{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 4((-3(1sin(2\u03c0(2|(2|x + 3| + 2) - 1| - 3) - 3) - 3) - 2)/(-2(1sin(2\u03c0(2|(2|x + 3| + 2) - 1| - 3) - 3) - 3) + 1))^2 - 5((-3(1sin(2\u03c0(2|(2|x + 3| + 2) - 1| - 3) - 3) - 3) - 2)/(-2(1sin(2\u03c0(2|(2|x + 3| + 2) - 1| - 3) - 3) - 3) + 1)) + 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "161", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -3sin(3\u03c0(5((-2(-2|(5x) + 1| - 1) + 2)/(-1(-2|(5x) + 1| - 1) + 2)) + 5) + 2) - 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = (-3(-5(3|(-2sin(1\u03c0(4x) - 1) + 3) + 1| - 2)^2 - 2(3|(-2sin(1\u03c0(4x) - 1) + 3) + 1| - 2) + 4) - 3)/(2(-5(3|(-2sin(1\u03c0(4x) - 1) + 3) + 1| - 2)^2 - 2(3|(-2sin(1\u03c0(4x) - 1) + 3) + 1| - 2) + 4)) 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) = 3(5(1(-2(-2sin(3\u03c0x + 3) + 2) - 1) + 5)^2 + 2)^2 + 2(5(1(-2(-2sin(3\u03c0x + 3) + 2) - 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": "118", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 2cos(2\u03c0((-3(-4(5(-3|x + 3| + 2)^2 - 5(-3|x + 3| + 2) - 2)^2 - 5(5(-3|x + 3| + 2)^2 - 5(-3|x + 3| + 2) - 2)) + 1)/(-2(-4(5(-3|x + 3| + 2)^2 - 5(-3|x + 3| + 2) - 2)^2 - 5(5(-3|x + 3| + 2)^2 - 5(-3|x + 3| + 2) - 2)) - 1)) - 2) + 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = (-3((2(3sin(3\u03c0(-2(-2|x + 1|)^2 - 4(-2|x + 1|) + 2) - 3) - 3) + 1)/(3(3sin(3\u03c0(-2(-2|x + 1|)^2 - 4(-2|x + 1|) + 2) - 3) - 3) - 2)) + 3)/(3((2(3sin(3\u03c0(-2(-2|x + 1|)^2 - 4(-2|x + 1|) + 2) - 3) - 3) + 1)/(3(3sin(3\u03c0(-2(-2|x + 1|)^2 - 4(-2|x + 1|) + 2) - 3) - 3) - 2)) - 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "481", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 2cos(3\u03c0(1((2(-2((1x - 3)/(1x)) + 5) - 1)/(-2(-2((1x - 3)/(1x)) + 5) - 1)) - 3) - 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|(1cos(3\u03c0(1(-1|(1|x + 1| - 2) + 3| - 2) - 3) + 3) + 2) + 3| + 2 where -10 \u2264 x \u2264 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 minimum points for f(x) = -5(1sin(2\u03c0(2|(-1((-1x - 1)/(1x - 2)) + 5) - 3| - 1) - 1) + 3)^2 - 4(1sin(2\u03c0(2|(-1((-1x - 1)/(1x - 2)) + 5) - 3| - 1) - 1) + 3) + 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = (1(3(-4((2(-2sin(3\u03c0x) + 1))/(1(-2sin(3\u03c0x) + 1) - 3))^2 - 4((2(-2sin(3\u03c0x) + 1))/(1(-2sin(3\u03c0x) + 1) - 3)) - 3)^2 - 5(-4((2(-2sin(3\u03c0x) + 1))/(1(-2sin(3\u03c0x) + 1) - 3))^2 - 4((2(-2sin(3\u03c0x) + 1))/(1(-2sin(3\u03c0x) + 1) - 3)) - 3)) + 1)/(-2(3(-4((2(-2sin(3\u03c0x) + 1))/(1(-2sin(3\u03c0x) + 1) - 3))^2 - 4((2(-2sin(3\u03c0x) + 1))/(1(-2sin(3\u03c0x) + 1) - 3)) - 3)^2 - 5(-4((2(-2sin(3\u03c0x) + 1))/(1(-2sin(3\u03c0x) + 1) - 3))^2 - 4((2(-2sin(3\u03c0x) + 1))/(1(-2sin(3\u03c0x) + 1) - 3)) - 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) = -1(-2(3|(-3sin(2\u03c0((-1x - 2)/(3x + 2)) + 3) - 3)| - 2)^2 + 2(3|(-3sin(2\u03c0((-1x - 2)/(3x + 2)) + 3) - 3)| - 2)) - 2 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 count of local minima for the function f(x) = (1(-5(-1cos(1\u03c0(-1(1x^2 + 5x + 3) - 4) + 1) - 1)^2 - 4(-1cos(1\u03c0(-1(1x^2 + 5x + 3) - 4) + 1) - 1) + 4) + 2)/(3(-5(-1cos(1\u03c0(-1(1x^2 + 5x + 3) - 4) + 1) - 1)^2 - 4(-1cos(1\u03c0(-1(1x^2 + 5x + 3) - 4) + 1) - 1) + 4) - 1) 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) = -1|(1(5(3cos(3\u03c0((2x)/(-3x + 1)) + 2) + 2)^2 - 2(3cos(3\u03c0((2x)/(-3x + 1)) + 2) + 2))^2 - 4(5(3cos(3\u03c0((2x)/(-3x + 1)) + 2) + 2)^2 - 2(3cos(3\u03c0((2x)/(-3x + 1)) + 2) + 2)) + 5) - 1| - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = (-1(3(3(1(5x^2 - 5x - 4)^2 - 2(5x^2 - 5x - 4) - 3)^2 + 2(1(5x^2 - 5x - 4)^2 - 2(5x^2 - 5x - 4) - 3) - 5)^2 - 2(3(1(5x^2 - 5x - 4)^2 - 2(5x^2 - 5x - 4) - 3)^2 + 2(1(5x^2 - 5x - 4)^2 - 2(5x^2 - 5x - 4) - 3) - 5) - 4) + 3)/(1(3(3(1(5x^2 - 5x - 4)^2 - 2(5x^2 - 5x - 4) - 3)^2 + 2(1(5x^2 - 5x - 4)^2 - 2(5x^2 - 5x - 4) - 3) - 5)^2 - 2(3(1(5x^2 - 5x - 4)^2 - 2(5x^2 - 5x - 4) - 3)^2 + 2(1(5x^2 - 5x - 4)^2 - 2(5x^2 - 5x - 4) - 3) - 5) - 4) + 3) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -1|(-4(1|(1(4x^2 + 3x - 5) + 4) - 2| - 3) + 5) - 3| have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -3(-1|(1sin(1\u03c0(5(-2x^2 - 3x + 2) - 4)) + 2) - 3| - 1) + 4 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "250", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 5(-3sin(3\u03c0(4((2(-1x^2 + 4x + 5) + 2)/(-2(-1x^2 + 4x + 5) - 3))^2 + 5((2(-1x^2 + 4x + 5) + 2)/(-2(-1x^2 + 4x + 5) - 3)) - 2) + 3) - 1)^2 + 4(-3sin(3\u03c0(4((2(-1x^2 + 4x + 5) + 2)/(-2(-1x^2 + 4x + 5) - 3))^2 + 5((2(-1x^2 + 4x + 5) + 2)/(-2(-1x^2 + 4x + 5) - 3)) - 2) + 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": "How many local extrema (minima and maxima combined) does the function f(x) = (1(1(2((1(2x + 2) - 2)/(-3(2x + 2) - 1))^2 - 4((1(2x + 2) - 2)/(-3(2x + 2) - 1)) - 4)^2 + 2(2((1(2x + 2) - 2)/(-3(2x + 2) - 1))^2 - 4((1(2x + 2) - 2)/(-3(2x + 2) - 1)) - 4) - 4) + 2)/(2(1(2((1(2x + 2) - 2)/(-3(2x + 2) - 1))^2 - 4((1(2x + 2) - 2)/(-3(2x + 2) - 1)) - 4)^2 + 2(2((1(2x + 2) - 2)/(-3(2x + 2) - 1))^2 - 4((1(2x + 2) - 2)/(-3(2x + 2) - 1)) - 4) - 4) - 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 maximum points for f(x) = -1(1|(1(1sin(1\u03c0(-3x^2 - 2x - 3) - 2) - 3)^2 + 2(1sin(1\u03c0(-3x^2 - 2x - 3) - 2) - 3) + 4) + 3| - 2) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "334", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -1|(-3|(-3(-2e^(-1(1x^2 - 4x + 3)) - 1) - 4) + 2| + 3) - 1| + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = (-1(2cos(2\u03c0(3|((3(-4x - 2) - 3)/(-2(-4x - 2) + 3)) + 2|) + 1) + 2))/(3(2cos(2\u03c0(3|((3(-4x - 2) - 3)/(-2(-4x - 2) + 3)) + 2|) + 1) + 2)) 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) = -3|(-3|(-4(1|(2x^2 - 5x - 3) - 1| - 1) + 2) - 1|) - 2| - 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = 4(2(1|((3(2sin(1\u03c0x + 3) - 1) + 2)/(3(2sin(1\u03c0x + 3) - 1) + 1)) - 2| + 2)^2 + 3(1|((3(2sin(1\u03c0x + 3) - 1) + 2)/(3(2sin(1\u03c0x + 3) - 1) + 1)) - 2| + 2) - 5)^2 - 4(2(1|((3(2sin(1\u03c0x + 3) - 1) + 2)/(3(2sin(1\u03c0x + 3) - 1) + 1)) - 2| + 2)^2 + 3(1|((3(2sin(1\u03c0x + 3) - 1) + 2)/(3(2sin(1\u03c0x + 3) - 1) + 1)) - 2| + 2) - 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": "How many local extrema (minima and maxima combined) does the function f(x) = -1|((-1(-1(-3|((3x + 2)/(2x + 3))| - 2)^2 - 5(-3|((3x + 2)/(2x + 3))| - 2) - 5) + 3)/(-3(-1(-3|((3x + 2)/(2x + 3))| - 2)^2 - 5(-3|((3x + 2)/(2x + 3))| - 2) - 5) - 1)) + 1| have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = 2cos(3\u03c0((-3(-1(1(3x^2 - 4) - 5) + 3))/(-1(-1(1(3x^2 - 4) - 5) + 3) + 2)) - 1) + 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "26", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -3|(-1(1(-1cos(2\u03c0(-1x + 2) - 3) + 2)^2 - 5(-1cos(2\u03c0(-1x + 2) - 3) + 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": "100", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -2(1e^(-1((3(4(-2|x + 2| + 3)^2 - 2(-2|x + 2| + 3) - 4) + 3)/(1(4(-2|x + 2| + 3)^2 - 2(-2|x + 2| + 3) - 4) - 2))) + 3) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -3(4((-1((3(3cos(1\u03c0x - 3) + 2) - 3)/(-2(3cos(1\u03c0x - 3) + 2) - 3)) + 3)/(3((3(3cos(1\u03c0x - 3) + 2) - 3)/(-2(3cos(1\u03c0x - 3) + 2) - 3)) - 2))^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": "Find the number of local maximum points for f(x) = 1|(3((-1(1sin(1\u03c0((2x - 3)/(-3x - 1)) - 3) - 2) + 1)/(2(1sin(1\u03c0((2x - 3)/(-3x - 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": "How many local maxima does the function f(x) = 4(3(1sin(1\u03c0(-3|(3|x - 1| - 1) - 3| - 1) + 3)) + 4)^2 + 5(3(1sin(1\u03c0(-3|(3|x - 1| - 1) - 3| - 1) + 3)) + 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": "Find the number of local minimum points for f(x) = 2|(2|((-2(1cos(1\u03c0(1x^2 + 4) - 3) - 2) + 3)/(1(1cos(1\u03c0(1x^2 + 4) - 3) - 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": "101", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -2(-5(-2((2(-4x^2 - 1x + 5) + 1)/(1(-4x^2 - 1x + 5) - 3))^2 + 1((2(-4x^2 - 1x + 5) + 1)/(1(-4x^2 - 1x + 5) - 3)) + 4) - 5) - 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 maxima for the function f(x) = (3(2|(1cos(1\u03c0(-2(-3x - 1) - 3) + 3) + 3) + 3| - 2) + 2)/(2(2|(1cos(1\u03c0(-2(-3x - 1) - 3) + 3) + 3) + 3| - 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": "Determine the count of local minima for the function f(x) = -2(3|(1sin(3\u03c0(1(1|x - 1| + 1)^2 + 2(1|x - 1| + 1) + 4) - 3)) - 1| + 2)^2 + 4 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "271", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = -1|(1sin(1\u03c0(2((-3(3x^2 + 5x - 3) - 2)/(2(3x^2 + 5x - 3)))^2 + 3((-3(3x^2 + 5x - 3) - 2)/(2(3x^2 + 5x - 3))) + 3) - 1) - 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": "Find the number of local maximum points for f(x) = 3(-4(-2|(-2(-2x^2 + 2)^2 - 2(-2x^2 + 2) - 3) + 3| - 1) + 3)^2 + 3(-4(-2|(-2(-2x^2 + 2)^2 - 2(-2x^2 + 2) - 3) + 3| - 1) + 3) - 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 2sin(3\u03c0(-3|(-2(-2|(3x^2 + 4x + 3) - 3| - 1)^2 - 1(-2|(3x^2 + 4x + 3) - 3| - 1) - 4) + 2|)) - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "102", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 4(2cos(3\u03c0(-4(-3|(-1|x + 1| + 2) + 1| + 3)^2 - 2) + 2) - 3)^2 - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "432", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = 1sin(1\u03c0((-1(2|(4((-1x)/(1x - 3)) - 3)| - 1))/(3(2|(4((-1x)/(1x - 3)) - 3)| - 1) - 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": "Determine the count of local minima for the function f(x) = -3(1sin(3\u03c0(5((3(2|x| - 3) + 2)/(3(2|x| - 3) - 1))^2 - 4) - 1) - 1)^2 + 5(1sin(3\u03c0(5((3(2|x| - 3) + 2)/(3(2|x| - 3) - 1))^2 - 4) - 1) - 1) - 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "50", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = 2((-3(3sin(3\u03c0(4(-3|x + 1| + 1)^2 + 2) - 2) + 1) - 3)/(-1(3sin(3\u03c0(4(-3|x + 1| + 1)^2 + 2) - 2) + 1)))^2 + 3((-3(3sin(3\u03c0(4(-3|x + 1| + 1)^2 + 2) - 2) + 1) - 3)/(-1(3sin(3\u03c0(4(-3|x + 1| + 1)^2 + 2) - 2) + 1))) + 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "211", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 1(1sin(1\u03c0(3(-1|(5x + 3) + 2| + 3) + 5) + 3) - 2) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "301", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -4(4(-3(-2cos(3\u03c0(1x^2 - 4x - 1) + 1) - 1)^2 + 5(-2cos(3\u03c0(1x^2 - 4x - 1) + 1) - 1) - 1) + 3)^2 + 3(4(-3(-2cos(3\u03c0(1x^2 - 4x - 1) + 1) - 1)^2 + 5(-2cos(3\u03c0(1x^2 - 4x - 1) + 1) - 1) - 1) + 3) + 5 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "315", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = (1(2|(4(-3sin(1\u03c0(3|x - 3| - 3) + 2) + 3) - 1) + 2| + 3))/(1(2|(4(-3sin(1\u03c0(3|x - 3| - 3) + 2) + 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": "61", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = 1sin(3\u03c0(1|((1(2(3|x| + 1) - 3) + 1)/(-2(2(3|x| + 1) - 3) - 1)) + 1| - 2) - 1) + 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 3sin(2\u03c0((2((-2(-2|((-3x - 3)/(1x + 2)) - 2| + 3) - 3)/(1(-2|((-3x - 3)/(1x + 2)) - 2| + 3) - 2)))/(2((-2(-2|((-3x - 3)/(1x + 2)) - 2| + 3) - 3)/(1(-2|((-3x - 3)/(1x + 2)) - 2| + 3) - 2)) - 1)) - 1) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = (-3(5(-3(-2(-2cos(3\u03c0x) - 1)^2 - 4(-2cos(3\u03c0x) - 1)) + 2)^2 - 1(-3(-2(-2cos(3\u03c0x) - 1)^2 - 4(-2cos(3\u03c0x) - 1)) + 2) - 3) + 2)/(-1(5(-3(-2(-2cos(3\u03c0x) - 1)^2 - 4(-2cos(3\u03c0x) - 1)) + 2)^2 - 1(-3(-2(-2cos(3\u03c0x) - 1)^2 - 4(-2cos(3\u03c0x) - 1)) + 2) - 3) + 3) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "161", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = (-1(-2|(-5((-2(-3sin(2\u03c0x + 2) - 3) - 2)/(1(-3sin(2\u03c0x + 2) - 3) - 2))^2 - 1((-2(-3sin(2\u03c0x + 2) - 3) - 2)/(1(-3sin(2\u03c0x + 2) - 3) - 2)) + 1)| + 3) - 1)/(-1(-2|(-5((-2(-3sin(2\u03c0x + 2) - 3) - 2)/(1(-3sin(2\u03c0x + 2) - 3) - 2))^2 - 1((-2(-3sin(2\u03c0x + 2) - 3) - 2)/(1(-3sin(2\u03c0x + 2) - 3) - 2)) + 1)| + 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 total number of local minima and maxima for f(x) = (-1((2(1cos(3\u03c0(1(2x^2 - 1x - 3) + 5) + 3) - 1) - 3)/(2(1cos(3\u03c0(1(2x^2 - 1x - 3) + 5) + 3) - 1) - 1)) + 1)/(-2((2(1cos(3\u03c0(1(2x^2 - 1x - 3) + 5) + 3) - 1) - 3)/(2(1cos(3\u03c0(1(2x^2 - 1x - 3) + 5) + 3) - 1) - 1)) - 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "451", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 3(3|(-2(3|(3cos(3\u03c0x + 3) + 2) + 2| + 3)^2 + 5(3|(3cos(3\u03c0x + 3) + 2) + 2| + 3) + 4) - 3| - 3)^2 + 2(3|(-2(3|(3cos(3\u03c0x + 3) + 2) + 2| + 3)^2 + 5(3|(3cos(3\u03c0x + 3) + 2) + 2| + 3) + 4) - 3| - 3) + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "26", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -3e^(2(-2((3(-3(1|x - 1| - 2)) + 1)/(-2(-3(1|x - 1| - 2)) + 3))^2 + 4((3(-3(1|x - 1| - 2)) + 1)/(-2(-3(1|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": "5", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = (-3(-4(-2sin(1\u03c0(-5(-2x - 4) + 5) - 2) - 3) + 4))/(1(-4(-2sin(1\u03c0(-5(-2x - 4) + 5) - 2) - 3) + 4) + 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": "Find the number of local minimum points for f(x) = (-2(2|(2(-2sin(3\u03c0(1x^2 - 5x - 2) - 3) + 2) - 2) - 1| + 2))/(-2(2|(2(-2sin(3\u03c0(1x^2 - 5x - 2) - 3) + 2) - 2) - 1| + 2) + 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "516", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = 2|(-1|(5(-2(-3sin(2\u03c0x - 2) + 1)^2 + 4(-3sin(2\u03c0x - 2) + 1) + 1) + 3)| + 3) + 2| + 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "179", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -1(-3(-3(-2|(1x^2 - 4x + 3) - 1| + 1)^2 + 5(-2|(1x^2 - 4x + 3) - 1| + 1) + 1)^2 - 3(-3(-2|(1x^2 - 4x + 3) - 1| + 1)^2 + 5(-2|(1x^2 - 4x + 3) - 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": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = -5(-4((1(2|(-2sin(2\u03c0x - 1) - 2) - 2|) + 1)/(-2(2|(-2sin(2\u03c0x - 1) - 2) - 2|)))^2 - 3((1(2|(-2sin(2\u03c0x - 1) - 2) - 2|) + 1)/(-2(2|(-2sin(2\u03c0x - 1) - 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|(2cos(2\u03c0(1|((-2(2|x - 2| - 1) + 2)/(1(2|x - 2| - 1) - 3)) - 2| + 2) + 3) - 1)| - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "107", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 5(-4((-1((2(-3|x| + 2))/(-1(-3|x| + 2) - 3)) - 3)/(3((2(-3|x| + 2))/(-1(-3|x| + 2) - 3)) + 2))^2 - 5((-1((2(-3|x| + 2))/(-1(-3|x| + 2) - 3)) - 3)/(3((2(-3|x| + 2))/(-1(-3|x| + 2) - 3)) + 2)))^2 - 4(-4((-1((2(-3|x| + 2))/(-1(-3|x| + 2) - 3)) - 3)/(3((2(-3|x| + 2))/(-1(-3|x| + 2) - 3)) + 2))^2 - 5((-1((2(-3|x| + 2))/(-1(-3|x| + 2) - 3)) - 3)/(3((2(-3|x| + 2))/(-1(-3|x| + 2) - 3)) + 2))) + 5 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = (-2(-3(1|(-2|(-1sin(3\u03c0x))| + 2) - 2| + 2) + 3))/(-1(-3(1|(-2|(-1sin(3\u03c0x))| + 2) - 2| + 2) + 3) - 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "119", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -1(-3sin(2\u03c0((3((3(1|x + 1| - 2))/(1(1|x + 1| - 2) + 2)) + 3)/(-2((3(1|x + 1| - 2))/(1(1|x + 1| - 2) + 2)) + 1)) + 3) + 1)^2 + 2(-3sin(2\u03c0((3((3(1|x + 1| - 2))/(1(1|x + 1| - 2) + 2)) + 3)/(-2((3(1|x + 1| - 2))/(1(1|x + 1| - 2) + 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": "114", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = (3(-2(3e^(-2(-4(-1x) + 2)) + 3) - 2) + 2)/(1(-2(3e^(-2(-4(-1x) + 2)) + 3) - 2) + 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": "Find the number of local maximum points for f(x) = -1cos(3\u03c0(5(3|(-2|((2x + 3)/(-2x - 2)) - 2| - 1) + 2| + 3) + 1) + 2) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "68", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 3|((2(-1(1(-2cos(2\u03c0x - 3) + 2) - 4)^2 - 5(1(-2cos(2\u03c0x - 3) + 2) - 4) + 1) - 1)/(2(-1(1(-2cos(2\u03c0x - 3) + 2) - 4)^2 - 5(1(-2cos(2\u03c0x - 3) + 2) - 4) + 