(3\u03c0(2x^2 - 4x + 1) + 1) + 2) - 3) + 2) 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 minima for the function f(x) = (3(-2|(3cos(3\u03c0(-1x^2 + 2x + 4)) - 1)| + 3) + 1)/(1(-2|(3cos(3\u03c0(-1x^2 + 2x + 4)) - 1)| + 3) + 2) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "231", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 1(3sin(3\u03c0(1(-5x + 3) - 3)) + 1)^2 - 1(3sin(3\u03c0(1(-5x + 3) - 3)) + 1) + 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "600", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = 1((1(-1sin(3\u03c0(1|x - 3| + 3)) - 1) - 3)/(2(-1sin(3\u03c0(1|x - 3| + 3)) - 1) - 3)) - 2 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) = -3|(-3(4(-2cos(3\u03c0x + 3) + 2)^2 - 4(-2cos(3\u03c0x + 3) + 2) + 1)^2 - 1(4(-2cos(3\u03c0x + 3) + 2)^2 - 4(-2cos(3\u03c0x + 3) + 2) + 1) - 1) + 3| 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 extrema (minima and maxima combined) does the function f(x) = 1|((2(-4(3cos(1\u03c0x) - 3)^2 + 5(3cos(1\u03c0x) - 3) - 5))/(3(-4(3cos(1\u03c0x) - 3)^2 + 5(3cos(1\u03c0x) - 3) - 5) - 2)) - 1| - 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": "How many local extrema (minima and maxima combined) does the function f(x) = 4((2(-3(2|x - 3| - 3)^2 + 4(2|x - 3| - 3) + 3) - 2)/(-1(-3(2|x - 3| - 3)^2 + 4(2|x - 3| - 3) + 3) + 3))^2 - 3((2(-3(2|x - 3| - 3)^2 + 4(2|x - 3| - 3) + 3) - 2)/(-1(-3(2|x - 3| - 3)^2 + 4(2|x - 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": "10", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = (-1(-3cos(1\u03c0(1(-3x^2 - 4x + 2)^2 + 3(-3x^2 - 4x + 2) - 5)) + 1) - 1)/(-3(-3cos(1\u03c0(1(-3x^2 - 4x + 2)^2 + 3(-3x^2 - 4x + 2) - 5)) + 1) + 4) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "132", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = (-2(-1(-3|(-1|x - 2| + 1) + 2| + 1)^2 - 2(-3|(-1|x - 2| + 1) + 2| + 1) - 5) + 3)/(2(-1(-3|(-1|x - 2| + 1) + 2| + 1)^2 - 2(-3|(-1|x - 2| + 1) + 2| + 1) - 5) + 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 extrema (minima and maxima combined) does the function f(x) = 3(3(-1(-2cos(3\u03c0x + 1) + 1) - 3)) - 5 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) = 4(-1|(1sin(1\u03c0(-4x - 5)) - 1) + 1|)^2 - 2(-1|(1sin(1\u03c0(-4x - 5)) - 1) + 1|) + 4 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "155", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -1cos(3\u03c0(1|(2|(-5x^2 - 5x - 2) + 1| - 1) - 1|)) + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "492", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = 3sin(1\u03c0(5((1((1x - 3)/(-2x)) + 1)/(-2((1x - 3)/(-2x)) + 1))^2 - 3((1((1x - 3)/(-2x)) + 1)/(-2((1x - 3)/(-2x)) + 1))) + 3) + 1 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 minimum points for f(x) = -4(-5((-2(-3sin(2\u03c0x) - 2) - 3)/(1(-3sin(2\u03c0x) - 2) + 3)) - 1) + 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": "How many local minima does the function f(x) = 1(-3|((-1(-2cos(1\u03c0x) - 2) + 3)/(-3(-2cos(1\u03c0x) - 2) - 3)) + 1| + 1)^2 + 3(-3|((-1(-2cos(1\u03c0x) - 2) + 3)/(-3(-2cos(1\u03c0x) - 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": "47", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = (3((1(1cos(1\u03c0(1|x - 3| - 3) + 3) + 3) + 3)/(-3(1cos(1\u03c0(1|x - 3| - 3) + 3) + 3) - 2)))/(3((1(1cos(1\u03c0(1|x - 3| - 3) + 3) + 3) + 3)/(-3(1cos(1\u03c0(1|x - 3| - 3) + 3) + 3) - 2)) + 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|(-1((-3((-1x + 2)/(-1x - 3)) - 3)/(2((-1x + 2)/(-1x - 3)) + 2)) - 5)| - 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) = 2sin(3\u03c0((-2(4(-1x^2 - 5x + 2) + 2) + 1)/(-1(4(-1x^2 - 5x + 2) + 2) - 2)) + 1) + 2 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 maximum points for f(x) = -2|(5(3(-1cos(2\u03c0x + 2) - 1)^2 + 2(-1cos(2\u03c0x + 2) - 1) + 3)^2 - 2(3(-1cos(2\u03c0x + 2) - 1)^2 + 2(-1cos(2\u03c0x + 2) - 1) + 3) + 5) + 3| + 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": "How many local maxima does the function f(x) = (2((-3(3e^(1(3|x| + 2))) + 1)/(-1(3e^(1(3|x| + 2))) - 2)))/(-3((-3(3e^(1(3|x| + 2))) + 1)/(-1(3e^(1(3|x| + 2))) - 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": "How many local extrema (minima and maxima combined) does the function f(x) = 2cos(3\u03c0((-2(5(1x - 5) - 3) - 2)/(-1(5(1x - 5) - 3) - 3)) + 3) 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": "How many local minima does the function f(x) = -2sin(3\u03c0(-5(-1|(2|x|) + 1| + 2)) + 2) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "300", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -2|(1(-5(-1x^2 - 5x + 2)^2 + 5)^2 - 5(-5(-1x^2 - 5x + 2)^2 + 5)) - 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": "Find the total number of local minima and maxima for f(x) = -1(-3(-2cos(1\u03c0((3x)/(-2x - 1))) + 2)^2 + 5) 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": "How many local minima does the function f(x) = 3sin(3\u03c0(-1|((-2(-2|x - 1| + 2) + 1)/(1(-2|x - 1| + 2) + 1)) + 3| + 3) + 1) + 2 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": "How many local maxima does the function f(x) = 1cos(3\u03c0(-5((-2(-1x - 5) - 2)/(-1(-1x - 5) + 2))^2 - 5) - 3) + 2 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": "Find the total number of local minima and maxima for f(x) = -1cos(2\u03c0(1(-4(-3|x + 2| - 2)^2 - 1(-3|x + 2| - 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": "460", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = (3((2(-4(1cos(1\u03c0x - 2)) - 2) + 3)/(1(-4(1cos(1\u03c0x - 2)) - 2))) + 3)/(3((2(-4(1cos(1\u03c0x - 2)) - 2) + 3)/(1(-4(1cos(1\u03c0x - 2)) - 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": "Determine the total count of local extrema points for the function f(x) = 1|(-2(1(-3x^2 - 3x - 2) + 3)^2 - 4(1(-3x^2 - 3x - 2) + 3) - 3) + 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": "Find the number of local maximum points for f(x) = 2|(-5(-2sin(3\u03c0(5x^2 - 5x + 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": "491", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = (1(5(2|(-3cos(2\u03c0x + 1) + 2) - 3| - 2)^2 + 4(2|(-3cos(2\u03c0x + 1) + 2) - 3| - 2) - 3) - 1)/(-2(5(2|(-3cos(2\u03c0x + 1) + 2) - 3| - 2)^2 + 4(2|(-3cos(2\u03c0x + 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": "80", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = (-2((1(5(-3sin(2\u03c0x + 2) + 2) + 2) - 1)/(2(5(-3sin(2\u03c0x + 2) + 2) + 2) + 2)) + 1)/(3((1(5(-3sin(2\u03c0x + 2) + 2) + 2) - 1)/(2(5(-3sin(2\u03c0x + 2) + 2) + 2) + 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 extrema (minima and maxima combined) does the function f(x) = (1(-4((1(3cos(2\u03c0x - 1) + 3) + 1)/(2(3cos(2\u03c0x - 1) + 3) + 1)) + 2) + 2)/(2(-4((1(3cos(2\u03c0x - 1) + 3) + 1)/(2(3cos(2\u03c0x - 1) + 3) + 1)) + 2) - 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) = 3cos(2\u03c0(3|(2|(-4x + 5) - 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": "480", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -3|((-1(2(2cos(2\u03c0x + 1) + 3)^2 + 5(2cos(2\u03c0x + 1) + 3) - 1) + 3)/(3(2(2cos(2\u03c0x + 1) + 3)^2 + 5(2cos(2\u03c0x + 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": "40", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = (-1((1(-1cos(1\u03c0(-5x^2 - 2x - 3)) + 3) - 1)/(2(-1cos(1\u03c0(-5x^2 - 2x - 3)) + 3) - 1)) - 1)/(1((1(-1cos(1\u03c0(-5x^2 - 2x - 3)) + 3) - 1)/(2(-1cos(1\u03c0(-5x^2 - 2x - 3)) + 3) - 1))) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "336", "dataset": "MATH"}