1) + 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 minima does the function f(x) = (2(-4(-3sin(3\u03c0(5(4x^2 - 2x + 3)^2 + 2(4x^2 - 2x + 3) - 5) - 1) + 3) + 1) - 2)/(-2(-4(-3sin(3\u03c0(5(4x^2 - 2x + 3)^2 + 2(4x^2 - 2x + 3) - 5) - 1) + 3) + 1) - 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = (-2((-2(-5(-2sin(1\u03c0(-1|x - 2| + 2) + 1) + 1)^2 + 4(-2sin(1\u03c0(-1|x - 2| + 2) + 1) + 1) + 5))/(-1(-5(-2sin(1\u03c0(-1|x - 2| + 2) + 1) + 1)^2 + 4(-2sin(1\u03c0(-1|x - 2| + 2) + 1) + 1) + 5) + 2)) + 2)/(2((-2(-5(-2sin(1\u03c0(-1|x - 2| + 2) + 1) + 1)^2 + 4(-2sin(1\u03c0(-1|x - 2| + 2) + 1) + 1) + 5))/(-1(-5(-2sin(1\u03c0(-1|x - 2| + 2) + 1) + 1)^2 + 4(-2sin(1\u03c0(-1|x - 2| + 2) + 1) + 1) + 5) + 2)) - 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) = -3|(5(1cos(3\u03c0(-4(-4x + 1) + 2) - 3) - 1)^2 + 5(1cos(3\u03c0(-4(-4x + 1) + 2) - 3) - 1) - 3) + 3| + 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "648", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -5(-2(1cos(3\u03c0((-2(4x^2 - 3x) - 1)/(3(4x^2 - 3x) - 2)) + 2) - 3) + 3) - 5 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": "Determine the count of local minima for the function f(x) = -2|((-1(-1(-2(-3sin(3\u03c0x - 1) + 3) + 2) + 2) + 3)/(-3(-1(-2(-3sin(3\u03c0x - 1) + 3) + 2) + 2) - 3)) - 3| + 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = (-2(2(3sin(1\u03c0(5(1x^2 + 3x - 5)^2 - 1(1x^2 + 3x - 5) - 1) - 3))^2 + 3(3sin(1\u03c0(5(1x^2 + 3x - 5)^2 - 1(1x^2 + 3x - 5) - 1) - 3)) + 3) - 3)/(-2(2(3sin(1\u03c0(5(1x^2 + 3x - 5)^2 - 1(1x^2 + 3x - 5) - 1) - 3))^2 + 3(3sin(1\u03c0(5(1x^2 + 3x - 5)^2 - 1(1x^2 + 3x - 5) - 1) - 3)) + 3) + 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "294", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -4(2(-3sin(1\u03c0(4(-1x + 4)^2 - 1(-1x + 4) - 4) - 2) + 2) - 3)^2 - 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "439", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = (-3(-1(-2(-3(-2sin(2\u03c0x + 2)))^2 - 3(-3(-2sin(2\u03c0x + 2))) - 1)^2 + 2(-2(-3(-2sin(2\u03c0x + 2)))^2 - 3(-3(-2sin(2\u03c0x + 2))) - 1) - 3) + 1)/(1(-1(-2(-3(-2sin(2\u03c0x + 2)))^2 - 3(-3(-2sin(2\u03c0x + 2))) - 1)^2 + 2(-2(-3(-2sin(2\u03c0x + 2)))^2 - 3(-3(-2sin(2\u03c0x + 2))) - 1) - 3) + 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 maxima for the function f(x) = -5(2|((1(-1sin(1\u03c0(-2x^2 + 4x + 1) - 2) - 2) - 1)/(3(-1sin(1\u03c0(-2x^2 + 4x + 1) - 2) - 2) + 2)) + 1| + 1) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "299", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 5(4(-2cos(3\u03c0(5(1x^2 + 5x + 2)) + 1) + 2)^2 - 2) + 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "485", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 2sin(1\u03c0(-2|(2|(3(1x + 3) - 1) + 1| - 1) + 3| - 3) - 3) - 1 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": "Find the number of local maximum points for f(x) = -4((2(3cos(1\u03c0(-1((-3x - 2)/(-2x + 3))^2 - 4((-3x - 2)/(-2x + 3)) + 2) - 1) + 3))/(2(3cos(1\u03c0(-1((-3x - 2)/(-2x + 3))^2 - 4((-3x - 2)/(-2x + 3)) + 2) - 1) + 3) - 1)) + 5 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) = -4((3(-1cos(3\u03c0((2(-5x - 1) - 1)/(-2(-5x - 1) + 3)) - 3) - 2) + 2)/(2(-1cos(3\u03c0((2(-5x - 1) - 1)/(-2(-5x - 1) + 3)) - 3) - 2) - 3))^2 + 5((3(-1cos(3\u03c0((2(-5x - 1) - 1)/(-2(-5x - 1) + 3)) - 3) - 2) + 2)/(2(-1cos(3\u03c0((2(-5x - 1) - 1)/(-2(-5x - 1) + 3)) - 3) - 2) - 3)) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 1|(2|(2sin(2\u03c0(-3|(3|x + 2| - 2)| - 3) - 2) + 3) + 2| + 3) + 1| - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "180", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 4((-2(1|(-5(3cos(2\u03c0x + 1)) + 4) - 1| + 3))/(-2(1|(-5(3cos(2\u03c0x + 1)) + 4) - 1| + 3) - 2)) + 4 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 maximum points for f(x) = -2(1|(-3(5(1sin(1\u03c0x + 3) + 3)^2 - 5(1sin(1\u03c0x + 3) + 3) + 2)^2 + 5(5(1sin(1\u03c0x + 3) + 3)^2 - 5(1sin(1\u03c0x + 3) + 3) + 2) - 3) - 3| - 3) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -2(-5(2(2sin(2\u03c0(-2|x - 1|))) + 1)^2 - 5(2(2sin(2\u03c0(-2|x - 1|))) + 1) + 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "161", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -1sin(2\u03c0(-4(4(1(-1x^2 - 3x - 4) + 3)^2 - 1(1(-1x^2 - 3x - 4) + 3) - 3) - 5)) + 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "124", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 5(3sin(2\u03c0(4(2|(2|x - 3| + 1)| - 2) + 1) + 1) - 3)^2 - 3(3sin(2\u03c0(4(2|(2|x - 3| + 1)| - 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": "357", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = (-3(-4(2|(-4(-3sin(2\u03c0x) - 1) + 2) - 2| - 3)^2 + 1(2|(-4(-3sin(2\u03c0x) - 1) + 2) - 2| - 3) + 1) + 1)/(1(-4(2|(-4(-3sin(2\u03c0x) - 1) + 2) - 2| - 3)^2 + 1(2|(-4(-3sin(2\u03c0x) - 1) + 2) - 2| - 3) + 1) - 3) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "160", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = 1|(-5(1sin(3\u03c0(1(-3|x - 2| - 1) - 4) + 2) - 1)^2 + 3(1sin(3\u03c0(1(-3|x - 2| - 1) - 4) + 2) - 1)) - 3| + 1 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 minima does the function f(x) = -2(2|(2|(3cos(3\u03c0(-4x - 3) + 1) - 3) + 3| - 2) - 2| + 3) + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "913", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -1((2(-3|(-3|(-2sin(3\u03c0x + 2) - 2) + 1| + 1) + 2| - 1) - 1)/(1(-3|(-3|(-2sin(3\u03c0x + 2) - 2) + 1| + 1) + 2| - 1) + 2)) + 4 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) = (1(5(1cos(3\u03c0(-2|(5x^2 + 1x - 5) + 3| - 2) - 2) - 2)^2 + 3(1cos(3\u03c0(-2|(5x^2 + 1x - 5) + 3| - 2) - 2) - 2) - 5) - 2)/(-3(5(1cos(3\u03c0(-2|(5x^2 + 1x - 5) + 3| - 2) - 2) - 2)^2 + 3(1cos(3\u03c0(-2|(5x^2 + 1x - 5) + 3| - 2) - 2) - 2) - 5) - 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "319", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -1((-3(2(-3sin(1\u03c0(-3x^2 + 1x + 5) + 3) - 2)^2 + 4(-3sin(1\u03c0(-3x^2 + 1x + 5) + 3) - 2) + 1) - 3)/(-1(2(-3sin(1\u03c0(-3x^2 + 1x + 5) + 3) - 2)^2 + 4(-3sin(1\u03c0(-3x^2 + 1x + 5) + 3) - 2) + 1) - 2)) + 4 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "471", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = (-3(1e^(-1(2|(-1((2x - 3)/(-2x - 3))^2 + 1((2x - 3)/(-2x - 3)))|)) + 1) + 2)/(2(1e^(-1(2|(-1((2x - 3)/(-2x - 3))^2 + 1((2x - 3)/(-2x - 3)))|)) + 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) = 1(3((2(-1cos(1\u03c0((2x + 3)/(-1x - 2))) + 2) + 3)/(-1(-1cos(1\u03c0((2x + 3)/(-1x - 2))) + 2) - 3))^2 - 3((2(-1cos(1\u03c0((2x + 3)/(-1x - 2))) + 2) + 3)/(-1(-1cos(1\u03c0((2x + 3)/(-1x - 2))) + 2) - 3)) + 2)^2 - 2(3((2(-1cos(1\u03c0((2x + 3)/(-1x - 2))) + 2) + 3)/(-1(-1cos(1\u03c0((2x + 3)/(-1x - 2))) + 2) - 3))^2 - 3((2(-1cos(1\u03c0((2x + 3)/(-1x - 2))) + 2) + 3)/(-1(-1cos(1\u03c0((2x + 3)/(-1x - 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": "9", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = (2((3((3(-2cos(1\u03c0(-1x - 2) + 3) - 2) + 1)/(-1(-2cos(1\u03c0(-1x - 2) + 3) - 2) - 2)) - 3)/(-3((3(-2cos(1\u03c0(-1x - 2) + 3) - 2) + 1)/(-1(-2cos(1\u03c0(-1x - 2) + 3) - 2) - 2)) - 3)) + 2)/(-2((3((3(-2cos(1\u03c0(-1x - 2) + 3) - 2) + 1)/(-1(-2cos(1\u03c0(-1x - 2) + 3) - 2) - 2)) - 3)/(-3((3(-2cos(1\u03c0(-1x - 2) + 3) - 2) + 1)/(-1(-2cos(1\u03c0(-1x - 2) + 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 total count of local extrema points for the function f(x) = 1(-3|((-1(3|(2x - 3) - 1| - 1) + 3)/(1(3|(2x - 3) - 1| - 1) - 2)) - 1| + 3)^2 + 2(-3|((-1(3|(2x - 3) - 1| - 1) + 3)/(1(3|(2x - 3) - 1| - 1) - 2)) - 1| + 3) + 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": "Determine the total count of local extrema points for the function f(x) = 1|(-4(-2(-1(2|x - 1|)^2 - 5(2|x - 1|) + 5)^2 + 1(-1(2|x - 1|)^2 - 5(2|x - 1|) + 5) + 4)^2) - 3| - 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = 4(-1(1(-2|(-1x^2 + 2x + 1)| + 2) + 1)^2 + 2(1(-2|(-1x^2 + 2x + 1)| + 2) + 1) - 3) - 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = 3(-2|(-2|(-3(3sin(2\u03c0x - 2) - 2)^2 + 2(3sin(2\u03c0x - 2) - 2) - 5)|) - 3| + 2)^2 + 3(-2|(-2|(-3(3sin(2\u03c0x - 2) - 2)^2 + 2(3sin(2\u03c0x - 2) - 2) - 5)|) - 3| + 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -3(2sin(2\u03c0(-2(5(4x^2 - 3x - 4)^2 + 1(4x^2 - 3x - 4) - 1) - 2)) + 2) - 3 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": "Determine the count of local minima for the function f(x) = 3((2(-2|(-1|(3sin(3\u03c0x - 1) + 1) - 2| + 1) - 1| + 1) + 1)/(2(-2|(-1|(3sin(3\u03c0x - 1) + 1) - 2| + 1) - 1| + 1) + 2))^2 - 1((2(-2|(-1|(3sin(3\u03c0x - 1) + 1) - 2| + 1) - 1| + 1) + 1)/(2(-2|(-1|(3sin(3\u03c0x - 1) + 1) - 2| + 1) - 1| + 1) + 2)) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "189", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -3|(2(-3(-3|(-1sin(1\u03c0x - 1) - 3) - 1| + 3)^2 - 1) + 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": "How many local maxima does the function f(x) = (-1(2|(-1cos(1\u03c0(3(-2x + 1) + 1) + 2) + 2)| + 3) - 1)/(-3(2|(-1cos(1\u03c0(3(-2x + 1) + 1) + 2) + 2)| + 3)) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 1sin(2\u03c0(-2(-5(-2((2x)/(2x - 3))^2 - 4((2x)/(2x - 3)) - 3) + 2)) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "142", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = (2(3|(1((-1(1x^2 - 4x + 3) - 2)/(3(1x^2 - 4x + 3) - 1))^2 - 5((-1(1x^2 - 4x + 3) - 2)/(3(1x^2 - 4x + 3) - 1)) - 4) - 2| - 2) - 2)/(2(3|(1((-1(1x^2 - 4x + 3) - 2)/(3(1x^2 - 4x + 3) - 1))^2 - 5((-1(1x^2 - 4x + 3) - 2)/(3(1x^2 - 4x + 3) - 1)) - 4) - 2| - 2) - 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -4((3(-5(-3sin(2\u03c0((-2x + 3)/(-1x + 2)) + 3) - 2)^2 - 5(-3sin(2\u03c0((-2x + 3)/(-1x + 2)) + 3) - 2) + 4) + 2)/(-1(-5(-3sin(2\u03c0((-2x + 3)/(-1x + 2)) + 3) - 2)^2 - 5(-3sin(2\u03c0((-2x + 3)/(-1x + 2)) + 3) - 2) + 4) - 1)) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 1(-2|(3(2e^(-1(-5x)) + 2) - 4)| - 2) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 3(-2(-1(2e^(1(-1x^2 - 5x + 2)) + 1)^2 + 3(2e^(1(-1x^2 - 5x + 2)) + 1) + 2)^2 + 4(-1(2e^(1(-1x^2 - 5x + 2)) + 1)^2 + 3(2e^(1(-1x^2 - 5x + 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": "7", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 1|(3sin(2\u03c0(-3|((3(1x^2 - 5) + 1)/(-1(1x^2 - 5) + 2)) - 2| - 3) - 3) - 2) + 3| - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "133", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -2|(-1((1(-1(2cos(1\u03c0x + 2) - 3)^2 + 4(2cos(1\u03c0x + 2) - 3) - 5) - 2)/(-1(-1(2cos(1\u03c0x + 2) - 3)^2 + 4(2cos(1\u03c0x + 2) - 3) - 5) - 3)) - 2) - 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 count of local minima for the function f(x) = -4(-1|(1|(-3(2x^2 - 3)^2 - 1(2x^2 - 3)) + 2| - 2) - 3| - 1) + 4 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) = -1e^(1(-5((3(-1|(-2|x - 1| + 2) + 3| + 2) + 1)/(-2(-1|(-2|x - 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": "7", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 4(2e^(1(-3(1|(-1x) - 2| - 2)^2 - 5(1|(-1x) - 2| - 2) + 5))) + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 2(1(1cos(1\u03c0(-5(-1x^2 + 2x + 4) + 3)) + 1)^2 - 3(1cos(1\u03c0(-5(-1x^2 + 2x + 4) + 3)) + 1) - 3) + 3 where -10 \u2264 x \u2264 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) = -2|(-4(5(3|(1cos(1\u03c0x) - 3) + 2| - 2)^2 - 3)^2 - 4(5(3|(1cos(1\u03c0x) - 3) + 2| - 2)^2 - 3) - 5) - 1| - 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 count of local maxima for the function f(x) = 5(2cos(1\u03c0(-5(-2(-5x - 1)^2 + 4(-5x - 1) - 1) + 2) - 3)) - 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "163", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -1|(-1|(3|((-3(-2sin(3\u03c0x - 1) + 3) + 2)/(-1(-2sin(3\u03c0x - 1) + 3))) + 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": "60", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = (2(-1|((1(-2cos(2\u03c0(5x + 4) - 3) + 1) + 2)/(-3(-2cos(2\u03c0(5x + 4) - 3) + 1) - 2)) - 3| - 2) - 3)/(3(-1|((1(-2cos(2\u03c0(5x + 4) - 3) + 1) + 2)/(-3(-2cos(2\u03c0(5x + 4) - 3) + 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": "56", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = 1(1sin(2\u03c0(-3((-2(-2|x - 2| + 2) + 3)/(-2(-2|x - 2| + 2) - 3))^2 + 2((-2(-2|x - 2| + 2) + 3)/(-2(-2|x - 2| + 2) - 3)) + 4) - 2)) - 5 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "75", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = (2(1((-3(-3cos(2\u03c0(1x + 3)) - 2) + 2)/(3(-3cos(2\u03c0(1x + 3)) - 2) - 1))^2 + 3((-3(-3cos(2\u03c0(1x + 3)) - 2) + 2)/(3(-3cos(2\u03c0(1x + 3)) - 2) - 1)) - 2) - 2)/(1(1((-3(-3cos(2\u03c0(1x + 3)) - 2) + 2)/(3(-3cos(2\u03c0(1x + 3)) - 2) - 1))^2 + 3((-3(-3cos(2\u03c0(1x + 3)) - 2) + 2)/(3(-3cos(2\u03c0(1x + 3)) - 2) - 1)) - 2) - 3) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "119", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -3((2(1|(-1(-1cos(3\u03c0x + 1) + 1) + 4)| + 1) + 2)/(2(1|(-1(-1cos(3\u03c0x + 1) + 1) + 4)| + 1) + 3))^2 + 4((2(1|(-1(-1cos(3\u03c0x + 1) + 1) + 4)| + 1) + 2)/(2(1|(-1(-1cos(3\u03c0x + 1) + 1) + 4)| + 1) + 3)) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -2sin(1\u03c0(3(-5(4((2x + 3)/(-2x + 3))^2 + 1((2x + 3)/(-2x + 3)) + 1)^2) + 5) + 2) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "139", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -4(1(-3(-1sin(2\u03c0((-2x - 1)/(3x - 2)) + 2) + 1)^2 + 4(-1sin(2\u03c0((-2x - 1)/(3x - 2)) + 2) + 1) + 4)^2 - 3(-3(-1sin(2\u03c0((-2x - 1)/(3x - 2)) + 2) + 1)^2 + 4(-1sin(2\u03c0((-2x - 1)/(3x - 2)) + 2) + 1) + 4) + 4) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "23", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -4(-1cos(1\u03c0(-1|(-1|(-1|x| + 3) + 2| + 1) + 2| - 3) + 3) - 2)^2 + 2(-1cos(1\u03c0(-1|(-1|(-1|x| + 3) + 2| + 1) + 2| - 3) + 3) - 2) + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "27", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 2(-3(3(3|(3sin(2\u03c0x - 2) + 3) + 3| + 3) + 5)^2 - 2(3(3|(3sin(2\u03c0x - 2) + 3) + 3| + 3) + 5) - 5)^2 + 1(-3(3(3|(3sin(2\u03c0x - 2) + 3) + 3| + 3) + 5)^2 - 2(3(3|(3sin(2\u03c0x - 2) + 3) + 3| + 3) + 5) - 5) + 3 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 number of local minimum points for f(x) = (-2(-2|((1(5(-5x^2 - 4x + 3)^2 - 1(-5x^2 - 4x + 3) - 5) + 3)/(-1(5(-5x^2 - 4x + 3)^2 - 1(-5x^2 - 4x + 3) - 5) + 2)) + 1| - 2) - 1)/(-1(-2|((1(5(-5x^2 - 4x + 3)^2 - 1(-5x^2 - 4x + 3) - 5) + 3)/(-1(5(-5x^2 - 4x + 3)^2 - 1(-5x^2 - 4x + 3) - 5) + 2)) + 1| - 2) + 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = (-1((-1(3(-3cos(1\u03c0((-3x + 1)/(1x + 1)) + 1) - 1)) - 2)/(2(3(-3cos(1\u03c0((-3x + 1)/(1x + 1)) + 1) - 1)) + 3)) + 1)/(-2((-1(3(-3cos(1\u03c0((-3x + 1)/(1x + 1)) + 1) - 1)) - 2)/(2(3(-3cos(1\u03c0((-3x + 1)/(1x + 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": "43", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = -1|(-3|(-4(1(-2sin(3\u03c0x + 2) - 1)^2 + 2(-2sin(3\u03c0x + 2) - 1) - 5) + 2) + 1|) + 1| + 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 2(-4(4((2(1cos(3\u03c0x - 2) - 2) + 2)/(-3(1cos(3\u03c0x - 2) - 2) + 2)) + 2)^2 + 4(4((2(1cos(3\u03c0x - 2) - 2) + 2)/(-3(1cos(3\u03c0x - 2) - 2) + 2)) + 2) + 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) = (-3((2(-1((-1(-2cos(1\u03c0x + 2) - 1) + 1)/(3(-2cos(1\u03c0x + 2) - 1) + 2)) + 1) - 1)/(-3(-1((-1(-2cos(1\u03c0x + 2) - 1) + 1)/(3(-2cos(1\u03c0x + 2) - 1) + 2)) + 1) + 1)) + 1)/(1((2(-1((-1(-2cos(1\u03c0x + 2) - 1) + 1)/(3(-2cos(1\u03c0x + 2) - 1) + 2)) + 1) - 1)/(-3(-1((-1(-2cos(1\u03c0x + 2) - 1) + 1)/(3(-2cos(1\u03c0x + 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": "How many local minima does the function f(x) = -1|(2cos(2\u03c0(2|(3|(-4x - 1) + 3| - 2) - 2| - 1))) - 2| - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "482", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -1(2|(-2|(-4((1x)/(2x - 1)) + 4) + 2| + 2) - 1| + 3)^2 + 2(2|(-2|(-4((1x)/(2x - 1)) + 4) + 2| + 2) - 1| + 3) + 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = (3(2sin(2\u03c0(1|(-5((1x - 3)/(-1x + 2))^2 + 2((1x - 3)/(-1x + 2)) + 2)| + 1)) - 1) - 1)/(-1(2sin(2\u03c0(1|(-5((1x - 3)/(-1x + 2))^2 + 2((1x - 3)/(-1x + 2)) + 2)| + 1)) - 1) - 2) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "78", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = (3((-2((2((-3(1|x + 2| + 1) + 2)/(-1(1|x + 2| + 1) + 3)) + 1)/(-3((-3(1|x + 2| + 1) + 2)/(-1(1|x + 2| + 1) + 3)) - 1)) - 2)/(1((2((-3(1|x + 2| + 1) + 2)/(-1(1|x + 2| + 1) + 3)) + 1)/(-3((-3(1|x + 2| + 1) + 2)/(-1(1|x + 2| + 1) + 3)) - 1)) - 3)) + 3)/(-1((-2((2((-3(1|x + 2| + 1) + 2)/(-1(1|x + 2| + 1) + 3)) + 1)/(-3((-3(1|x + 2| + 1) + 2)/(-1(1|x + 2| + 1) + 3)) - 1)) - 2)/(1((2((-3(1|x + 2| + 1) + 2)/(-1(1|x + 2| + 1) + 3)) + 1)/(-3((-3(1|x + 2| + 1) + 2)/(-1(1|x + 2| + 1) + 3)) - 1)) - 3)) - 1) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "290", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 2cos(2\u03c0(-2|(2(-2(2x^2 + 1x + 1) + 5) + 5) + 2| + 1) - 3) + 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) = (2(5(4(-3|(-1sin(2\u03c0x - 1) + 3) + 1| + 2)^2 + 1(-3|(-1sin(2\u03c0x - 1) + 3) + 1| + 2) + 2) - 2) + 2)/(1(5(4(-3|(-1sin(2\u03c0x - 1) + 3) + 1| + 2)^2 + 1(-3|(-1sin(2\u03c0x - 1) + 3) + 1| + 2) + 2) - 2) + 3) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = -1(-3((2(3sin(3\u03c0(2|x + 3| - 3) - 2)) + 3)/(2(3sin(3\u03c0(2|x + 3| - 3) - 2)) + 1))^2 - 4((2(3sin(3\u03c0(2|x + 3| - 3) - 2)) + 3)/(2(3sin(3\u03c0(2|x + 3| - 3) - 2)) + 1)) - 3) - 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": "How many local maxima does the function f(x) = 2(3cos(2\u03c0(-4(-5(1x + 1)^2 + 5(1x + 1) + 5)^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": "53", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 3sin(1\u03c0(2|(-2|(-5(2x + 4)^2 - 2(2x + 4) + 5) + 3| - 2) + 3| - 1)) + 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "447", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 1sin(3\u03c0(-4(5(-1|(-4x^2 - 2x + 1) - 3| + 3)^2 + 1(-1|(-4x^2 - 2x + 1) - 3| + 3)) + 5) - 2) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "99", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 3cos(3\u03c0(-2|(-1|(3(1x^2 - 3x) - 3) - 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": "484", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = (1(3(-2(-2e^(2(5x^2 - 1x)) - 2) - 4) - 4) - 1)/(3(3(-2(-2e^(2(5x^2 - 1x)) - 2) - 4) - 4) + 3) 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) = -1|(-5(-2cos(1\u03c0(5(-4x - 3)^2 + 2(-4x - 3) + 2) + 2) - 3) + 5) + 1| - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "211", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -2(-5(-3sin(2\u03c0(1(1x - 2) - 2) + 1))^2 + 1(-3sin(2\u03c0(1(1x - 2) - 2) + 1)) - 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 total count of local extrema points for the function f(x) = (2(1(-2|(-3sin(2\u03c0(4x^2 - 3x + 4) - 3) - 3)| + 1)^2 + 2(-2|(-3sin(2\u03c0(4x^2 - 3x + 4) - 3) - 3)| + 1) - 4) - 2)/(-3(1(-2|(-3sin(2\u03c0(4x^2 - 3x + 4) - 3) - 3)| + 1)^2 + 2(-2|(-3sin(2\u03c0(4x^2 - 3x + 4) - 3) - 3)| + 1) - 4) + 1) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "501", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = 5((2(-5(-1(2cos(3\u03c0x + 2) - 3)^2 - 2(2cos(3\u03c0x + 2) - 3) - 4)^2 - 2(-1(2cos(3\u03c0x + 2) - 3)^2 - 2(2cos(3\u03c0x + 2) - 3) - 4) + 3) - 1)/(1(-5(-1(2cos(3\u03c0x + 2) - 3)^2 - 2(2cos(3\u03c0x + 2) - 3) - 4)^2 - 2(-1(2cos(3\u03c0x + 2) - 3)^2 - 2(2cos(3\u03c0x + 2) - 3) - 4) + 3) + 2)) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = (-1(-3|(-2sin(1\u03c0(2((-3x - 1)/(1x - 2))^2 - 1((-3x - 1)/(1x - 2))) + 1) + 2) - 2| - 1) - 2)/(-1(-3|(-2sin(1\u03c0(2((-3x - 1)/(1x - 2))^2 - 1((-3x - 1)/(1x - 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": "208", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -1(3|(-5(1|(-3|x + 2| + 2) + 3| - 1)^2 + 1(1|(-3|x + 2| + 2) + 3| - 1) + 4) + 2|) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = (1(-1|(5(1e^(1(-5x - 4)) + 2)^2 - 4(1e^(1(-5x - 4)) + 2) + 3)| - 1) + 1)/(1(-1|(5(1e^(1(-5x - 4)) + 2)^2 - 4(1e^(1(-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": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = 1(-4(1|(3(-1|x| + 3)^2 - 4) - 3|) - 5) + 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 3|(-5(-4(-3sin(2\u03c0(-2x - 3) + 2) + 3) - 4) + 2)| - 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": "How many local minima does the function f(x) = 1(2cos(1\u03c0(-4(-1(-2x^2 + 3x + 2)^2 + 2(-2x^2 + 3x + 2) + 5)^2 - 3(-1(-2x^2 + 3x + 2)^2 + 2(-2x^2 + 3x + 2) + 5)) + 1) - 2) - 4 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 number of local maximum points for f(x) = 2(4((-3((-3((2x - 1)/(1x + 2)) - 3)/(-1((2x - 1)/(1x + 2)))))/(-1((-3((2x - 1)/(1x + 2)) - 3)/(-1((2x - 1)/(1x + 2))))))^2 - 1((-3((-3((2x - 1)/(1x + 2)) - 3)/(-1((2x - 1)/(1x + 2)))))/(-1((-3((2x - 1)/(1x + 2)) - 3)/(-1((2x - 1)/(1x + 2)))))) + 5) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "125", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = 2(-3sin(3\u03c0((1(-1(4x + 5) - 1) + 1)/(-3(-1(4x + 5) - 1) + 4)) + 3) + 1)^2 + 2(-3sin(3\u03c0((1(-1(4x + 5) - 1) + 1)/(-3(-1(4x + 5) - 1) + 4)) + 3) + 1) - 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 1(1|(-5(3|(4x^2 + 5x) + 1| - 1) - 5) + 3| - 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": "How many local minima does the function f(x) = 3(-1cos(1\u03c0((1(-3|((3x - 2)/(1x + 2)) - 2| + 3) - 3)/(1(-3|((3x - 2)/(1x + 2)) - 2| + 3))) + 1) + 3) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 3(-1|(-1|(-1(1x^2 + 5x + 3)^2 + 1(1x^2 + 5x + 3) + 1) - 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": "9", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = (1(5(-1|(-2(1e^(-2x) + 1)) + 2| - 2)^2 - 1(-1|(-2(1e^(-2x) + 1)) + 2| - 2) + 1) + 3)/(3(5(-1|(-2(1e^(-2x) + 1)) + 2| - 2)^2 - 1(-1|(-2(1e^(-2x) + 1)) + 2| - 2) + 1) - 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 4(1|(1sin(3\u03c0(-2(-1x^2 + 1x - 3) - 4) + 1) - 3) - 2| + 3)^2 + 3(1|(1sin(3\u03c0(-2(-1x^2 + 1x - 3) - 4) + 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": "235", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -3|(-2|(1sin(1\u03c0(-5(-2x^2 - 1x - 3)^2 + 1(-2x^2 - 1x - 3) + 4) - 3) - 1) - 1| - 3) - 2| + 1 where -10 \u2264 x \u2264 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 maxima for the function f(x) = 2cos(2\u03c0(-3(-1(5(-1x^2 - 1x + 5)^2 - 4(-1x^2 - 1x + 5) + 1))^2 - 5(-1(5(-1x^2 - 1x + 5)^2 - 4(-1x^2 - 1x + 5) + 1)) - 4) + 2) - 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 minima does the function f(x) = 1cos(2\u03c0(2|(-1|(5(-2|x - 3| - 3) - 1) - 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": "401", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 1cos(1\u03c0(-1(-1(5((2x - 1)/(2x + 3))^2 - 3((2x - 1)/(2x + 3)) - 4)^2 + 2(5((2x - 1)/(2x + 3))^2 - 3((2x - 1)/(2x + 3)) - 4) + 1) + 5) - 1) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "142", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -2|(1(4((3(1cos(3\u03c0x) - 3))/(3(1cos(3\u03c0x) - 3) - 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": "30", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = 4(1(2(-3sin(1\u03c0(-2|x + 3|) - 2) + 2) + 2) + 5) + 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 1(-2|(-3sin(2\u03c0(2((-2x - 3)/(-2x - 2))^2 + 2((-2x - 3)/(-2x - 2)) + 2) + 1) - 2) + 1| + 1)^2 - 5(-2|(-3sin(2\u03c0(2((-2x - 3)/(-2x - 2))^2 + 2((-2x - 3)/(-2x - 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": "59", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -3|(3(3sin(2\u03c0(1(3|x + 2|)^2 - 5(3|x + 2|) - 2) - 1) - 1) - 3) + 1| - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = 1((3((1(-2sin(3\u03c0(1x - 5) + 2) - 2) - 3)/(2(-2sin(3\u03c0(1x - 5) + 2) - 2) + 2)) + 2)/(1((1(-2sin(3\u03c0(1x - 5) + 2) - 2) - 3)/(2(-2sin(3\u03c0(1x - 5) + 2) - 2) + 2)))) + 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 3cos(3\u03c0(-1((-2(1|(1x - 3) - 1| - 1) - 3)/(1(1|(1x - 3) - 1| - 1) + 1))^2 + 3((-2(1|(1x - 3) - 1| - 1) - 3)/(1(1|(1x - 3) - 1| - 1) + 1))) - 2) - 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "96", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = (1(-4(-2((-3((3x)/(-3x - 3)))/(-2((3x)/(-3x - 3)))) + 2)^2 + 5))/(1(-4(-2((-3((3x)/(-3x - 3)))/(-2((3x)/(-3x - 3)))) + 2)^2 + 5) + 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "117", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = 2((-3(1sin(2\u03c0((3(-1|x + 2| - 2) + 2)/(-2(-1|x + 2| - 2) - 3)) - 3) + 3))/(1(1sin(2\u03c0((3(-1|x + 2| - 2) + 2)/(-2(-1|x + 2| - 2) - 3)) - 3) + 3) + 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 number of local minimum points for f(x) = (-2(3cos(3\u03c0(4(3|(-5x - 1) + 2| - 2)^2 + 2(3|(-5x - 1) + 2| - 2) - 4) + 1) - 1))/(3(3cos(3\u03c0(4(3|(-5x - 1) + 2| - 2)^2 + 2(3|(-5x - 1) + 2| - 2) - 4) + 1) - 1) - 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "113", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -3cos(1\u03c0(-2|(-1(3(-4x^2 - 4x - 4) - 3) - 3) + 1| + 3) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "238", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -5(5(-3cos(2\u03c0(3(-5x^2 + 2) + 1) - 3)) - 2) - 1 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 minima for the function f(x) = -3|(1((-2((3(-2sin(3\u03c0x + 1) - 2) - 2)/(-1(-2sin(3\u03c0x + 1) - 2) + 2)) + 3)/(-2((3(-2sin(3\u03c0x + 1) - 2) - 2)/(-1(-2sin(3\u03c0x + 1) - 2) + 2)) + 1))^2 + 3((-2((3(-2sin(3\u03c0x + 1) - 2) - 2)/(-1(-2sin(3\u03c0x + 1) - 2) + 2)) + 3)/(-2((3(-2sin(3\u03c0x + 1) - 2) - 2)/(-1(-2sin(3\u03c0x + 1) - 2) + 2)) + 1)) + 2) + 3| + 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 total count of local extrema points for the function f(x) = -1cos(3\u03c0(1(-2(1|(3|x + 2| + 2) + 1|)^2 + 4(1|(3|x + 2| + 2) + 1|) + 3) + 5)) - 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "475", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -1(2|(-1cos(1\u03c0(1|(-2x - 2) + 3| - 1) - 2) + 3)| - 3) + 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -3sin(3\u03c0(1((-3(-5(-4x - 3) + 2) - 1)/(1(-5(-4x - 3) + 2) + 2)) - 4) - 3) + 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": "Determine the count of local maxima for the function f(x) = 1|(1(2|(5(-2|x - 3| + 1)^2 + 4(-2|x - 3| + 1) - 5)| + 3) + 4) + 3| - 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = 3(1|(3|(1cos(3\u03c0(-3|x + 3| - 3) - 3) + 1) - 3| - 2) + 2| + 2)^2 - 1(1|(3|(1cos(3\u03c0(-3|x + 3| - 3) - 3) + 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": "90", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -3|(-5(-2(3|((2x + 3)/(3x - 1)) - 2|)^2 + 1(3|((2x + 3)/(3x - 1)) - 2|) - 3)^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": "How many local minima does the function f(x) = -2|(-2(-3((-1(-3cos(1\u03c0x - 2) - 2) - 2)/(-2(-3cos(1\u03c0x - 2) - 2) - 1))^2 + 3) - 3) + 3| - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "49", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -1(-2(4(-2|(-1sin(3\u03c0x) + 2) + 3| + 3) + 4) + 3)^2 - 3(-2(4(-2|(-1sin(3\u03c0x) + 2) + 3| + 3) + 4) + 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 minima does the function f(x) = 3sin(2\u03c0(1(2|(3((-2x + 1)/(-3x))^2 + 4((-2x + 1)/(-3x)))|)) - 1) - 1 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 total number of local minima and maxima for f(x) = -5((-3(3|(1cos(3\u03c0(-1x^2 - 1x + 3) + 2) - 3) + 1| - 2) - 3)/(-3(3|(1cos(3\u03c0(-1x^2 - 1x + 3) + 2) - 3) + 1| - 2) - 1)) + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "566", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = -3(2|(-3cos(1\u03c0(-2|(2|x - 1| - 3) + 1| + 1) - 1) + 3) + 2| - 3)^2 + 3(2|(-3cos(1\u03c0(-2|(2|x - 1| - 3) + 1| + 1) - 1) + 3) + 2| - 3) + 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -2|(5(1cos(1\u03c0((-1(1x + 5) + 1)/(1(1x + 5))) + 1) + 2)^2 + 2(1cos(1\u03c0((-1(1x + 5) + 1)/(1(1x + 5))) + 1) + 2) - 1) + 3| - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 1(5(-3(-2cos(1\u03c0((1x)/(-2x - 2)) - 1) - 1)^2 - 5(-2cos(1\u03c0((1x)/(-2x - 2)) - 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": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 4(-3|(-2cos(2\u03c0(2(-3|x + 2| - 1)^2 - 1(-3|x + 2| - 1) - 2) - 2) + 2) + 2| + 2) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "238", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = (-3(-1cos(1\u03c0(3|(-5(5x - 1) - 2) - 2| - 1) - 2) + 1) + 2)/(-2(-1cos(1\u03c0(3|(-5(5x - 1) - 2) - 2| - 1) - 2) + 1) + 3) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "250", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -1|(2(-2cos(2\u03c0(-3(-2x + 1) + 4) - 1) + 1)^2 + 5(-2cos(2\u03c0(-3(-2x + 1) + 4) - 1) + 1) - 2) - 3| + 3 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": "Determine the count of local maxima for the function f(x) = (-3(-2(-1(2(-1cos(2\u03c0x + 1) + 1) - 4) + 2)^2 - 3(-1(2(-1cos(2\u03c0x + 1) + 1) - 4) + 2) - 2) - 3)/(3(-2(-1(2(-1cos(2\u03c0x + 1) + 1) - 4) + 2)^2 - 3(-1(2(-1cos(2\u03c0x + 1) + 1) - 4) + 2) - 2) + 1) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 5(5(2(1(-5x^2 + 5x + 1)^2 - 2(-5x^2 + 5x + 1) - 2)^2 - 5(1(-5x^2 + 5x + 1)^2 - 2(-5x^2 + 5x + 1) - 2))^2 + 5(2(1(-5x^2 + 5x + 1)^2 - 2(-5x^2 + 5x + 1) - 2)^2 - 5(1(-5x^2 + 5x + 1)^2 - 2(-5x^2 + 5x + 1) - 2)) - 5) + 5 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(-2sin(1\u03c0(4(1(-2x - 1)^2 + 2(-2x - 1) + 5)^2 - 4(1(-2x - 1)^2 + 2(-2x - 1) + 5) + 5) - 1) - 3) - 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "77", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = (3(-2sin(1\u03c0(5(-4(-3x + 2) + 2) + 3) - 2) - 2) + 2)/(2(-2sin(1\u03c0(5(-4(-3x + 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": "797", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -2((3(5(-2sin(3\u03c0(2|x + 1| + 2) - 2) + 1)^2 + 2(-2sin(3\u03c0(2|x + 1| + 2) - 2) + 1) - 4) + 2)/(-1(5(-2sin(3\u03c0(2|x + 1| + 2) - 2) + 1)^2 + 2(-2sin(3\u03c0(2|x + 1| + 2) - 2) + 1) - 4) + 3))^2 + 4((3(5(-2sin(3\u03c0(2|x + 1| + 2) - 2) + 1)^2 + 2(-2sin(3\u03c0(2|x + 1| + 2) - 2) + 1) - 4) + 2)/(-1(5(-2sin(3\u03c0(2|x + 1| + 2) - 2) + 1)^2 + 2(-2sin(3\u03c0(2|x + 1| + 2) - 2) + 1) - 4) + 3)) + 4 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "329", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 2|(1((-3(-1e^(1(-5x - 4)) - 2) - 3)/(1(-1e^(1(-5x - 4)) - 2) + 2)) - 3) - 2| 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": "How many local maxima does the function f(x) = 5(-4((1(2sin(2\u03c0((2x + 2)/(-2x + 3)) + 2) + 2) - 3)/(-3(2sin(2\u03c0((2x + 2)/(-2x + 3)) + 2) + 2) - 3))^2 - 4((1(2sin(2\u03c0((2x + 2)/(-2x + 3)) + 2) + 2) - 3)/(-3(2sin(2\u03c0((2x + 2)/(-2x + 3)) + 2) + 2) - 3)) + 2) + 5 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": "Find the number of local minimum points for f(x) = (1((3(-2|(-3|((2x - 3)/(2x + 3)) + 2| - 3) + 2| - 1) + 3)/(-2(-2|(-3|((2x - 3)/(2x + 3)) + 2| - 3) + 2| - 1) - 2)) + 1)/(-2((3(-2|(-3|((2x - 3)/(2x + 3)) + 2| - 3) + 2| - 1) + 3)/(-2(-2|(-3|((2x - 3)/(2x + 3)) + 2| - 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": "55", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = 1(-5(-1(4(-3sin(3\u03c0x - 1) + 2)^2 - 1(-3sin(3\u03c0x - 1) + 2) + 3)^2 + 4(4(-3sin(3\u03c0x - 1) + 2)^2 - 1(-3sin(3\u03c0x - 1) + 2) + 3) - 4)^2 - 3(-1(4(-3sin(3\u03c0x - 1) + 2)^2 - 1(-3sin(3\u03c0x - 1) + 2) + 3)^2 + 4(4(-3sin(3\u03c0x - 1) + 2)^2 - 1(-3sin(3\u03c0x - 1) + 2) + 3) - 4))^2 - 3(-5(-1(4(-3sin(3\u03c0x - 1) + 2)^2 - 1(-3sin(3\u03c0x - 1) + 2) + 3)^2 + 4(4(-3sin(3\u03c0x - 1) + 2)^2 - 1(-3sin(3\u03c0x - 1) + 2) + 3) - 4)^2 - 3(-1(4(-3sin(3\u03c0x - 1) + 2)^2 - 1(-3sin(3\u03c0x - 1) + 2) + 3)^2 + 4(4(-3sin(3\u03c0x - 1) + 2)^2 - 1(-3sin(3\u03c0x - 1) + 2) + 3) - 4)) 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) = -1cos(3\u03c0(4((2((2(1x + 3) - 1)/(-2(1x + 3) + 3)) + 3)/(1((2(1x + 3) - 1)/(-2(1x + 3) + 3)) + 2))^2 - 5((2((2(1x + 3) - 1)/(-2(1x + 3) + 3)) + 3)/(1((2(1x + 3) - 1)/(-2(1x + 3) + 3)) + 2)) + 4) + 3) + 1 have in the interval [-10, 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((3(3cos(3\u03c0(-1|((2x - 2)/(-1x - 3)) - 2| - 2) + 3) + 3) - 3)/(-1(3cos(3\u03c0(-1|((2x - 2)/(-1x - 3)) - 2| - 2) + 3) + 3) - 1))^2 - 1((3(3cos(3\u03c0(-1|((2x - 2)/(-1x - 3)) - 2| - 2) + 3) + 3) - 3)/(-1(3cos(3\u03c0(-1|((2x - 2)/(-1x - 3)) - 2| - 2) + 3) + 3) - 1)) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "123", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = (1(-5(-2sin(3\u03c0(-1|(-2|x| - 3) + 2| - 2) - 2) - 3) + 1) + 2)/(2(-5(-2sin(3\u03c0(-1|(-2|x| - 3) + 2| - 2) - 2) - 3) + 1) - 1) 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 maxima does the function f(x) = -4(5(-3|(4(-2cos(3\u03c0x - 1) - 2) + 1) + 3| - 2) + 4)^2 - 5(5(-3|(4(-2cos(3\u03c0x - 1) - 2) + 1) + 3| - 2) + 4) + 4 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": "Determine the count of local maxima for the function f(x) = 2cos(2\u03c0(-5(-1|(-1(-3x + 4) - 3) + 3| + 1) - 2)) + 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "299", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = (3((3(4(-2|(1sin(1\u03c0x - 2) - 3) - 1| - 2) - 5) + 1)/(1(4(-2|(1sin(1\u03c0x - 2) - 3) - 1| - 2) - 5))) - 2)/(-1((3(4(-2|(1sin(1\u03c0x - 2) - 3) - 1| - 2) - 5) + 1)/(1(4(-2|(1sin(1\u03c0x - 2) - 3) - 1| - 2) - 5))) + 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) = 3|(3sin(1\u03c0(-2|(-3(-1|x + 3| + 2) - 1) + 1| + 3) + 2) - 2) + 2| + 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": "How many local extrema (minima and maxima combined) does the function f(x) = 2cos(3\u03c0(-2|((-1((-2(-3x - 3) + 1)/(-1(-3x - 3) + 2)) - 3)/(-1((-2(-3x - 3) + 1)/(-1(-3x - 3) + 2)) - 2)) - 3|) - 2) - 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": "Determine the total count of local extrema points for the function f(x) = -1((-1(-3|(2(2cos(3\u03c0x + 3) - 3) - 3) + 2| - 3) - 1)/(-3(-3|(2(2cos(3\u03c0x + 3) - 3) - 3) + 2| - 3) + 1))^2 - 4 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((3(2sin(3\u03c0(5x^2 + 1x - 3) - 1) + 1) - 1)/(-1(2sin(3\u03c0(5x^2 + 1x - 3) - 1) + 1) - 3)))/(2((3(2sin(3\u03c0(5x^2 + 1x - 3) - 1) + 1) - 1)/(-1(2sin(3\u03c0(5x^2 + 1x - 3) - 1) + 1) - 3)) - 1)) + 3)/(2((-1((3(2sin(3\u03c0(5x^2 + 1x - 3) - 1) + 1) - 1)/(-1(2sin(3\u03c0(5x^2 + 1x - 3) - 1) + 1) - 3)))/(2((3(2sin(3\u03c0(5x^2 + 1x - 3) - 1) + 1) - 1)/(-1(2sin(3\u03c0(5x^2 + 1x - 3) - 1) + 1) - 3)) - 1)) + 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "497", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = (2(-3(3cos(2\u03c0((-3(-1x^2 - 4x - 2) - 3)/(1(-1x^2 - 4x - 2) + 3)) - 2) + 3) + 2) - 2)/(2(-3(3cos(2\u03c0((-3(-1x^2 - 4x - 2) - 3)/(1(-1x^2 - 4x - 2) + 3)) - 2) + 3) + 2) + 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "26", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 3(-3sin(2\u03c0((1((1(1x + 1) - 2)/(-1(1x + 1) + 3)) - 2)/(2((1(1x + 1) - 2)/(-1(1x + 1) + 3)) + 2))) + 2)^2 - 4(-3sin(2\u03c0((1((1(1x + 1) - 2)/(-1(1x + 1) + 3)) - 2)/(2((1(1x + 1) - 2)/(-1(1x + 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": "120", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 5(-3(4(1(1x^2 - 5x + 5)^2 - 2(1x^2 - 5x + 5) - 2)^2 + 4(1(1x^2 - 5x + 5)^2 - 2(1x^2 - 5x + 5) - 2) - 4) + 4)^2 + 2(-3(4(1(1x^2 - 5x + 5)^2 - 2(1x^2 - 5x + 5) - 2)^2 + 4(1(1x^2 - 5x + 5)^2 - 2(1x^2 - 5x + 5) - 2) - 4) + 4) - 4 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 minimum points for f(x) = (-2((-1(-4(-1(2x^2 - 3) - 3)^2 - 1(-1(2x^2 - 3) - 3) + 4) - 1)/(-3(-4(-1(2x^2 - 3) - 3)^2 - 1(-1(2x^2 - 3) - 3) + 4) - 3)) + 2)/(3((-1(-4(-1(2x^2 - 3) - 3)^2 - 1(-1(2x^2 - 3) - 3) + 4) - 1)/(-3(-4(-1(2x^2 - 3) - 3)^2 - 1(-1(2x^2 - 3) - 3) + 4) - 3))) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "72", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 2(3cos(2\u03c0(1(4((-1x + 2)/(-2x - 1))^2 - 5((-1x + 2)/(-2x - 1)) + 4) - 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": "Determine the count of local minima for the function f(x) = -3(2cos(1\u03c0(1(-4((-2x)/(3x - 1)) + 5)^2 - 1(-4((-2x)/(3x - 1)) + 5) + 3)) + 3) + 5 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(-5(5(-2sin(2\u03c0(4x + 1) - 2) - 2) + 4)^2) - 1)/(-1(-5(5(-2sin(2\u03c0(4x + 1) - 2) - 2) + 4)^2) + 2) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "318", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 5(-1(3cos(2\u03c0(-2(-1x^2 - 2x + 3) + 1) + 2) - 3)^2 - 4(3cos(2\u03c0(-2(-1x^2 - 2x + 3) + 1) + 2) - 3) - 3)^2 - 5(-1(3cos(2\u03c0(-2(-1x^2 - 2x + 3) + 1) + 2) - 3)^2 - 4(3cos(2\u03c0(-2(-1x^2 - 2x + 3) + 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": "222", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 1(-3cos(2\u03c0(-1(-4(-1|x + 1| - 2)^2 - 4(-1|x + 1| - 2) + 2) + 1) + 3) - 3)^2 - 4(-3cos(2\u03c0(-1(-4(-1|x + 1| - 2)^2 - 4(-1|x + 1| - 2) + 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": "237", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -2((2(2(1|(-2sin(1\u03c0x - 1) + 2) - 2| - 1) + 2) - 2)/(-1(2(1|(-2sin(1\u03c0x - 1) + 2) - 2| - 1) + 2) - 2))^2 + 5((2(2(1|(-2sin(1\u03c0x - 1) + 2) - 2| - 1) + 2) - 2)/(-1(2(1|(-2sin(1\u03c0x - 1) + 2) - 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": "20", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 1(-3cos(1\u03c0(1((3((1x)/(-1x + 2)) + 2)/(1((1x)/(-1x + 2)))) - 5) + 3) - 1) - 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": "How many local maxima does the function f(x) = -4((3(-1sin(1\u03c0((-1(-4x - 5) + 2)/(-3(-4x - 5) + 2))) + 1) - 1)/(-2(-1sin(1\u03c0((-1(-4x - 5) + 2)/(-3(-4x - 5) + 2))) + 1) + 1))^2 + 1((3(-1sin(1\u03c0((-1(-4x - 5) + 2)/(-3(-4x - 5) + 2))) + 1) - 1)/(-2(-1sin(1\u03c0((-1(-4x - 5) + 2)/(-3(-4x - 5) + 2))) + 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 total count of local extrema points for the function f(x) = -4(-1((-3(3sin(2\u03c0((1x + 2)/(2x - 1)) - 2) - 2) + 3)/(2(3sin(2\u03c0((1x + 2)/(2x - 1)) - 2) - 2) - 3)) + 1)^2 - 4(-1((-3(3sin(2\u03c0((1x + 2)/(2x - 1)) - 2) - 2) + 3)/(2(3sin(2\u03c0((1x + 2)/(2x - 1)) - 2) - 2) - 3)) + 1) + 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = (-2(1((-1(-2|((-1x - 1)/(3x - 1)) - 1| + 3))/(1(-2|((-1x - 1)/(3x - 1)) - 1| + 3) - 3))^2 - 1((-1(-2|((-1x - 1)/(3x - 1)) - 1| + 3))/(1(-2|((-1x - 1)/(3x - 1)) - 1| + 3) - 3)) + 2) + 3)/(-1(1((-1(-2|((-1x - 1)/(3x - 1)) - 1| + 3))/(1(-2|((-1x - 1)/(3x - 1)) - 1| + 3) - 3))^2 - 1((-1(-2|((-1x - 1)/(3x - 1)) - 1| + 3))/(1(-2|((-1x - 1)/(3x - 1)) - 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": "4", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -3sin(2\u03c0(-3|(-1|((-3(1x^2 - 2x - 3) - 2)/(2(1x^2 - 2x - 3) + 3)) - 3| + 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": "59", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 3cos(3\u03c0((2(3(-2((2x - 2)/(-2x - 1))^2 + 4((2x - 2)/(-2x - 1)) + 3)^2 - 1))/(2(3(-2((2x - 2)/(-2x - 1))^2 + 4((2x - 2)/(-2x - 1)) + 3)^2 - 1) - 1)) - 3) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 1(-2sin(3\u03c0(3(-2(4x - 1) - 4)^2 - 4(-2(4x - 1) - 4) - 1) + 2) + 2) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "149", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 1|((-2(-1e^(-2(5(3|x + 2| - 1)^2 - 1(3|x + 2| - 1) + 4)) - 3) + 1)/(2(-1e^(-2(5(3|x + 2| - 1)^2 - 1(3|x + 2| - 1) + 4)) - 3) + 1)) - 3| + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -1(5((1(2((-3x)/(2x - 1))^2 + 5((-3x)/(2x - 1)) - 3) - 1)/(1(2((-3x)/(2x - 1))^2 + 5((-3x)/(2x - 1)) - 3) + 1)) - 3)^2 + 2(5((1(2((-3x)/(2x - 1))^2 + 5((-3x)/(2x - 1)) - 3) - 1)/(1(2((-3x)/(2x - 1))^2 + 5((-3x)/(2x - 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": "5", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 3cos(3\u03c0((-1(5(-5(-5x^2 + 2x - 1)^2 + 1(-5x^2 + 2x - 1))^2 - 5(-5(-5x^2 + 2x - 1)^2 + 1(-5x^2 + 2x - 1)) - 5) - 2)/(-1(5(-5(-5x^2 + 2x - 1)^2 + 1(-5x^2 + 2x - 1))^2 - 5(-5(-5x^2 + 2x - 1)^2 + 1(-5x^2 + 2x - 1)) - 5) - 1)) + 2) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 3(-2cos(1\u03c0(-4(4((-3x - 3)/(-3x - 2))^2 - 4((-3x - 3)/(-3x - 2)) + 3) - 2)) - 3)^2 + 2(-2cos(1\u03c0(-4(4((-3x - 3)/(-3x - 2))^2 - 4((-3x - 3)/(-3x - 2)) + 3) - 2)) - 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 count of local minima for the function f(x) = -3|((-3(-3|(3|(-4x^2 - 3x + 1)| - 3) - 1| - 1) - 3)/(3(-3|(3|(-4x^2 - 3x + 1)| - 3) - 1| - 1) + 2))| + 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -2(2sin(3\u03c0(-2|(4(1x^2 - 3x + 5) + 3) + 2| - 1) - 1) - 2)^2 - 3(2sin(3\u03c0(-2|(4(1x^2 - 3x + 5) + 3) + 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": "132", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = (2((1((-2(3(-3sin(1\u03c0x - 1) - 3) + 4) + 3)/(1(3(-3sin(1\u03c0x - 1) - 3) + 4) + 1)) - 1)/(-2((-2(3(-3sin(1\u03c0x - 1) - 3) + 4) + 3)/(1(3(-3sin(1\u03c0x - 1) - 3) + 4) + 1)) + 1)) - 3)/(1((1((-2(3(-3sin(1\u03c0x - 1) - 3) + 4) + 3)/(1(3(-3sin(1\u03c0x - 1) - 3) + 4) + 1)) - 1)/(-2((-2(3(-3sin(1\u03c0x - 1) - 3) + 4) + 3)/(1(3(-3sin(1\u03c0x - 1) - 3) + 4) + 1)) + 1))) 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) = 1|((-3(-1|(-2sin(3\u03c0(-1x - 3) + 3) + 2) - 3| + 2) - 2)/(-2(-1|(-2sin(3\u03c0(-1x - 3) + 3) + 2) - 3| + 2) + 3)) - 1| + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "235", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -1|(2cos(2\u03c0((-3(-5(-2|x + 1| + 2) - 4))/(1(-5(-2|x + 1| + 2) - 4) - 2)))) - 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": "Find the number of local maximum points for f(x) = -4(3(-3(-3sin(2\u03c0(3x + 2) + 3))^2 + 1(-3sin(2\u03c0(3x + 2) + 3)) + 1) - 3)^2 + 2(3(-3(-3sin(2\u03c0(3x + 2) + 3))^2 + 1(-3sin(2\u03c0(3x + 2) + 3)) + 1) - 3) - 4 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) = -4(-3|(1(-2sin(2\u03c0((-1x - 1)/(1x + 2)) - 2) + 1)^2 + 2(-2sin(2\u03c0((-1x - 1)/(1x + 2)) - 2) + 1) + 5) - 2| - 3) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = (-2(3|(4(3(2|x + 1| - 3)^2 - 5)^2 - 1) - 3| + 1) + 3)/(-3(3|(4(3(2|x + 1| - 3)^2 - 5)^2 - 1) - 3| + 1) - 1) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 1(4((1((3(1x^2 + 5x - 1) + 2)/(3(1x^2 + 5x - 1) + 3)) - 3)/(-3((3(1x^2 + 5x - 1) + 2)/(3(1x^2 + 5x - 1) + 3)) - 1)) + 5)^2 - 3(4((1((3(1x^2 + 5x - 1) + 2)/(3(1x^2 + 5x - 1) + 3)) - 3)/(-3((3(1x^2 + 5x - 1) + 2)/(3(1x^2 + 5x - 1) + 3)) - 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 minima for the function f(x) = -2((-3(-3sin(1\u03c0(4(1|x - 2| - 3)^2 - 2(1|x - 2| - 3)) + 1)) + 1)/(-3(-3sin(1\u03c0(4(1|x - 2| - 3)^2 - 2(1|x - 2| - 3)) + 1)) - 2))^2 + 4 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "211", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 1|(-2|(3cos(3\u03c0(-3(4x^2 - 5x + 5) + 1) - 3) - 3) - 1| + 1) - 2| + 1 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 maxima does the function f(x) = (2((2(-5((1(-3cos(2\u03c0x + 3) - 1) + 1)/(1(-3cos(2\u03c0x + 3) - 1) - 3)) - 4) - 1)/(2(-5((1(-3cos(2\u03c0x + 3) - 1) + 1)/(1(-3cos(2\u03c0x + 3) - 1) - 3)) - 4) + 2)) - 1)/(3((2(-5((1(-3cos(2\u03c0x + 3) - 1) + 1)/(1(-3cos(2\u03c0x + 3) - 1) - 3)) - 4) - 1)/(2(-5((1(-3cos(2\u03c0x + 3) - 1) + 1)/(1(-3cos(2\u03c0x + 3) - 1) - 3)) - 4) + 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) = -2|(-2(-1cos(3\u03c0(-2(-1|x|)^2 - 3(-1|x|) - 1) + 3) - 3)^2 + 5(-1cos(3\u03c0(-2(-1|x|)^2 - 3(-1|x|) - 1) + 3) - 3) - 1) + 3| - 2 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) = 2(2sin(3\u03c0(-1(-5(-5x + 2)^2 - 2) + 4) - 2) + 3) - 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "335", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = 1((-3((2(-3cos(2\u03c0(-3x^2 - 1x + 5) + 3) - 3) + 3)/(-2(-3cos(2\u03c0(-3x^2 - 1x + 5) + 3) - 3) + 3)) - 1)/(-2((2(-3cos(2\u03c0(-3x^2 - 1x + 5) + 3) - 3) + 3)/(-2(-3cos(2\u03c0(-3x^2 - 1x + 5) + 3) - 3) + 3)) + 1))^2 + 2((-3((2(-3cos(2\u03c0(-3x^2 - 1x + 5) + 3) - 3) + 3)/(-2(-3cos(2\u03c0(-3x^2 - 1x + 5) + 3) - 3) + 3)) - 1)/(-2((2(-3cos(2\u03c0(-3x^2 - 1x + 5) + 3) - 3) + 3)/(-2(-3cos(2\u03c0(-3x^2 - 1x + 5) + 3) - 3) + 3)) + 1)) + 5 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "289", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = 1(-2((1(-2cos(1\u03c0(2x - 1) + 2) - 3) + 3)/(2(-2cos(1\u03c0(2x - 1) + 2) - 3) + 2)) - 5) - 4 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|(-4((-1(1cos(1\u03c0x + 2) - 1) - 2)/(3(1cos(1\u03c0x + 2) - 1) + 2)) - 4) + 2| - 2))/(1(1|(-4((-1(1cos(1\u03c0x + 2) - 1) - 2)/(3(1cos(1\u03c0x + 2) - 1) + 2)) - 4) + 2| - 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": "Determine the count of local maxima for the function f(x) = -1cos(1\u03c0(1(2|(3(-3x + 5)^2 + 2(-3x + 5) - 3) - 3| + 1)^2 + 1(2|(3(-3x + 5)^2 + 2(-3x + 5) - 3) - 3| + 1) - 5)) - 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -3|(2((-1(3|(-2|x - 1| + 2)| - 3))/(-2(3|(-2|x - 1| + 2)| - 3) - 2)) - 4) + 1| + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = -1|((-1(-1e^(2(1|(4x + 2) + 2| - 3)) - 2) + 2)/(-3(-1e^(2(1|(4x + 2) + 2| - 3)) - 2) - 2)) + 1| + 3 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 total count of local extrema points for the function f(x) = -4(1|(-1|(2|(-2x^2 + 3x + 1) - 2|) + 1| + 3) + 1| + 1)^2 + 4(1|(-1|(2|(-2x^2 + 3x + 1) - 2|) + 1| + 3) + 1| + 1) - 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = (3(1(-1(-1e^(-1((-1x + 3)/(2x + 3))) + 1) + 5) + 1) + 2)/(2(1(-1(-1e^(-1((-1x + 3)/(2x + 3))) + 1) + 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 total number of local minima and maxima for f(x) = -1(2e^(-2(1(-2|(-5x^2 - 1x + 4) - 2| + 1)^2 - 3(-2|(-5x^2 - 1x + 4) - 2| + 1) + 5)) - 1)^2 + 3(2e^(-2(1(-2|(-5x^2 - 1x + 4) - 2| + 1)^2 - 3(-2|(-5x^2 - 1x + 4) - 2| + 1) + 5)) - 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) = 1(-2|(-1|(-3e^(1(-3x - 1)) + 2) + 2| - 1) - 1| - 1) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 3|(5(1(4(-1sin(1\u03c0x) - 1)) + 5)^2 - 3(1(4(-1sin(1\u03c0x) - 1)) + 5) - 5) - 1| 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) = (1(-3(-1|(-4(2cos(3\u03c0x - 3) - 1) + 5) - 3| - 3) + 1) - 1)/(2(-3(-1|(-4(2cos(3\u03c0x - 3) - 1) + 5) - 3| - 3) + 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 minima for the function f(x) = -3(1cos(2\u03c0(-3(-3|(3|x + 2|) - 2| - 2) + 5) - 3))^2 - 4 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) = 3|(-1(-2sin(2\u03c0(1(-1x^2 + 1x - 4) + 5) - 2) - 1)^2 + 1(-2sin(2\u03c0(1(-1x^2 + 1x - 4) + 5) - 2) - 1) + 5)| - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "123", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 5(2sin(1\u03c0((-1((3(-1x^2 + 5x + 1) + 3)/(-3(-1x^2 + 5x + 1) - 2)) - 2)/(1((3(-1x^2 + 5x + 1) + 3)/(-3(-1x^2 + 5x + 1) - 2)) + 1))) + 2) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "266", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = (-1(-3|(3((-2(-1sin(2\u03c0x + 2) + 1) + 3)/(3(-1sin(2\u03c0x + 2) + 1) + 2))^2 + 4((-2(-1sin(2\u03c0x + 2) + 1) + 3)/(3(-1sin(2\u03c0x + 2) + 1) + 2)) + 2) + 3| - 1) - 3)/(-2(-3|(3((-2(-1sin(2\u03c0x + 2) + 1) + 3)/(3(-1sin(2\u03c0x + 2) + 1) + 2))^2 + 4((-2(-1sin(2\u03c0x + 2) + 1) + 3)/(3(-1sin(2\u03c0x + 2) + 1) + 2)) + 2) + 3| - 1) + 1) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = (2(-4((-3(-2(1cos(3\u03c0x - 1) - 3) - 2) + 2)/(-1(-2(1cos(3\u03c0x - 1) - 3) - 2) - 2))^2 + 4((-3(-2(1cos(3\u03c0x - 1) - 3) - 2) + 2)/(-1(-2(1cos(3\u03c0x - 1) - 3) - 2) - 2)) - 1) + 2)/(1(-4((-3(-2(1cos(3\u03c0x - 1) - 3) - 2) + 2)/(-1(-2(1cos(3\u03c0x - 1) - 3) - 2) - 2))^2 + 4((-3(-2(1cos(3\u03c0x - 1) - 3) - 2) + 2)/(-1(-2(1cos(3\u03c0x - 1) - 3) - 2) - 2)) - 1) + 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": "Find the number of local maximum points for f(x) = -1|(3|(-2|(-2e^(1(-1x^2 + 3x + 2)) + 1)| + 1) + 3| - 3) + 2| - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -2((1((2(2sin(1\u03c0((1x - 1)/(3x - 1)) + 2) + 2) + 3)/(2(2sin(1\u03c0((1x - 1)/(3x - 1)) + 2) + 2) - 1)) + 1)/(1((2(2sin(1\u03c0((1x - 1)/(3x - 1)) + 2) + 2) + 3)/(2(2sin(1\u03c0((1x - 1)/(3x - 1)) + 2) + 2) - 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) = -1(2|(-3|(1|(4x^2 - 2x - 3) - 1| + 1) - 1| + 1)| - 3)^2 - 3(2|(-3|(1|(4x^2 - 2x - 3) - 1| + 1) - 1| + 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": "Find the number of local minimum points for f(x) = -3cos(1\u03c0(-1(2(-1(3|x + 2|) - 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": "60", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 2((1(-4((-1(-3|x + 2| + 3) + 3)/(3(-3|x + 2| + 3) + 1))^2 - 3((-1(-3|x + 2| + 3) + 3)/(3(-3|x + 2| + 3) + 1))) - 2)/(-2(-4((-1(-3|x + 2| + 3) + 3)/(3(-3|x + 2| + 3) + 1))^2 - 3((-1(-3|x + 2| + 3) + 3)/(3(-3|x + 2| + 3) + 1))) + 3))^2 - 2((1(-4((-1(-3|x + 2| + 3) + 3)/(3(-3|x + 2| + 3) + 1))^2 - 3((-1(-3|x + 2| + 3) + 3)/(3(-3|x + 2| + 3) + 1))) - 2)/(-2(-4((-1(-3|x + 2| + 3) + 3)/(3(-3|x + 2| + 3) + 1))^2 - 3((-1(-3|x + 2| + 3) + 3)/(3(-3|x + 2| + 3) + 1))) + 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": "How many local minima does the function f(x) = -3((1(-1(3|(-1cos(3\u03c0x) - 1)| + 2)^2 + 4(3|(-1cos(3\u03c0x) - 1)| + 2) - 1) - 3)/(3(-1(3|(-1cos(3\u03c0x) - 1)| + 2)^2 + 4(3|(-1cos(3\u03c0x) - 1)| + 2) - 1) - 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": "How many local extrema (minima and maxima combined) does the function f(x) = 1((-2(-1((2(-1cos(3\u03c0x - 2) + 1) - 1)/(2(-1cos(3\u03c0x - 2) + 1) + 2))^2 - 3((2(-1cos(3\u03c0x - 2) + 1) - 1)/(2(-1cos(3\u03c0x - 2) + 1) + 2)) - 3) + 1)/(-1(-1((2(-1cos(3\u03c0x - 2) + 1) - 1)/(2(-1cos(3\u03c0x - 2) + 1) + 2))^2 - 3((2(-1cos(3\u03c0x - 2) + 1) - 1)/(2(-1cos(3\u03c0x - 2) + 1) + 2)) - 3) + 3))^2 - 1((-2(-1((2(-1cos(3\u03c0x - 2) + 1) - 1)/(2(-1cos(3\u03c0x - 2) + 1) + 2))^2 - 3((2(-1cos(3\u03c0x - 2) + 1) - 1)/(2(-1cos(3\u03c0x - 2) + 1) + 2)) - 3) + 1)/(-1(-1((2(-1cos(3\u03c0x - 2) + 1) - 1)/(2(-1cos(3\u03c0x - 2) + 1) + 2))^2 - 3((2(-1cos(3\u03c0x - 2) + 1) - 1)/(2(-1cos(3\u03c0x - 2) + 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": "60", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = (2(-2sin(3\u03c0(-5(4(1x + 2) + 5) + 3) - 2) - 1) - 3)/(-2(-2sin(3\u03c0(-5(4(1x + 2) + 5) + 3) - 2) - 1) - 1) have 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) = -3|(4(-2e^(-1(-1|(-4x^2 - 3x + 3) + 3| - 2)) + 1)^2 + 2(-2e^(-1(-1|(-4x^2 - 3x + 3) + 3| - 2)) + 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 count of local maxima for the function f(x) = (-3(-3sin(3\u03c0((1(4(-1|x + 3| + 1) - 2))/(-1(4(-1|x + 3| + 1) - 2) + 2))) + 3) + 2)/(-1(-3sin(3\u03c0((1(4(-1|x + 3| + 1) - 2))/(-1(4(-1|x + 3| + 1) - 2) + 2))) + 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": "How many local extrema (minima and maxima combined) does the function f(x) = (-1(-1(-4(2((-3x - 1)/(1x))^2 - 3((-3x - 1)/(1x)) - 3)^2 + 1(2((-3x - 1)/(1x))^2 - 3((-3x - 1)/(1x)) - 3) + 5)^2 - 4(-4(2((-3x - 1)/(1x))^2 - 3((-3x - 1)/(1x)) - 3)^2 + 1(2((-3x - 1)/(1x))^2 - 3((-3x - 1)/(1x)) - 3) + 5) + 2) + 2)/(2(-1(-4(2((-3x - 1)/(1x))^2 - 3((-3x - 1)/(1x)) - 3)^2 + 1(2((-3x - 1)/(1x))^2 - 3((-3x - 1)/(1x)) - 3) + 5)^2 - 4(-4(2((-3x - 1)/(1x))^2 - 3((-3x - 1)/(1x)) - 3)^2 + 1(2((-3x - 1)/(1x))^2 - 3((-3x - 1)/(1x)) - 3) + 5) + 2) + 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = (-2(-2|(4((2(-1sin(3\u03c0x) - 3) - 1)/(1(-1sin(3\u03c0x) - 3) - 2)) + 5) + 1| - 2) + 3)/(-1(-2|(4((2(-1sin(3\u03c0x) - 3) - 1)/(1(-1sin(3\u03c0x) - 3) - 2)) + 5) + 1| - 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": "How many local extrema (minima and maxima combined) does the function f(x) = 1e^(1(-2(1|((1(-3x - 3) - 1)/(1(-3x - 3) - 2)) + 3|)^2 + 4)) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "23", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = (-2(-1|(1sin(1\u03c0(-2(-1x^2 + 5x - 2)^2 - 1(-1x^2 + 5x - 2) - 3) - 2) + 3) + 3| - 2) + 3)/(-2(-1|(1sin(1\u03c0(-2(-1x^2 + 5x - 2)^2 - 1(-1x^2 + 5x - 2) - 3) - 2) + 3) + 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": "Determine the count of local maxima for the function f(x) = 3cos(1\u03c0(1|((-2((1(-2x^2 - 2x + 1) + 3)/(-3(-2x^2 - 2x + 1) - 3)) + 1)/(1((1(-2x^2 - 2x + 1) + 3)/(-3(-2x^2 - 2x + 1) - 3)) + 2)) + 3| - 2) - 3) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 1(1(2sin(2\u03c0((3(-5x^2 - 5x + 4) - 2)/(3(-5x^2 - 5x + 4) + 2)) - 1) + 1) - 3)^2 - 3(1(2sin(2\u03c0((3(-5x^2 - 5x + 4) - 2)/(3(-5x^2 - 5x + 4) + 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": "6", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -3cos(2\u03c0((-3(4(5(-2|x + 1|)^2 - 1)) + 3)/(-3(4(5(-2|x + 1|)^2 - 1)) - 1)) - 3) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -3((2(-3e^(-2(-2|(-5x) + 3|))) + 3)/(1(-3e^(-2(-2|(-5x) + 3|))))) + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 3|(3(1cos(1\u03c0((2(-5x - 2) + 2)/(-1(-5x - 2) + 2)) + 1) + 3)^2 + 3(1cos(1\u03c0((2(-5x - 2) + 2)/(-1(-5x - 2) + 2)) + 1) + 3) - 5) - 1| - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -3(-4(-2sin(1\u03c0(1(-3x + 5)^2 + 1(-3x + 5) + 4) + 3) - 1)^2 - 2(-2sin(1\u03c0(1(-3x + 5)^2 + 1(-3x + 5) + 4) + 3) - 1) - 1) + 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "415", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -2|(5(3(-4(3sin(2\u03c0x - 3) + 2)^2 + 3(3sin(2\u03c0x - 3) + 2) - 1) - 4)^2 + 4(3(-4(3sin(2\u03c0x - 3) + 2)^2 + 3(3sin(2\u03c0x - 3) + 2) - 1) - 4) + 2) - 2| 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": "Find the number of local minimum points for f(x) = (2(1(-3|(1(-1x - 5) - 1) - 2|)^2 + 4(-3|(1(-1x - 5) - 1) - 2|) - 3) + 2)/(3(1(-3|(1(-1x - 5) - 1) - 2|)^2 + 4(-3|(1(-1x - 5) - 1) - 2|) - 3) + 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "88", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -5(3|((3(-5(2x^2 + 4x + 3) + 1) + 3)/(2(-5(2x^2 + 4x + 3) + 1) + 2))| + 2)^2 - 2(3|((3(-5(2x^2 + 4x + 3) + 1) + 3)/(2(-5(2x^2 + 4x + 3) + 1) + 2))| + 2) + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "213", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -3|(-1((-2(-1|(2|x| + 3) - 3| + 3) + 3)/(-2(-1|(2|x| + 3) - 3| + 3) - 1))^2 - 1) - 2| - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 3|(-1|(2(-3e^(2(3x^2 + 4x - 3)) + 2) + 3) + 3| + 3) - 1| - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = (2(3cos(3\u03c0(-2|((-2(2x + 4) - 2)/(-3(2x + 4) + 1)) + 1|) - 2) - 3) - 1)/(-3(3cos(3\u03c0(-2|((-2(2x + 4) - 2)/(-3(2x + 4) + 1)) + 1|) - 2) - 3) + 2) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "24", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = (-2(-3sin(3\u03c0(-5(-1(3|x + 3| + 1)^2 - 5(3|x + 3| + 1) + 4) + 3) - 1) - 3) - 3)/(1(-3sin(3\u03c0(-5(-1(3|x + 3| + 1)^2 - 5(3|x + 3| + 1) + 4) + 3) - 1) - 3) - 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "413", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -2|((1(-1e^(-1(-1(3x - 4)^2 - 1(3x - 4) - 4)) + 1) - 2)/(-3(-1e^(-1(-1(3x - 4)^2 - 1(3x - 4) - 4)) + 1))) - 1| - 2 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) = 2|(1|(3(-1(1x - 2)^2 + 5(1x - 2) + 1)^2 + 3(-1(1x - 2)^2 + 5(1x - 2) + 1) - 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": "7", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -3|(-1sin(3\u03c0(-5(5(2x^2 - 2x + 4) + 4) - 5) - 3) - 1) + 2| + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "207", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 1|(-1|(2sin(2\u03c0((2(1|x + 1| - 2) - 1)/(2(1|x + 1| - 2) + 2)) - 1) + 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": "64", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = (1(-4(-1sin(1\u03c0((-3((1x - 3)/(2x - 3)) - 2)/(-3((1x - 3)/(2x - 3)) + 4)) + 3) + 2) - 2))/(2(-4(-1sin(1\u03c0((-3((1x - 3)/(2x - 3)) - 2)/(-3((1x - 3)/(2x - 3)) + 4)) + 3) + 2) - 2) - 1) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -5(-2|(-1|(-2|(-3sin(2\u03c0x - 3) + 3) - 1| + 1) - 1| - 2) - 1| - 1)^2 - 4(-2|(-1|(-2|(-3sin(2\u03c0x - 3) + 3) - 1| + 1) - 1| - 2) - 1| - 1) + 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "78", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = (-3(3|(-1(1((-1x + 2)/(2x - 1))^2 - 1((-1x + 2)/(2x - 1)) - 3) + 1) + 1| - 2))/(-1(3|(-1(1((-1x + 2)/(2x - 1))^2 - 1((-1x + 2)/(2x - 1)) - 3) + 1) + 1| - 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": "Determine the total count of local extrema points for the function f(x) = -2((-2(1((1(2|x|) - 1)/(-1(2|x|) + 2))^2 - 3((1(2|x|) - 1)/(-1(2|x|) + 2)) + 3) - 2)/(-2(1((1(2|x|) - 1)/(-1(2|x|) + 2))^2 - 3((1(2|x|) - 1)/(-1(2|x|) + 2)) + 3) + 3)) + 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": "How many local extrema (minima and maxima combined) does the function f(x) = 2|(1|(-3(4((-3x + 2)/(-2x)) + 5)^2 - 1(4((-3x + 2)/(-2x)) + 5) + 5) - 3| - 2)| + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -4(-1(2(1((-2x - 1)/(3x - 2))^2 + 4((-2x - 1)/(3x - 2)) + 2)^2 - 3) - 1)^2 + 3(-1(2(1((-2x - 1)/(3x - 2))^2 + 4((-2x - 1)/(3x - 2)) + 2)^2 - 3) - 1) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -1(-3(-1(1sin(2\u03c0(-2|x| + 2) - 1) - 3) - 3) + 4) + 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((3((-1(-1(-3|x - 2| + 2) + 1) - 1)/(3(-1(-3|x - 2| + 2) + 1) + 1)) + 3)/(2((-1(-1(-3|x - 2| + 2) + 1) - 1)/(3(-1(-3|x - 2| + 2) + 1) + 1)) + 2)) - 2)/(-1((3((-1(-1(-3|x - 2| + 2) + 1) - 1)/(3(-1(-3|x - 2| + 2) + 1) + 1)) + 3)/(2((-1(-1(-3|x - 2| + 2) + 1) - 1)/(3(-1(-3|x - 2| + 2) + 1) + 1)) + 2)) + 2) 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) = -2(-3(3cos(3\u03c0(3|(5x - 4) - 2| - 1) - 3) - 3) - 4)^2 - 4(-3(3cos(3\u03c0(3|(5x - 4) - 2| - 1) - 3) - 3) - 4) - 3 have 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 maxima does the function f(x) = -1e^(1(5(-4((2(-3|x| + 3) - 2)/(-2(-3|x| + 3) - 3))^2 + 1((2(-3|x| + 3) - 2)/(-2(-3|x| + 3) - 3)))^2 + 3(-4((2(-3|x| + 3) - 2)/(-2(-3|x| + 3) - 3))^2 + 1((2(-3|x| + 3) - 2)/(-2(-3|x| + 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": "Find the total number of local minima and maxima for f(x) = (3(2|((-2((1(1sin(3\u03c0x - 1) - 2) + 3)/(-1(1sin(3\u03c0x - 1) - 2) + 2)) + 1)/(-3((1(1sin(3\u03c0x - 1) - 2) + 3)/(-1(1sin(3\u03c0x - 1) - 2) + 2)) + 2)) + 1| - 1) - 2)/(-3(2|((-2((1(1sin(3\u03c0x - 1) - 2) + 3)/(-1(1sin(3\u03c0x - 1) - 2) + 2)) + 1)/(-3((1(1sin(3\u03c0x - 1) - 2) + 3)/(-1(1sin(3\u03c0x - 1) - 2) + 2)) + 2)) + 1| - 1) - 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": "Find the number of local minimum points for f(x) = 1(1((2(1((-3x + 2)/(2x - 3))^2 + 5((-3x + 2)/(2x - 3)) + 4) - 3)/(1(1((-3x + 2)/(2x - 3))^2 + 5((-3x + 2)/(2x - 3)) + 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 number of local minimum points for f(x) = -5(1(-1sin(1\u03c0(1(1x^2 + 2x + 2)^2 + 2(1x^2 + 2x + 2) + 2) + 2) + 3) + 1) - 3 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": "Find the number of local maximum points for f(x) = (-1(-1cos(1\u03c0(2|(-2(-2|x - 1| - 2)^2 - 4(-2|x - 1| - 2) - 5) + 2| - 1) - 3)) - 1)/(3(-1cos(1\u03c0(2|(-2(-2|x - 1| - 2)^2 - 4(-2|x - 1| - 2) - 5) + 2| - 1) - 3)) + 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "248", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -1(3((2(2sin(1\u03c0(-2x) + 3) - 1))/(3(2sin(1\u03c0(-2x) + 3) - 1) - 1))^2 + 4)^2 - 3(3((2(2sin(1\u03c0(-2x) + 3) - 1))/(3(2sin(1\u03c0(-2x) + 3) - 1) - 1))^2 + 4) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "100", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 2|(-1cos(2\u03c0(3|(-5((-2x - 2)/(-1x - 3))^2 + 5((-2x - 2)/(-1x - 3)) + 5)| - 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": "121", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 1|(-1cos(2\u03c0(-1(1(5x) - 3) + 5) + 1) + 3) + 3| + 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": "How many local extrema (minima and maxima combined) does the function f(x) = 2cos(3\u03c0(2(1|((-1(-3x^2 - 3x + 3) - 1)/(2(-3x^2 - 3x + 3) - 3)) - 3| - 1)^2 - 5(1|((-1(-3x^2 - 3x + 3) - 1)/(2(-3x^2 - 3x + 3) - 3)) - 3| - 1) + 5)) + 1 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": "How many local extrema (minima and maxima combined) does the function f(x) = (2((-1((-3((-3(-3cos(2\u03c0x) + 2) - 1)/(3(-3cos(2\u03c0x) + 2) - 2)) - 1)/(-2((-3(-3cos(2\u03c0x) + 2) - 1)/(3(-3cos(2\u03c0x) + 2) - 2)) - 1)) - 3)/(2((-3((-3(-3cos(2\u03c0x) + 2) - 1)/(3(-3cos(2\u03c0x) + 2) - 2)) - 1)/(-2((-3(-3cos(2\u03c0x) + 2) - 1)/(3(-3cos(2\u03c0x) + 2) - 2)) - 1)) + 2)) + 3)/(-3((-1((-3((-3(-3cos(2\u03c0x) + 2) - 1)/(3(-3cos(2\u03c0x) + 2) - 2)) - 1)/(-2((-3(-3cos(2\u03c0x) + 2) - 1)/(3(-3cos(2\u03c0x) + 2) - 2)) - 1)) - 3)/(2((-3((-3(-3cos(2\u03c0x) + 2) - 1)/(3(-3cos(2\u03c0x) + 2) - 2)) - 1)/(-2((-3(-3cos(2\u03c0x) + 2) - 1)/(3(-3cos(2\u03c0x) + 2) - 2)) - 1)) + 2))) 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) = 1(-2(2|(2(-1sin(1\u03c0x + 2) + 1) - 4) - 2| - 2) - 4)^2 + 5(-2(2|(2(-1sin(1\u03c0x + 2) + 1) - 4) - 2| - 2) - 4) + 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": "Determine the count of local maxima for the function f(x) = 1|(-1|(-1sin(2\u03c0(-5(-1|x - 2|)^2 + 4(-1|x - 2|) - 1) - 1) - 2)| + 1)| + 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "268", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 3(-3|(-2|(2(5x - 4)^2 + 1(5x - 4)) - 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": "How many local minima does the function f(x) = -3|(-2cos(3\u03c0(4((3(-3x^2 + 2x - 1) - 2)/(-3(-3x^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": "32", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -3(-4(-2cos(3\u03c0((2((-2x - 2)/(-1x + 3)) + 1)/(3((-2x - 2)/(-1x + 3))))) + 3)^2 - 4(-2cos(3\u03c0((2((-2x - 2)/(-1x + 3)) + 1)/(3((-2x - 2)/(-1x + 3))))) + 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": "Find the total number of local minima and maxima for f(x) = -4(1(2|((-1(-3cos(3\u03c0x + 1) + 2) + 2)/(1(-3cos(3\u03c0x + 1) + 2) - 3)) + 3| - 1)^2 + 3(2|((-1(-3cos(3\u03c0x + 1) + 2) + 2)/(1(-3cos(3\u03c0x + 1) + 2) - 3)) + 3| - 1) + 1) - 4 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": "How many local extrema (minima and maxima combined) does the function f(x) = 2|(1(2cos(1\u03c0(5(-2x - 2) + 2) - 3) - 2) + 3) - 2| + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "399", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = 1|(-1(-5(-4(1x^2 - 4x + 3)^2 - 3(1x^2 - 4x + 3) + 5))^2 + 1(-5(-4(1x^2 - 4x + 3)^2 - 3(1x^2 - 4x + 3) + 5)) - 1) + 1| + 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -3((2(2|(-1(1sin(3\u03c0x) - 2) - 5) - 1| - 3))/(-1(2|(-1(1sin(3\u03c0x) - 2) - 5) - 1| - 3) - 3))^2 - 3((2(2|(-1(1sin(3\u03c0x) - 2) - 5) - 1| - 3))/(-1(2|(-1(1sin(3\u03c0x) - 2) - 5) - 1| - 3) - 3)) - 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = (-1(-1sin(3\u03c0((1(-1|(-3x^2 - 4x + 5) + 3| + 2) - 3)/(-3(-1|(-3x^2 - 4x + 5) + 3| + 2) - 3)) + 2) - 1))/(-2(-1sin(3\u03c0((1(-1|(-3x^2 - 4x + 5) + 3| + 2) - 3)/(-3(-1|(-3x^2 - 4x + 5) + 3| + 2) - 3)) + 2) - 1) - 2) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "48", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -1|(-4(2sin(3\u03c0(-4(-4x - 3) + 4) - 3) - 1) + 3)| - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "708", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 2sin(1\u03c0(3(3(-1(-3|x - 3| - 3) - 3)^2 - 4(-1(-3|x - 3| - 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": "456", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 1|(-2(-3(-1cos(1\u03c0(3x^2 + 3x - 5) - 3)) - 3)^2 + 4(-3(-1cos(1\u03c0(3x^2 + 3x - 5) - 3)) - 3)) - 3| - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "344", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 2|((-1(1(3|(-2|x - 2| + 1) + 3| - 3)^2 - 3(3|(-2|x - 2| + 1) + 3| - 3) - 5))/(1(1(3|(-2|x - 2| + 1) + 3| - 3)^2 - 3(3|(-2|x - 2| + 1) + 3| - 3) - 5) + 3)) - 1| + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = -1((-2(-5(-3(2sin(2\u03c0x - 2)) + 1) - 2) + 2)/(-3(-5(-3(2sin(2\u03c0x - 2)) + 1) - 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) = -3sin(1\u03c0(-2(4(-1|((-2x)/(1x - 2))| + 1) - 1) - 5) + 3) - 3 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 total count of local extrema points for the function f(x) = (-1(1(3(-3(-2x^2 - 2x + 2)^2 - 4(-2x^2 - 2x + 2) + 3)^2 + 1)^2 + 1(3(-3(-2x^2 - 2x + 2)^2 - 4(-2x^2 - 2x + 2) + 3)^2 + 1) + 4) - 1)/(-3(1(3(-3(-2x^2 - 2x + 2)^2 - 4(-2x^2 - 2x + 2) + 3)^2 + 1)^2 + 1(3(-3(-2x^2 - 2x + 2)^2 - 4(-2x^2 - 2x + 2) + 3)^2 + 1) + 4) - 2) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "238", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 5((-2((-3(3cos(1\u03c0((1x - 1)/(1x)) - 3) - 3) + 3)/(2(3cos(1\u03c0((1x - 1)/(1x)) - 3) - 3) - 3)) + 1)/(2((-3(3cos(1\u03c0((1x - 1)/(1x)) - 3) - 3) + 3)/(2(3cos(1\u03c0((1x - 1)/(1x)) - 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": "19", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = (2(3(2(5(-3cos(2\u03c0x + 3) - 1) - 3)^2 + 2(5(-3cos(2\u03c0x + 3) - 1) - 3))^2 - 1(2(5(-3cos(2\u03c0x + 3) - 1) - 3)^2 + 2(5(-3cos(2\u03c0x + 3) - 1) - 3)) - 1) + 2)/(3(3(2(5(-3cos(2\u03c0x + 3) - 1) - 3)^2 + 2(5(-3cos(2\u03c0x + 3) - 1) - 3))^2 - 1(2(5(-3cos(2\u03c0x + 3) - 1) - 3)^2 + 2(5(-3cos(2\u03c0x + 3) - 1) - 3)) - 1)) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "77", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 5((-1(1cos(2\u03c0((-2(-5x^2 - 1x + 1) + 3)/(2(-5x^2 - 1x + 1) + 2)) - 2) + 3) + 2)/(2(1cos(2\u03c0((-2(-5x^2 - 1x + 1) + 3)/(2(-5x^2 - 1x + 1) + 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": "26", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 5(-2|(-1sin(1\u03c0((-2(-1x^2 - 5x - 3) + 1)/(1(-1x^2 - 5x - 3))) + 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": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -5(-1cos(2\u03c0(4(-2((2x)/(1x + 1)))^2 - 2(-2((2x)/(1x + 1))) + 2) + 2) + 3)^2 - 2(-1cos(2\u03c0(4(-2((2x)/(1x + 1)))^2 - 2(-2((2x)/(1x + 1))) + 2) + 2) + 3) + 5 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": "Determine the total count of local extrema points for the function f(x) = 3(-1((-3((3(-5x - 2))/(-2(-5x - 2))))/(-3((3(-5x - 2))/(-2(-5x - 2))) - 3)) + 3) + 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "191", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -2|(-4(2cos(1\u03c0(-1|((3x - 3)/(-1x - 2)) - 1| - 1) + 1) + 3)^2 - 4(2cos(1\u03c0(-1|((3x - 3)/(-1x - 2)) - 1| - 1) + 1) + 3) - 3) + 1| - 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 maxima for the function f(x) = 2(-2cos(1\u03c0(1((3(1x - 4) + 1)/(3(1x - 4) + 3)) - 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": "Find the number of local minimum points for f(x) = (2(-4(-4(-1|(3sin(2\u03c0x - 2) - 1) - 3|)^2 + 3(-1|(3sin(2\u03c0x - 2) - 1) - 3|))^2 + 2(-4(-1|(3sin(2\u03c0x - 2) - 1) - 3|)^2 + 3(-1|(3sin(2\u03c0x - 2) - 1) - 3|)) - 1) - 1)/(-2(-4(-4(-1|(3sin(2\u03c0x - 2) - 1) - 3|)^2 + 3(-1|(3sin(2\u03c0x - 2) - 1) - 3|))^2 + 2(-4(-1|(3sin(2\u03c0x - 2) - 1) - 3|)^2 + 3(-1|(3sin(2\u03c0x - 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": "20", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -3(3sin(1\u03c0(-2|(-4(1x + 3) - 1) - 1| + 1) - 3) - 1) - 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "81", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = 2(-1(3cos(1\u03c0((-1((-1x - 2)/(2x + 1)) - 1)/(-2((-1x - 2)/(2x + 1)) + 1)) + 2))^2 + 5(3cos(1\u03c0((-1((-1x - 2)/(2x + 1)) - 1)/(-2((-1x - 2)/(2x + 1)) + 1)) + 2)) + 4)^2 - 5(-1(3cos(1\u03c0((-1((-1x - 2)/(2x + 1)) - 1)/(-2((-1x - 2)/(2x + 1)) + 1)) + 2))^2 + 5(3cos(1\u03c0((-1((-1x - 2)/(2x + 1)) - 1)/(-2((-1x - 2)/(2x + 1)) + 1)) + 2)) + 4) - 4 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 maxima for the function f(x) = -1cos(2\u03c0(5(-2|((-2(-4x - 5) - 1)/(-2(-4x - 5))) + 2| + 2)^2 - 4(-2|((-2(-4x - 5) - 1)/(-2(-4x - 5))) + 2| + 2))) + 2 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 number of local maximum points for f(x) = -1(2e^(1(-2|(-1|(1x + 4) + 3|) + 2| - 3)) - 1)^2 + 4(2e^(1(-2|(-1|(1x + 4) + 3|) + 2| - 3)) - 1) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = 1|(3e^(-1(-4(-1(-2x - 4) + 4) - 4)) - 3) - 1| - 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 5((-1((2(1cos(2\u03c0((-3x + 1)/(1x - 2)) - 3)) - 1)/(-1(1cos(2\u03c0((-3x + 1)/(1x - 2)) - 3)) + 3)) - 3)/(2((2(1cos(2\u03c0((-3x + 1)/(1x - 2)) - 3)) - 1)/(-1(1cos(2\u03c0((-3x + 1)/(1x - 2)) - 3)) + 3)) - 3))^2 + 4((-1((2(1cos(2\u03c0((-3x + 1)/(1x - 2)) - 3)) - 1)/(-1(1cos(2\u03c0((-3x + 1)/(1x - 2)) - 3)) + 3)) - 3)/(2((2(1cos(2\u03c0((-3x + 1)/(1x - 2)) - 3)) - 1)/(-1(1cos(2\u03c0((-3x + 1)/(1x - 2)) - 3)) + 3)) - 3)) - 5 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) = -3(2(2(-2sin(1\u03c0((2x - 2)/(-2x + 3)) - 2) - 1)^2 - 5(-2sin(1\u03c0((2x - 2)/(-2x + 3)) - 2) - 1) + 5)^2 - 2(2(-2sin(1\u03c0((2x - 2)/(-2x + 3)) - 2) - 1)^2 - 5(-2sin(1\u03c0((2x - 2)/(-2x + 3)) - 2) - 1) + 5) + 4)^2 - 5(2(2(-2sin(1\u03c0((2x - 2)/(-2x + 3)) - 2) - 1)^2 - 5(-2sin(1\u03c0((2x - 2)/(-2x + 3)) - 2) - 1) + 5)^2 - 2(2(-2sin(1\u03c0((2x - 2)/(-2x + 3)) - 2) - 1)^2 - 5(-2sin(1\u03c0((2x - 2)/(-2x + 3)) - 2) - 1) + 5) + 4) - 4 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = (-3(1(-3cos(3\u03c0(-3((3x - 2)/(2x - 3))) - 2) + 2) - 4) + 3)/(-2(1(-3cos(3\u03c0(-3((3x - 2)/(2x - 3))) - 2) + 2) - 4) - 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 maxima does the function f(x) = 2(-1(-5((-2(-1cos(2\u03c0x - 1) + 1) + 2)/(3(-1cos(2\u03c0x - 1) + 1) + 3))^2 - 2((-2(-1cos(2\u03c0x - 1) + 1) + 2)/(3(-1cos(2\u03c0x - 1) + 1) + 3)) + 1)^2 + 1(-5((-2(-1cos(2\u03c0x - 1) + 1) + 2)/(3(-1cos(2\u03c0x - 1) + 1) + 3))^2 - 2((-2(-1cos(2\u03c0x - 1) + 1) + 2)/(3(-1cos(2\u03c0x - 1) + 1) + 3)) + 1) + 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": "How many local maxima does the function f(x) = 1|(-2sin(1\u03c0(1|(4(1x + 5)^2 - 3(1x + 5) - 5) + 2| + 1) - 2) - 3) - 3| + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "226", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -2(-1e^(-1(-3(1|(-1|x + 1| - 1) + 2| + 3)^2 - 5(1|(-1|x + 1| - 1) + 2| + 3) + 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 maxima for the function f(x) = (-3(-3e^(-2(-1|(-3((2x + 3)/(-1x)) + 5) - 3| - 1)) + 3) + 3)/(-3(-3e^(-2(-1|(-3((2x + 3)/(-1x)) + 5) - 3| - 1)) + 3) + 4) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -5(1|(1((1((3x + 3)/(-1x + 2)) + 3)/(-3((3x + 3)/(-1x + 2)) - 1))^2 + 2((1((3x + 3)/(-1x + 2)) + 3)/(-3((3x + 3)/(-1x + 2)) - 1)) - 5)|)^2 - 5(1|(1((1((3x + 3)/(-1x + 2)) + 3)/(-3((3x + 3)/(-1x + 2)) - 1))^2 + 2((1((3x + 3)/(-1x + 2)) + 3)/(-3((3x + 3)/(-1x + 2)) - 1)) - 5)|) + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = (1(1cos(3\u03c0(-1(-1(2x + 1) + 1) - 1) + 3) + 1) - 3)/(3(1cos(3\u03c0(-1(-1(2x + 1) + 1) - 1) + 3) + 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": "How many local extrema (minima and maxima combined) does the function f(x) = -3(1(4(3cos(1\u03c0(-5x^2 - 3x - 2) + 3) - 3)^2 - 4(3cos(1\u03c0(-5x^2 - 3x - 2) + 3) - 3))^2 - 4(4(3cos(1\u03c0(-5x^2 - 3x - 2) + 3) - 3)^2 - 4(3cos(1\u03c0(-5x^2 - 3x - 2) + 3) - 3)) + 3)^2 + 4(1(4(3cos(1\u03c0(-5x^2 - 3x - 2) + 3) - 3)^2 - 4(3cos(1\u03c0(-5x^2 - 3x - 2) + 3) - 3))^2 - 4(4(3cos(1\u03c0(-5x^2 - 3x - 2) + 3) - 3)^2 - 4(3cos(1\u03c0(-5x^2 - 3x - 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": "183", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -3(-3((1(-2((-3x + 1)/(-1x - 2))^2 + 1((-3x + 1)/(-1x - 2)) + 3) + 3)/(-3(-2((-3x + 1)/(-1x - 2))^2 + 1((-3x + 1)/(-1x - 2)) + 3) + 1))^2 + 1((1(-2((-3x + 1)/(-1x - 2))^2 + 1((-3x + 1)/(-1x - 2)) + 3) + 3)/(-3(-2((-3x + 1)/(-1x - 2))^2 + 1((-3x + 1)/(-1x - 2)) + 3) + 1)) - 2)^2 - 3(-3((1(-2((-3x + 1)/(-1x - 2))^2 + 1((-3x + 1)/(-1x - 2)) + 3) + 3)/(-3(-2((-3x + 1)/(-1x - 2))^2 + 1((-3x + 1)/(-1x - 2)) + 3) + 1))^2 + 1((1(-2((-3x + 1)/(-1x - 2))^2 + 1((-3x + 1)/(-1x - 2)) + 3) + 3)/(-3(-2((-3x + 1)/(-1x - 2))^2 + 1((-3x + 1)/(-1x - 2)) + 3) + 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": "Find the total number of local minima and maxima for f(x) = (-3((-2(-3(-1(-1sin(2\u03c0x - 3) - 3)^2 - 5(-1sin(2\u03c0x - 3) - 3) - 1)^2 + 3(-1(-1sin(2\u03c0x - 3) - 3)^2 - 5(-1sin(2\u03c0x - 3) - 3) - 1) + 3) + 3)/(-1(-3(-1(-1sin(2\u03c0x - 3) - 3)^2 - 5(-1sin(2\u03c0x - 3) - 3) - 1)^2 + 3(-1(-1sin(2\u03c0x - 3) - 3)^2 - 5(-1sin(2\u03c0x - 3) - 3) - 1) + 3) + 2)) + 3)/(3((-2(-3(-1(-1sin(2\u03c0x - 3) - 3)^2 - 5(-1sin(2\u03c0x - 3) - 3) - 1)^2 + 3(-1(-1sin(2\u03c0x - 3) - 3)^2 - 5(-1sin(2\u03c0x - 3) - 3) - 1) + 3) + 3)/(-1(-3(-1(-1sin(2\u03c0x - 3) - 3)^2 - 5(-1sin(2\u03c0x - 3) - 3) - 1)^2 + 3(-1(-1sin(2\u03c0x - 3) - 3)^2 - 5(-1sin(2\u03c0x - 3) - 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": "80", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = (-1(1cos(1\u03c0(-3|(-1((-1x + 1)/(-2x + 1))^2 - 1((-1x + 1)/(-2x + 1)) - 5) + 2| - 1) + 3) + 1) - 1)/(-1(1cos(1\u03c0(-3|(-1((-1x + 1)/(-2x + 1))^2 - 1((-1x + 1)/(-2x + 1)) - 5) + 2| - 1) + 3) + 1) - 2) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 1cos(2\u03c0(-5(2|(-5(4x - 4) - 4) + 1|)^2 + 4(2|(-5(4x - 4) - 4) + 1|) - 5) + 1) + 1 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": "Determine the count of local maxima for the function f(x) = -5(-4(-3(2|(4x + 1) - 1| - 2)^2 + 4) - 1)^2 + 3(-4(-3(2|(4x + 1) - 1| - 2)^2 + 4) - 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": "How many local extrema (minima and maxima combined) does the function f(x) = 1(-1((1(-2cos(3\u03c0(1x + 5) - 2) + 2) + 3)/(-3(-2cos(3\u03c0(1x + 5) - 2) + 2) + 4))^2 - 5((1(-2cos(3\u03c0(1x + 5) - 2) + 2) + 3)/(-3(-2cos(3\u03c0(1x + 5) - 2) + 2) + 4))) + 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 extrema (minima and maxima combined) does the function f(x) = 3sin(2\u03c0(-1(3(-2|(5x + 5) - 3| - 2)^2 + 4)^2 - 1(3(-2|(5x + 5) - 3| - 2)^2 + 4) - 2)) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -4(3(2(3(3sin(1\u03c0x))^2 - 4(3sin(1\u03c0x)) - 3)^2 + 2(3(3sin(1\u03c0x))^2 - 4(3sin(1\u03c0x)) - 3) + 5)^2 - 3(2(3(3sin(1\u03c0x))^2 - 4(3sin(1\u03c0x)) - 3)^2 + 2(3(3sin(1\u03c0x))^2 - 4(3sin(1\u03c0x)) - 3) + 5) - 3) - 5 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "76", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 1(2|(1cos(2\u03c0(-3(-1x^2 + 3x + 1) + 4) + 2) + 3) + 2| + 3)^2 - 2(2|(1cos(2\u03c0(-3(-1x^2 + 3x + 1) + 4) + 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": "474", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -3(3cos(1\u03c0(3((1((-3x + 2)/(-1x)) - 2)/(2((-3x + 2)/(-1x)) - 3)) + 5) - 3) + 1)^2 + 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -2|(1((2(-2cos(3\u03c0(2|x - 2| - 1) + 3) - 1))/(-2(-2cos(3\u03c0(2|x - 2| - 1) + 3) - 1) - 1))^2 - 3((2(-2cos(3\u03c0(2|x - 2| - 1) + 3) - 1))/(-2(-2cos(3\u03c0(2|x - 2| - 1) + 3) - 1) - 1)) + 4)| + 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "177", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -1(-1(-3cos(3\u03c0((1(3x - 4) + 2)/(1(3x - 4)))) + 1)^2 + 1(-3cos(3\u03c0((1(3x - 4) + 2)/(1(3x - 4)))) + 1) + 3) + 4 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 extrema (minima and maxima combined) does the function f(x) = 1|(-4(4(-4(-1|x - 2| + 1)^2 + 5(-1|x - 2| + 1) + 3) - 4) + 2)| - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 5(4((3(3|(3x^2 - 4x - 2)|) - 1)/(-3(3|(3x^2 - 4x - 2)|) - 3))^2 - 1((3(3|(3x^2 - 4x - 2)|) - 1)/(-3(3|(3x^2 - 4x - 2)|) - 3)) - 3)^2 - 4(4((3(3|(3x^2 - 4x - 2)|) - 1)/(-3(3|(3x^2 - 4x - 2)|) - 3))^2 - 1((3(3|(3x^2 - 4x - 2)|) - 1)/(-3(3|(3x^2 - 4x - 2)|) - 3)) - 3) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = -3|(1cos(3\u03c0(2|(-5(1x + 2)^2 + 3(1x + 2) - 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": "242", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 4(-4(-3cos(3\u03c0(1|((3x + 3)/(-2x + 3)) - 3| + 3) - 2) - 2)^2 - 3(-3cos(3\u03c0(1|((3x + 3)/(-2x + 3)) - 3| + 3) - 2) - 2) - 2)^2 - 3(-4(-3cos(3\u03c0(1|((3x + 3)/(-2x + 3)) - 3| + 3) - 2) - 2)^2 - 3(-3cos(3\u03c0(1|((3x + 3)/(-2x + 3)) - 3| + 3) - 2) - 2) - 2) + 5 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "77", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 2|(-2cos(3\u03c0(-2|(-2|(1x^2 + 5x + 3) - 2| - 3) - 1| + 3)) - 3)| - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "512", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -2|(-2(4(-2sin(1\u03c0(3|x + 3| - 1) - 2) + 1) + 4) + 1) + 3| + 2 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) = 1(-3sin(1\u03c0((1(-5((2x + 3)/(2x - 1)) - 4) + 3)/(2(-5((2x + 3)/(2x - 1)) - 4) + 2)) - 3))^2 - 4(-3sin(1\u03c0((1(-5((2x + 3)/(2x - 1)) - 4) + 3)/(2(-5((2x + 3)/(2x - 1)) - 4) + 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) = -5(3cos(3\u03c0(1(3((-2x - 2)/(3x - 1))^2 + 5((-2x - 2)/(3x - 1)) - 4)^2 - 1(3((-2x - 2)/(3x - 1))^2 + 5((-2x - 2)/(3x - 1)) - 4) - 3) + 2) + 2) - 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "68", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 1sin(1\u03c0(-3|(1(-4((-3x)/(1x + 3))^2 + 2((-3x)/(1x + 3)) - 3) + 3) - 1| - 3) + 3) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "163", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 1|(-3(-3|(2|(-2cos(2\u03c0x - 2) - 3) + 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": "100", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = 1|(3((-1(-2sin(1\u03c0((2x + 1)/(-1x - 2)) + 3) - 1) - 2)/(2(-2sin(1\u03c0((2x + 1)/(-1x - 2)) + 3) - 1) + 2)) + 5) - 1| - 1 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) = -3e^(-2(1|((1(4(-2|x + 1| + 2) + 4) + 1)/(1(4(-2|x + 1| + 2) + 4) + 3))| - 2)) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = (-2(1(3cos(1\u03c0((2(-3x^2 + 3x + 2) + 3)/(1(-3x^2 + 3x + 2))) + 1) + 2)^2 + 3(3cos(1\u03c0((2(-3x^2 + 3x + 2) + 3)/(1(-3x^2 + 3x + 2))) + 1) + 2) + 3))/(2(1(3cos(1\u03c0((2(-3x^2 + 3x + 2) + 3)/(1(-3x^2 + 3x + 2))) + 1) + 2)^2 + 3(3cos(1\u03c0((2(-3x^2 + 3x + 2) + 3)/(1(-3x^2 + 3x + 2))) + 1) + 2) + 3) + 3) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -3(3((-3(-4(-2x^2 - 4x - 1)^2 + 4(-2x^2 - 4x - 1) + 1) - 1)/(-2(-4(-2x^2 - 4x - 1)^2 + 4(-2x^2 - 4x - 1) + 1)))^2 + 5((-3(-4(-2x^2 - 4x - 1)^2 + 4(-2x^2 - 4x - 1) + 1) - 1)/(-2(-4(-2x^2 - 4x - 1)^2 + 4(-2x^2 - 4x - 1) + 1))) - 2)^2 + 2(3((-3(-4(-2x^2 - 4x - 1)^2 + 4(-2x^2 - 4x - 1) + 1) - 1)/(-2(-4(-2x^2 - 4x - 1)^2 + 4(-2x^2 - 4x - 1) + 1)))^2 + 5((-3(-4(-2x^2 - 4x - 1)^2 + 4(-2x^2 - 4x - 1) + 1) - 1)/(-2(-4(-2x^2 - 4x - 1)^2 + 4(-2x^2 - 4x - 1) + 1))) - 2) - 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -1|((1(-1cos(2\u03c0(5((1x + 3)/(3x + 3))^2 + 5((1x + 3)/(3x + 3)) + 5) + 2) - 3))/(2(-1cos(2\u03c0(5((1x + 3)/(3x + 3))^2 + 5((1x + 3)/(3x + 3)) + 5) + 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": "41", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = (3(1((1(3(-1|x - 1|)^2 + 3(-1|x - 1|) - 2) - 3)/(-1(3(-1|x - 1|)^2 + 3(-1|x - 1|) - 2) - 1))^2 + 2((1(3(-1|x - 1|)^2 + 3(-1|x - 1|) - 2) - 3)/(-1(3(-1|x - 1|)^2 + 3(-1|x - 1|) - 2) - 1)) - 3) + 1)/(-2(1((1(3(-1|x - 1|)^2 + 3(-1|x - 1|) - 2) - 3)/(-1(3(-1|x - 1|)^2 + 3(-1|x - 1|) - 2) - 1))^2 + 2((1(3(-1|x - 1|)^2 + 3(-1|x - 1|) - 2) - 3)/(-1(3(-1|x - 1|)^2 + 3(-1|x - 1|) - 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": "Determine the count of local minima for the function f(x) = -4(-2sin(1\u03c0(1|(-1|((1x + 3)/(2x - 1)) - 2| + 3) - 2| + 3) + 2))^2 - 2(-2sin(1\u03c0(1|(-1|((1x + 3)/(2x - 1)) - 2| + 3) - 2| + 3) + 2)) - 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": "Determine the total count of local extrema points for the function f(x) = 5(1|(1(1cos(1\u03c0((3x - 2)/(3x - 1))) + 2) - 1)| + 1)^2 + 3(1|(1(1cos(1\u03c0((3x - 2)/(3x - 1))) + 2) - 1)| + 1) + 4 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|(-3|(-3sin(2\u03c0(-4(-5x^2 - 4) + 2) + 2) + 2) + 2| + 3) - 1| + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "230", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 5(-5(1(-1cos(2\u03c0((-3x + 1)/(1x)) + 1) - 3)^2 + 2(-1cos(2\u03c0((-3x + 1)/(1x)) + 1) - 3) - 5)^2 - 5(1(-1cos(2\u03c0((-3x + 1)/(1x)) + 1) - 3)^2 + 2(-1cos(2\u03c0((-3x + 1)/(1x)) + 1) - 3) - 5) + 4)^2 + 5(-5(1(-1cos(2\u03c0((-3x + 1)/(1x)) + 1) - 3)^2 + 2(-1cos(2\u03c0((-3x + 1)/(1x)) + 1) - 3) - 5)^2 - 5(1(-1cos(2\u03c0((-3x + 1)/(1x)) + 1) - 3)^2 + 2(-1cos(2\u03c0((-3x + 1)/(1x)) + 1) - 3) - 5) + 4) + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "25", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -1|(-4((-1(-3(3sin(1\u03c0x + 3) + 2) + 1) + 2)/(-1(-3(3sin(1\u03c0x + 3) + 2) + 1) - 3))^2 + 1((-1(-3(3sin(1\u03c0x + 3) + 2) + 1) + 2)/(-1(-3(3sin(1\u03c0x + 3) + 2) + 1) - 3)) + 5) - 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": "How many local minima does the function f(x) = -1|((1(2sin(2\u03c0((-1(-3x - 3) - 2)/(3(-3x - 3) + 3)) + 2) + 2))/(-2(2sin(2\u03c0((-1(-3x - 3) - 2)/(3(-3x - 3) + 3)) + 2) + 2) + 3)) - 1| - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = 3((2(3(3sin(3\u03c0(-4x) + 3) - 1) + 3))/(-3(3(3sin(3\u03c0(-4x) + 3) - 1) + 3) - 3))^2 - 5((2(3(3sin(3\u03c0(-4x) + 3) - 1) + 3))/(-3(3(3sin(3\u03c0(-4x) + 3) - 1) + 3) - 3)) - 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": "Determine the count of local maxima for the function f(x) = 3|(-1|(-2(-1(4x - 2)^2 - 1(4x - 2) + 4)^2 - 2) + 3| - 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": "Find the number of local maximum points for f(x) = -2e^(2((2(-1(1((1x - 1)/(1x - 3))^2 - 3)^2 - 1(1((1x - 1)/(1x - 3))^2 - 3) - 1) - 1)/(-1(-1(1((1x - 1)/(1x - 3))^2 - 3)^2 - 1(1((1x - 1)/(1x - 3))^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": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = (1(-4(-2|(2cos(3\u03c0(-3|x - 2| + 2) + 2) - 1) - 2| + 1) - 3))/(1(-4(-2|(2cos(3\u03c0(-3|x - 2| + 2) + 2) - 1) - 2| + 1) - 3) + 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "109", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 3|(-3(-3(3(-5x^2 - 4x + 4)^2 + 1(-5x^2 - 4x + 4) - 1) - 1) - 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": "Determine the total count of local extrema points for the function f(x) = 1sin(2\u03c0(-3|(1(3|((-3x - 3)/(1x - 3)) + 1| - 2)^2 - 4(3|((-3x - 3)/(1x - 3)) + 1| - 2) - 1) - 2| - 2) - 1) + 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "386", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 2sin(1\u03c0(-3|((2(-1(-5x)) + 1)/(2(-1(-5x)) + 3)) + 1| - 3)) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 1(1|(2|(-2|(1cos(1\u03c0x - 1) + 1)| + 1) - 1| + 1)| - 2) + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = 2cos(2\u03c0((-3(3(1|((-1x - 2)/(-2x - 2))| - 1) + 4))/(-3(3(1|((-1x - 2)/(-2x - 2))| - 1) + 4) + 4)) + 2) + 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 minimum points for f(x) = -3(-5(3(-3|(-1sin(2\u03c0x + 3) + 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": "20", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -3(1sin(2\u03c0(-1(-3|(-5x + 2) + 3| + 3)^2 - 4(-3|(-5x + 2) + 3| + 3) - 4) - 3) + 1) + 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "313", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = 3|(-3|(1cos(1\u03c0((3((2x - 1)/(-2x + 3)) + 3)/(-2((2x - 1)/(-2x + 3)) + 3)) - 2) - 3)| - 3)| + 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = 2((-2(1(3sin(2\u03c0(3x + 4) + 1) + 2)^2 - 2(3sin(2\u03c0(3x + 4) + 1) + 2) + 5) + 3)/(1(1(3sin(2\u03c0(3x + 4) + 1) + 2)^2 - 2(3sin(2\u03c0(3x + 4) + 1) + 2) + 5) + 1)) + 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": "How many local maxima does the function f(x) = 1|((-2(3((-2(-1cos(2\u03c0x + 3) - 3) + 1)/(3(-1cos(2\u03c0x + 3) - 3) + 2))^2 - 3((-2(-1cos(2\u03c0x + 3) - 3) + 1)/(3(-1cos(2\u03c0x + 3) - 3) + 2)) + 2) + 3)/(-1(3((-2(-1cos(2\u03c0x + 3) - 3) + 1)/(3(-1cos(2\u03c0x + 3) - 3) + 2))^2 - 3((-2(-1cos(2\u03c0x + 3) - 3) + 1)/(3(-1cos(2\u03c0x + 3) - 3) + 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": "20", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = (-1(-2cos(3\u03c0(-3|(-1|((3x + 1)/(2x + 1)) - 2| - 2)| - 1) - 1)) + 1)/(3(-2cos(3\u03c0(-3|(-1|((3x + 1)/(2x + 1)) - 2| - 2)| - 1) - 1)) + 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 3(-2cos(3\u03c0(-2(1((1x)/(-3x + 2)) + 2)^2 + 4(1((1x)/(-3x + 2)) + 2) + 3) - 1) - 1)^2 + 3(-2cos(3\u03c0(-2(1((1x)/(-3x + 2)) + 2)^2 + 4(1((1x)/(-3x + 2)) + 2) + 3) - 1) - 1) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -1(4((2((-1(-1cos(3\u03c0x - 3) - 1) - 3)/(2(-1cos(3\u03c0x - 3) - 1) - 1)) - 3)/(1((-1(-1cos(3\u03c0x - 3) - 1) - 3)/(2(-1cos(3\u03c0x - 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": "120", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -1sin(1\u03c0(-3|((3(-2|(1x^2 - 5x - 5) - 3|) + 3)/(2(-2|(1x^2 - 5x - 5) - 3|) - 3)) + 1| - 3) + 3) + 2 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) = (-1((-3(-1|(-3(-1x - 2) + 5) - 3| - 3))/(-2(-1|(-3(-1x - 2) + 5) - 3| - 3))) - 1)/(-2((-3(-1|(-3(-1x - 2) + 5) - 3| - 3))/(-2(-1|(-3(-1x - 2) + 5) - 3| - 3)))) 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": "Determine the count of local minima for the function f(x) = (-2((3(4(-4(-1cos(3\u03c0x + 3) - 2) - 3) + 4))/(-1(4(-4(-1cos(3\u03c0x + 3) - 2) - 3) + 4) - 2)) - 2)/(3((3(4(-4(-1cos(3\u03c0x + 3) - 2) - 3) + 4))/(-1(4(-4(-1cos(3\u03c0x + 3) - 2) - 3) + 4) - 2)) - 2) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -5(1|((-1(2sin(3\u03c0(-4x^2 + 5x + 4) - 2) - 3) + 1)/(3(2sin(3\u03c0(-4x^2 + 5x + 4) - 2) - 3) - 2)) - 1|)^2 + 5(1|((-1(2sin(3\u03c0(-4x^2 + 5x + 4) - 2) - 3) + 1)/(3(2sin(3\u03c0(-4x^2 + 5x + 4) - 2) - 3) - 2)) - 1|) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "357", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 1|(-3sin(2\u03c0(3((2(1|x - 2| - 2) - 2)/(2(1|x - 2| - 2) + 3)) - 4) - 1) + 1) - 2| - 2 have 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 extrema (minima and maxima combined) does the function f(x) = 4(3(-5(1cos(1\u03c0((3x - 2)/(1x + 2)) - 3) + 3)^2 - 1(1cos(1\u03c0((3x - 2)/(1x + 2)) - 3) + 3) - 2)^2 - 1(-5(1cos(1\u03c0((3x - 2)/(1x + 2)) - 3) + 3)^2 - 1(1cos(1\u03c0((3x - 2)/(1x + 2)) - 3) + 3) - 2) - 4)^2 + 1(3(-5(1cos(1\u03c0((3x - 2)/(1x + 2)) - 3) + 3)^2 - 1(1cos(1\u03c0((3x - 2)/(1x + 2)) - 3) + 3) - 2)^2 - 1(-5(1cos(1\u03c0((3x - 2)/(1x + 2)) - 3) + 3)^2 - 1(1cos(1\u03c0((3x - 2)/(1x + 2)) - 3) + 3) - 2) - 4) + 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": "Determine the total count of local extrema points for the function f(x) = -2sin(3\u03c0(-5(1(1(1|x + 3| - 1) + 3)^2 + 1(1(1|x + 3| - 1) + 3) + 2) + 1)) - 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "493", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -2|(1cos(1\u03c0(-1|(-1(1x - 4)^2 - 5(1x - 4) + 5) - 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": "207", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 2|(3|(-1(2((1x)/(-2x - 2))^2 - 5((1x)/(-2x - 2)) - 4)^2 - 5(2((1x)/(-2x - 2))^2 - 5((1x)/(-2x - 2)) - 4) + 5) + 3| + 3) - 2| - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -1|(-1(-3(-2sin(2\u03c0(-5x - 5) + 3) + 2)^2 - 3(-2sin(2\u03c0(-5x - 5) + 3) + 2) - 4)^2 - 3(-3(-2sin(2\u03c0(-5x - 5) + 3) + 2)^2 - 3(-2sin(2\u03c0(-5x - 5) + 3) + 2) - 4)) + 3| 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 minima does the function f(x) = (-2(-2(-1|(-3sin(2\u03c0((1x + 1)/(1x - 2)) - 1) + 3) - 3| - 1) - 3))/(-2(-2(-1|(-3sin(2\u03c0((1x + 1)/(1x - 2)) - 1) + 3) - 3| - 1) - 3) + 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "48", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = 5(3(-1sin(3\u03c0(-5(5x^2 + 1x + 5) + 2) + 1) + 1)^2 + 4(-1sin(3\u03c0(-5(5x^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": "212", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -2sin(3\u03c0((2(-1|(1(-1|x - 3| - 3) + 1) + 1| + 1))/(3(-1|(1(-1|x - 3| - 3) + 1) + 1| + 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": "How many local maxima does the function f(x) = 1((-3(4(-1(2x + 1)^2 + 4(2x + 1) + 2)^2 + 2(-1(2x + 1)^2 + 4(2x + 1) + 2) - 1))/(3(4(-1(2x + 1)^2 + 4(2x + 1) + 2)^2 + 2(-1(2x + 1)^2 + 4(2x + 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": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 1(1((-1(2|(-3x + 4)| - 2) - 2)/(-3(2|(-3x + 4)| - 2) + 2))^2 - 5((-1(2|(-3x + 4)| - 2) - 2)/(-3(2|(-3x + 4)| - 2) + 2)) - 3) - 4 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = (1((3(4(4(-2cos(1\u03c0x + 3) - 1)^2 - 1(-2cos(1\u03c0x + 3) - 1) + 3) + 3) + 1)/(3(4(4(-2cos(1\u03c0x + 3) - 1)^2 - 1(-2cos(1\u03c0x + 3) - 1) + 3) + 3) - 1)))/(-1((3(4(4(-2cos(1\u03c0x + 3) - 1)^2 - 1(-2cos(1\u03c0x + 3) - 1) + 3) + 3) + 1)/(3(4(4(-2cos(1\u03c0x + 3) - 1)^2 - 1(-2cos(1\u03c0x + 3) - 1) + 3) + 3) - 1)) - 1) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 1sin(2\u03c0(3(4((2(-3x + 4))/(2(-3x + 4) - 1)) + 5)^2 + 5(4((2(-3x + 4))/(2(-3x + 4) - 1)) + 5) + 3) - 3) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "163", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -2sin(3\u03c0(-3|(4((1(-1x^2 - 1x + 4))/(-3(-1x^2 - 1x + 4) - 2))^2 - 2((1(-1x^2 - 1x + 4))/(-3(-1x^2 - 1x + 4) - 2)) + 4) - 3| - 3) + 3) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "57", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = (-2(2((1(-2(1sin(3\u03c0x + 1))) - 1)/(2(-2(1sin(3\u03c0x + 1))) + 2))^2 - 5((1(-2(1sin(3\u03c0x + 1))) - 1)/(2(-2(1sin(3\u03c0x + 1))) + 2)) + 3) + 1)/(1(2((1(-2(1sin(3\u03c0x + 1))) - 1)/(2(-2(1sin(3\u03c0x + 1))) + 2))^2 - 5((1(-2(1sin(3\u03c0x + 1))) - 1)/(2(-2(1sin(3\u03c0x + 1))) + 2)) + 3) - 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -2(-2(1|((-3(1x^2 + 1x - 2) - 3)/(-2(1x^2 + 1x - 2) + 1)) + 1| - 3)^2 - 1(1|((-3(1x^2 + 1x - 2) - 3)/(-2(1x^2 + 1x - 2) + 1)) + 1| - 3) - 3)^2 + 1(-2(1|((-3(1x^2 + 1x - 2) - 3)/(-2(1x^2 + 1x - 2) + 1)) + 1| - 3)^2 - 1(1|((-3(1x^2 + 1x - 2) - 3)/(-2(1x^2 + 1x - 2) + 1)) + 1| - 3) - 3) - 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = (3((2((-1((-2(-1sin(1\u03c0x - 1)) + 2)/(-3(-1sin(1\u03c0x - 1)) - 3)) - 2)/(2((-2(-1sin(1\u03c0x - 1)) + 2)/(-3(-1sin(1\u03c0x - 1)) - 3)))) + 1)/(2((-1((-2(-1sin(1\u03c0x - 1)) + 2)/(-3(-1sin(1\u03c0x - 1)) - 3)) - 2)/(2((-2(-1sin(1\u03c0x - 1)) + 2)/(-3(-1sin(1\u03c0x - 1)) - 3)))) + 3)) + 1)/(3((2((-1((-2(-1sin(1\u03c0x - 1)) + 2)/(-3(-1sin(1\u03c0x - 1)) - 3)) - 2)/(2((-2(-1sin(1\u03c0x - 1)) + 2)/(-3(-1sin(1\u03c0x - 1)) - 3)))) + 1)/(2((-1((-2(-1sin(1\u03c0x - 1)) + 2)/(-3(-1sin(1\u03c0x - 1)) - 3)) - 2)/(2((-2(-1sin(1\u03c0x - 1)) + 2)/(-3(-1sin(1\u03c0x - 1)) - 3)))) + 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) = -4(2sin(2\u03c0(-2|(-3|(-2|x + 2| - 2) + 2| - 3) + 2| - 1) - 3) + 2) + 5 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 extrema (minima and maxima combined) does the function f(x) = -3sin(3\u03c0(3(-3(-5((3x)/(-2x - 2))^2 - 2((3x)/(-2x - 2)) - 1)^2 - 5(-5((3x)/(-2x - 2))^2 - 2((3x)/(-2x - 2)) - 1) - 3)^2 - 1(-3(-5((3x)/(-2x - 2))^2 - 2((3x)/(-2x - 2)) - 1)^2 - 5(-5((3x)/(-2x - 2))^2 - 2((3x)/(-2x - 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": "58", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -5(2(-5(-2e^(-2(-3x - 4)) - 3)^2 - 4(-2e^(-2(-3x - 4)) - 3) + 3) + 3)^2 - 2(2(-5(-2e^(-2(-3x - 4)) - 3)^2 - 4(-2e^(-2(-3x - 4)) - 3) + 3) + 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": "Determine the count of local minima for the function f(x) = (-2((1(3(3(3sin(1\u03c0x - 1) + 1) + 2) + 4) - 1)/(-3(3(3(3sin(1\u03c0x - 1) + 1) + 2) + 4) - 1)) + 3)/(-2((1(3(3(3sin(1\u03c0x - 1) + 1) + 2) + 4) - 1)/(-3(3(3(3sin(1\u03c0x - 1) + 1) + 2) + 4) - 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) = 4((-2(-1|(2(-2|x - 3| + 2) + 2) - 1| + 2))/(-1(-1|(2(-2|x - 3| + 2) + 2) - 1| + 2) - 2))^2 + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 4((-2(-1(-3cos(2\u03c0((-2x - 1)/(1x - 2)) - 3))^2 - 3(-3cos(2\u03c0((-2x - 1)/(1x - 2)) - 3)) + 4) - 3)/(2(-1(-3cos(2\u03c0((-2x - 1)/(1x - 2)) - 3))^2 - 3(-3cos(2\u03c0((-2x - 1)/(1x - 2)) - 3)) + 4) - 1))^2 - 3((-2(-1(-3cos(2\u03c0((-2x - 1)/(1x - 2)) - 3))^2 - 3(-3cos(2\u03c0((-2x - 1)/(1x - 2)) - 3)) + 4) - 3)/(2(-1(-3cos(2\u03c0((-2x - 1)/(1x - 2)) - 3))^2 - 3(-3cos(2\u03c0((-2x - 1)/(1x - 2)) - 3)) + 4) - 1)) - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "51", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -1|(-3(-1sin(2\u03c0(1(-2|x - 1| - 1) - 2) + 2) + 2) + 5) - 3| + 1 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": "Determine the count of local maxima for the function f(x) = -4((-3(2sin(3\u03c0(3(5x^2 - 1x + 4) - 5) + 1) - 1) - 2)/(-2(2sin(3\u03c0(3(5x^2 - 1x + 4) - 5) + 1) - 1) + 3)) - 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "57", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 3(-4(-4(-3sin(1\u03c0(-3|x - 3| + 2) + 3) - 2) - 3)^2 - 1)^2 + 5(-4(-4(-3sin(1\u03c0(-3|x - 3| + 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": "51", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 1(3(-1|(1|(1cos(1\u03c0x - 3) + 3) + 3| + 1) + 1| + 1) - 5) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = 2(2(-4(2cos(2\u03c0(3|x + 3| - 1) + 1) + 1) - 4) + 4) - 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) = -3((2((-3(-3|(3x - 2) - 2| + 1) - 3)/(-2(-3|(3x - 2) - 2| + 1))) - 3)/(2((-3(-3|(3x - 2) - 2| + 1) - 3)/(-2(-3|(3x - 2) - 2| + 1))) + 2))^2 - 5((2((-3(-3|(3x - 2) - 2| + 1) - 3)/(-2(-3|(3x - 2) - 2| + 1))) - 3)/(2((-3(-3|(3x - 2) - 2| + 1) - 3)/(-2(-3|(3x - 2) - 2| + 1))) + 2)) - 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = (3(3|(1(2cos(1\u03c0(-5x + 2) + 3)) - 2) + 2| - 2) + 1)/(-2(3|(1(2cos(1\u03c0(-5x + 2) + 3)) - 2) + 2| - 2) + 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": "Determine the total count of local extrema points for the function f(x) = 2sin(3\u03c0(-1(3((1(-2|x + 2| + 2) - 2)/(-3(-2|x + 2| + 2) + 2))^2 + 3((1(-2|x + 2| + 2) - 2)/(-3(-2|x + 2| + 2) + 2)) - 2) + 2) + 2) + 3 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 total count of local extrema points for the function f(x) = (-1((2(1(-4(-2e^(1x) + 1)^2 + 4)^2 + 4(-4(-2e^(1x) + 1)^2 + 4) + 3) - 2)/(1(1(-4(-2e^(1x) + 1)^2 + 4)^2 + 4(-4(-2e^(1x) + 1)^2 + 4) + 3) + 2)) - 1)/(2((2(1(-4(-2e^(1x) + 1)^2 + 4)^2 + 4(-4(-2e^(1x) + 1)^2 + 4) + 3) - 2)/(1(1(-4(-2e^(1x) + 1)^2 + 4)^2 + 4(-4(-2e^(1x) + 1)^2 + 4) + 3) + 2))) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -5(1|(-1(-3|(2cos(2\u03c0x + 2) + 2) - 3|) - 3) - 3| + 1)^2 + 2(1|(-1(-3|(2cos(2\u03c0x + 2) + 2) - 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": "89", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = (3(-1sin(3\u03c0(1|((2(-2|x - 2| + 2) - 1)/(-2(-2|x - 2| + 2) - 1))|) - 1) + 2) - 1)/(-1(-1sin(3\u03c0(1|((2(-2|x - 2| + 2) - 1)/(-2(-2|x - 2| + 2) - 1))|) - 1) + 2) + 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 total count of local extrema points for the function f(x) = -2(-1|(-4(-3|(3x^2 - 2x)| + 3)^2 - 3(-3|(3x^2 - 2x)| + 3) - 1) - 2| - 1) - 4 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -1(-2|(-2sin(3\u03c0(2(-3|x - 3| - 3)^2 - 2(-3|x - 3| - 3) + 5)))| + 3) + 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "430", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 1|((-2((3(-2sin(2\u03c0((-2x - 2)/(-3x + 1)) - 3) + 3) - 3)/(2(-2sin(2\u03c0((-2x - 2)/(-3x + 1)) - 3) + 3) - 1)) + 3)/(2((3(-2sin(2\u03c0((-2x - 2)/(-3x + 1)) - 3) + 3) - 3)/(2(-2sin(2\u03c0((-2x - 2)/(-3x + 1)) - 3) + 3) - 1)) + 1)) + 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 number of local maximum points for f(x) = (1((3(-1|(1(-2e^(2x) + 3)^2 + 4(-2e^(2x) + 3) - 4) + 2| - 2))/(-2(-1|(1(-2e^(2x) + 3)^2 + 4(-2e^(2x) + 3) - 4) + 2| - 2) + 1)) + 1)/(-1((3(-1|(1(-2e^(2x) + 3)^2 + 4(-2e^(2x) + 3) - 4) + 2| - 2))/(-2(-1|(1(-2e^(2x) + 3)^2 + 4(-2e^(2x) + 3) - 4) + 2| - 2) + 1))) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 1(3(2|(-3cos(1\u03c0((1x)/(1x - 3)) + 2) - 2) + 3| - 2)^2 + 3(2|(-3cos(1\u03c0((1x)/(1x - 3)) + 2) - 2) + 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": "How many local maxima does the function f(x) = 3|(1|(5(-1e^(-2(-2|x - 3| + 3)) + 2)^2 + 3) - 3| - 3) - 2| have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 1((3(-2sin(2\u03c0(2(-1|x + 2| + 2) - 2) + 2) + 3) + 1)/(-1(-2sin(2\u03c0(2(-1|x + 2| + 2) - 2) + 2) + 3))) - 3 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) = -4(3((2(3e^(2(-2|x + 1| - 2)) - 3) - 3)/(2(3e^(2(-2|x + 1| - 2)) - 3) - 1))^2 + 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -1(-1(4(3(4x^2 - 3x - 3)^2 + 3(4x^2 - 3x - 3) - 1)^2 + 3(3(4x^2 - 3x - 3)^2 + 3(4x^2 - 3x - 3) - 1) + 2))^2 - 2(-1(4(3(4x^2 - 3x - 3)^2 + 3(4x^2 - 3x - 3) - 1)^2 + 3(3(4x^2 - 3x - 3)^2 + 3(4x^2 - 3x - 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 minima does the function f(x) = -1(-2(-1(1sin(2\u03c0(1|x| - 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": "20", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 2sin(3\u03c0(-5(3(-1((-3x + 1)/(-2x - 2))^2 - 2)^2 + 5(-1((-3x + 1)/(-2x - 2))^2 - 2) - 4)^2 + 4(3(-1((-3x + 1)/(-2x - 2))^2 - 2)^2 + 5(-1((-3x + 1)/(-2x - 2))^2 - 2) - 4) + 2) - 1) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "148", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -3((-3(-2cos(1\u03c0(3|(-3x^2 + 1x - 1) - 1|) - 2) - 1))/(3(-2cos(1\u03c0(3|(-3x^2 + 1x - 1) - 1|) - 2) - 1) - 1))^2 - 3((-3(-2cos(1\u03c0(3|(-3x^2 + 1x - 1) - 1|) - 2) - 1))/(3(-2cos(1\u03c0(3|(-3x^2 + 1x - 1) - 1|) - 2) - 1) - 1)) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "489", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = -3(-2sin(1\u03c0(-2|(-1(-5x - 2)^2 + 1(-5x - 2) + 3) - 2|)) - 3)^2 + 3(-2sin(1\u03c0(-2|(-1(-5x - 2)^2 + 1(-5x - 2) + 3) - 2|)) - 3) + 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "167", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -3|(-2sin(2\u03c0(-3|((3(-2x + 1))/(2(-2x + 1) - 1)) - 1| - 1) + 1) + 1) + 3| - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 2(-4(2|(4(-2x^2 + 3x + 1) - 5) - 1|)^2 + 5(2|(4(-2x^2 + 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": "7", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -1|(2(-4((1(3cos(1\u03c0x) - 3) - 2)/(1(3cos(1\u03c0x) - 3) + 3))^2 + 2((1(3cos(1\u03c0x) - 3) - 2)/(1(3cos(1\u03c0x) - 3) + 3)) - 5) - 1) + 2| 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) = -4(1|(-2cos(2\u03c0(2|(-3x - 4)| - 3) - 2) - 2) + 1| + 3) - 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = (-2(3(2(1(2sin(3\u03c0x + 3) + 1) - 1)^2 + 3(1(2sin(3\u03c0x + 3) + 1) - 1) + 1)^2 + 5(2(1(2sin(3\u03c0x + 3) + 1) - 1)^2 + 3(1(2sin(3\u03c0x + 3) + 1) - 1) + 1) + 1) - 2)/(2(3(2(1(2sin(3\u03c0x + 3) + 1) - 1)^2 + 3(1(2sin(3\u03c0x + 3) + 1) - 1) + 1)^2 + 5(2(1(2sin(3\u03c0x + 3) + 1) - 1)^2 + 3(1(2sin(3\u03c0x + 3) + 1) - 1) + 1) + 1) - 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 total count of local extrema points for the function f(x) = -1((1(-3|(-2(-3|x + 2| + 3)^2 - 5(-3|x + 2| + 3) - 5) + 3| + 1))/(-2(-3|(-2(-3|x + 2| + 3)^2 - 5(-3|x + 2| + 3) - 5) + 3| + 1) + 3))^2 + 1((1(-3|(-2(-3|x + 2| + 3)^2 - 5(-3|x + 2| + 3) - 5) + 3| + 1))/(-2(-3|(-2(-3|x + 2| + 3)^2 - 5(-3|x + 2| + 3) - 5) + 3| + 1) + 3)) + 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -1(1sin(3\u03c0((2(-2(-2x) - 1) - 3)/(1(-2(-2x) - 1))) + 1) - 1) + 4 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) = -3((-3(-5((-2(-4x^2 - 5x + 3) - 1)/(2(-4x^2 - 5x + 3) + 2))^2 - 3((-2(-4x^2 - 5x + 3) - 1)/(2(-4x^2 - 5x + 3) + 2)) + 3) + 2)/(1(-5((-2(-4x^2 - 5x + 3) - 1)/(2(-4x^2 - 5x + 3) + 2))^2 - 3((-2(-4x^2 - 5x + 3) - 1)/(2(-4x^2 - 5x + 3) + 2)) + 3) - 2)) + 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 number of local minimum points for f(x) = -1|((-2(1|((1(1x^2 - 3x - 5) - 1)/(1(1x^2 - 3x - 5) - 3)) - 2| - 1))/(-2(1|((1(1x^2 - 3x - 5) - 1)/(1(1x^2 - 3x - 5) - 3)) - 2| - 1) + 3)) - 2| - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -4(-1(-3sin(3\u03c0(-3(-1x - 4) + 4) - 2) + 1) + 3) + 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 extrema (minima and maxima combined) does the function f(x) = 2sin(2\u03c0(-2|(-4(-4(3x^2 - 3x + 2) - 5)^2 - 3(-4(3x^2 - 3x + 2) - 5) - 2) - 1| + 2) - 3) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "59", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 1(3sin(2\u03c0(3(1((3x)/(2x - 1))^2 + 2((3x)/(2x - 1)) - 5) + 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": "92", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 2sin(2\u03c0(-5(-1((3((3x - 1)/(1x + 2)) - 1)/(-2((3x - 1)/(1x + 2)) - 1))^2 + 4((3((3x - 1)/(1x + 2)) - 1)/(-2((3x - 1)/(1x + 2)) - 1)) - 3)^2 + 1(-1((3((3x - 1)/(1x + 2)) - 1)/(-2((3x - 1)/(1x + 2)) - 1))^2 + 4((3((3x - 1)/(1x + 2)) - 1)/(-2((3x - 1)/(1x + 2)) - 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": "220", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 3((3(-2sin(2\u03c0((3((1x - 2)/(-1x - 3)) + 2)/(-1((1x - 2)/(-1x - 3)) - 1)) + 2) + 1) - 1)/(1(-2sin(2\u03c0((3((1x - 2)/(-1x - 3)) + 2)/(-1((1x - 2)/(-1x - 3)) - 1)) + 2) + 1) + 3)) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -2|((3(2e^(2(-5(-4x + 1) + 3)) - 3) + 1)/(-1(2e^(2(-5(-4x + 1) + 3)) - 3) - 2)) - 2| + 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = 2|(2((2((3(3x))/(-1(3x))))/(-3((3(3x))/(-1(3x))))) + 5) + 1| - 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = (-3(1(1|(-3sin(3\u03c0(-4x) - 3) + 3) - 3| - 2) - 4))/(-3(1(1|(-3sin(3\u03c0(-4x) - 3) + 3) - 3| - 2) - 4) - 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "443", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -1|((-2(3e^(-1(4(-2x - 4) + 3)) + 1) - 1)/(1(3e^(-1(4(-2x - 4) + 3)) + 1) + 3)) - 1| - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 3cos(3\u03c0(1(-3|(-2(-5x)^2 - 5(-5x) - 3) + 1| - 3)^2 + 2(-3|(-2(-5x)^2 - 5(-5x) - 3) + 1| - 3)) + 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 2(-4((-3(-4(-2x^2 - 1x + 3) - 4) - 1)/(-3(-4(-2x^2 - 1x + 3) - 4) + 4)) - 1)^2 + 1(-4((-3(-4(-2x^2 - 1x + 3) - 4) - 1)/(-3(-4(-2x^2 - 1x + 3) - 4) + 4)) - 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": "Find the number of local maximum points for f(x) = -1|(-1(2cos(3\u03c0(4((2x + 1)/(3x))^2 - 5((2x + 1)/(3x)) + 1) - 3) + 3)^2 + 3(2cos(3\u03c0(4((2x + 1)/(3x))^2 - 5((2x + 1)/(3x)) + 1) - 3) + 3) + 3) + 2| - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 3|((-1(2(4(-3cos(3\u03c0x) + 1) + 2)) - 1)/(-2(2(4(-3cos(3\u03c0x) + 1) + 2)))) + 3| + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 1(-1|(-1((-1(-1|x + 3| + 3) - 2)/(1(-1|x + 3| + 3) + 1)) - 1) - 3| + 1)^2 + 4(-1|(-1((-1(-1|x + 3| + 3) - 2)/(1(-1|x + 3| + 3) + 1)) - 1) - 3| + 1) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = (-1(-1(3sin(2\u03c0(-2(-1x^2 + 1x + 4) - 4) - 2) + 1) + 2) + 1)/(-3(-1(3sin(2\u03c0(-2(-1x^2 + 1x + 4) - 4) - 2) + 1) + 2) + 1) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "575", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -1|(4((-3(1e^(2((-2x - 1)/(1x + 2))) - 1) + 2)/(1(1e^(2((-2x - 1)/(1x + 2))) - 1) - 2))^2 - 2((-3(1e^(2((-2x - 1)/(1x + 2))) - 1) + 2)/(1(1e^(2((-2x - 1)/(1x + 2))) - 1) - 2)) - 3) - 3| in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -1|(2sin(2\u03c0(-2|(3|(-1x - 1) - 1| + 3) + 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": "479", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = -5(-2cos(1\u03c0(-2|(-2(-2|x + 2| - 1) - 2) + 2| - 3) - 1) - 3) - 3 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) = -2(4(-5(-1sin(1\u03c0(1x^2 - 3x + 4) + 3) + 1))^2 + 3(-5(-1sin(1\u03c0(1x^2 - 3x + 4) + 3) + 1)) + 5)^2 - 4(4(-5(-1sin(1\u03c0(1x^2 - 3x + 4) + 3) + 1))^2 + 3(-5(-1sin(1\u03c0(1x^2 - 3x + 4) + 3) + 1)) + 5) - 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 number of local maximum points for f(x) = (-1(-3sin(1\u03c0((1(-1|(4x + 1) - 3| + 1) + 1)/(-2(-1|(4x + 1) - 3| + 1) - 3)) - 2)) - 3)/(2(-3sin(1\u03c0((1(-1|(4x + 1) - 3| + 1) + 1)/(-2(-1|(4x + 1) - 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": "Determine the total count of local extrema points for the function f(x) = -2|(-1((-3(-1(-3x + 4) + 5) + 1)/(-2(-1(-3x + 4) + 5)))^2 + 4((-3(-1(-3x + 4) + 5) + 1)/(-2(-1(-3x + 4) + 5))) - 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": "Determine the total count of local extrema points for the function f(x) = 1(2|(-2sin(3\u03c0(2(-3x^2 + 1x - 1)) + 3) + 1)| - 1) - 4 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "477", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = 3|(-3cos(2\u03c0(4(-3((-1x - 2)/(2x + 3)) - 4) + 5) - 2) + 2) + 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": "Determine the total count of local extrema points for the function f(x) = 5((2(3(-3(1x - 3)^2 - 4(1x - 3) + 3) - 2) + 3)/(-1(3(-3(1x - 3)^2 - 4(1x - 3) + 3) - 2) + 2))^2 + 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -1|(1(-1(1|(-3cos(3\u03c0x - 1) + 2) - 3| + 3)^2 + 3(1|(-3cos(3\u03c0x - 1) + 2) - 3| + 3) - 3)^2 + 2(-1(1|(-3cos(3\u03c0x - 1) + 2) - 3| + 3)^2 + 3(1|(-3cos(3\u03c0x - 1) + 2) - 3| + 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": "59", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 3|(-2e^(-2(1(-1(-2|x + 1| + 3)^2 + 4(-2|x + 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": "6", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -5(1cos(2\u03c0(-1(1(5x + 5) - 4) - 2) - 2)) + 1 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) = 1(1|(1|((-2(-2cos(2\u03c0x + 2) + 3) + 2)/(1(-2cos(2\u03c0x + 2) + 3) + 2)) - 3| + 3) - 3|) - 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 maxima for the function f(x) = -4((1(-1|(2|(-3x - 4)| - 3) - 2| + 3))/(3(-1|(2|(-3x - 4)| - 3) - 2| + 3) + 2))^2 + 3((1(-1|(2|(-3x - 4)| - 3) - 2| + 3))/(3(-1|(2|(-3x - 4)| - 3) - 2| + 3) + 2)) + 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -1(-2|(3(-4(-2sin(2\u03c0x + 1) - 2)^2 + 4(-2sin(2\u03c0x + 1) - 2)) + 2) + 3| - 1) + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = 1cos(3\u03c0(-2(2(2|(4x^2 - 3x + 1) + 1| - 3) - 5) - 5) + 1) - 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "222", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -5(3|(3cos(2\u03c0(-2|(4x^2 + 1x + 3) - 2| + 3) + 3) - 1) - 1| - 1) + 5 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": "Determine the total count of local extrema points for the function f(x) = 5(2(-3cos(1\u03c0(1|(3x - 5) + 2| + 3) + 1) - 3) - 5)^2 - 3(2(-3cos(1\u03c0(1|(3x - 5) + 2| + 3) + 1) - 3) - 5) + 1 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 total count of local extrema points for the function f(x) = 1((-1(-3(-2|(-3sin(1\u03c0x + 3) - 1)| - 1)^2 - 1(-2|(-3sin(1\u03c0x + 3) - 1)| - 1) - 5) - 1)/(-2(-3(-2|(-3sin(1\u03c0x + 3) - 1)| - 1)^2 - 1(-2|(-3sin(1\u03c0x + 3) - 1)| - 1) - 5) + 3))^2 - 1((-1(-3(-2|(-3sin(1\u03c0x + 3) - 1)| - 1)^2 - 1(-2|(-3sin(1\u03c0x + 3) - 1)| - 1) - 5) - 1)/(-2(-3(-2|(-3sin(1\u03c0x + 3) - 1)| - 1)^2 - 1(-2|(-3sin(1\u03c0x + 3) - 1)| - 1) - 5) + 3)) + 3 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|(4(-1sin(2\u03c0(2|x + 2| - 2) + 1) + 1)^2 + 5(-1sin(2\u03c0(2|x + 2| - 2) + 1) + 1) - 3) - 2| + 1) - 2| + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "159", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = (-2(-1(3e^(-1(-2(-1x^2 + 5x + 5) - 5)) - 2)^2 - 4(3e^(-1(-2(-1x^2 + 5x + 5) - 5)) - 2) - 5) + 1)/(3(-1(3e^(-1(-2(-1x^2 + 5x + 5) - 5)) - 2)^2 - 4(3e^(-1(-2(-1x^2 + 5x + 5) - 5)) - 2) - 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 count of local maxima for the function f(x) = (-1(-3(-1e^(1(1(1|x - 1| + 1) + 5)) - 1)^2 + 5(-1e^(1(1(1|x - 1| + 1) + 5)) - 1) - 3) - 3)/(-1(-3(-1e^(1(1(1|x - 1| + 1) + 5)) - 1)^2 + 5(-1e^(1(1(1|x - 1| + 1) + 5)) - 1) - 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": "Determine the count of local maxima for the function f(x) = 1(3(1sin(1\u03c0(2(-2x^2 - 5x + 4)^2 + 1(-2x^2 - 5x + 4) + 1) + 1) - 1) + 4) - 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "154", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -5(1cos(3\u03c0(5(4((-1x + 3)/(1x)) + 1)^2 - 2) - 3))^2 + 5(1cos(3\u03c0(5(4((-1x + 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": "211", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -2cos(1\u03c0(4(-5(3(1x - 4) - 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": "399", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 1|(-5(1(-2(4x^2 - 2x - 2))^2 - 3(-2(4x^2 - 2x - 2)) - 2)^2 - 2(1(-2(4x^2 - 2x - 2))^2 - 3(-2(4x^2 - 2x - 2)) - 2) + 4) + 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": "Find the total number of local minima and maxima for f(x) = 1(2(-3|(2|(-2cos(1\u03c0x + 1) + 3) + 1| - 2)| + 1) - 5)^2 + 1(2(-3|(2|(-2cos(1\u03c0x + 1) + 3) + 1| - 2)| + 1) - 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 total number of local minima and maxima for f(x) = 1|(3|(-2|((-1(-3cos(2\u03c0x - 3) - 1) + 3)/(2(-3cos(2\u03c0x - 3) - 1) - 3)) + 2| - 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": "179", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 1e^(-2(-1|(1(1(5x^2 + 5x - 4)^2 + 2(5x^2 + 5x - 4) - 4) - 5) - 1|)) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = (-3(-1|(-4(-2(1x^2 - 5x - 3)^2 + 2(1x^2 - 5x - 3) + 2) + 3) + 2| + 3) + 3)/(2(-1|(-4(-2(1x^2 - 5x - 3)^2 + 2(1x^2 - 5x - 3) + 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": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -2(5((1((3(-2sin(1\u03c0x - 2) + 3) - 2)/(2(-2sin(1\u03c0x - 2) + 3) + 2)) + 2)/(-1((3(-2sin(1\u03c0x - 2) + 3) - 2)/(2(-2sin(1\u03c0x - 2) + 3) + 2)) + 3)) - 3) + 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -3cos(3\u03c0(2((-1(3((-2x + 3)/(3x - 2)) - 1) - 2)/(-2(3((-2x + 3)/(3x - 2)) - 1) - 1)) + 5) + 1) + 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = 5(-2|(-3cos(1\u03c0((3(4x^2 - 5x + 1) - 2)/(-3(4x^2 - 5x + 1) + 4)) + 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": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = 2(-1sin(2\u03c0(-4((-3(1|x + 2|))/(-1(1|x + 2|) - 3)) + 1) - 1) + 2)^2 + 5(-1sin(2\u03c0(-4((-3(1|x + 2|))/(-1(1|x + 2|) - 3)) + 1) - 1) + 2) + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 4(-3|(-2|(3((-1x + 1)/(3x + 2)) - 5) - 2|) + 2| + 2)^2 - 1(-3|(-2|(3((-1x + 1)/(3x + 2)) - 5) - 2|) + 2| + 2) - 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -2cos(3\u03c0(-2(2|(-1|(2|x - 1| + 3) + 2|) + 1| + 1)^2 - 4(2|(-1|(2|x - 1| + 3) + 2|) + 1| + 1) + 2) - 3) 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 number of local minimum points for f(x) = -3|(5((-2(4(-3cos(2\u03c0x + 1) + 1) - 5) - 2)/(-2(4(-3cos(2\u03c0x + 1) + 1) - 5))) + 4) + 3| + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 4(1e^(1(4(-1(2x^2 + 3x - 4)^2 + 2)^2 - 5(-1(2x^2 + 3x - 4)^2 + 2) + 3)) + 1) + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = (3(-4((2(3sin(3\u03c0(-2|x + 3| + 2) + 1) - 3) + 3)/(-1(3sin(3\u03c0(-2|x + 3| + 2) + 1) - 3) + 2)) + 3) + 1)/(-3(-4((2(3sin(3\u03c0(-2|x + 3| + 2) + 1) - 3) + 3)/(-1(3sin(3\u03c0(-2|x + 3| + 2) + 1) - 3) + 2)) + 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 number of local maximum points for f(x) = -1|((-2(-3(2|(-3sin(2\u03c0x) - 2) + 3| + 3) + 5) - 3)/(-1(-3(2|(-3sin(2\u03c0x) - 2) + 3| + 3) + 5) - 1)) - 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": "Determine the count of local minima for the function f(x) = (2(2(-1|(-1|(-1x^2 - 5x - 4) + 2| + 1)| - 2) + 3) - 2)/(3(2(-1|(-1|(-1x^2 - 5x - 4) + 2| + 1)| - 2) + 3) - 2) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 4(-4(1(1(-1|x + 1| + 3)^2 + 2(-1|x + 1| + 3) - 1) - 3)^2 + 5) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = (1(-2(-3(-2(-3|x - 1|) + 2) + 1) - 4) + 1)/(3(-2(-3(-2(-3|x - 1|) + 2) + 1) - 4) + 3) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "109", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = (-1(4((-2(2sin(3\u03c0(-5x - 4) + 1)) - 3)/(-1(2sin(3\u03c0(-5x - 4) + 1)) - 2)) - 4) - 3)/(-3(4((-2(2sin(3\u03c0(-5x - 4) + 1)) - 3)/(-1(2sin(3\u03c0(-5x - 4) + 1)) - 2)) - 4) - 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "300", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = 1((2(-2|((3(3|x + 3|) + 1)/(-3(3|x + 3|) + 1)) + 3| + 1))/(2(-2|((3(3|x + 3|) + 1)/(-3(3|x + 3|) + 1)) + 3| + 1) + 1))^2 - 1((2(-2|((3(3|x + 3|) + 1)/(-3(3|x + 3|) + 1)) + 3| + 1))/(2(-2|((3(3|x + 3|) + 1)/(-3(3|x + 3|) + 1)) + 3| + 1) + 1)) - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -5(-2cos(3\u03c0(-4(-2|((3x + 1)/(2x - 1)) - 3| + 2)^2 - 1) + 2) - 2)^2 + 1(-2cos(3\u03c0(-4(-2|((3x + 1)/(2x - 1)) - 3| + 2)^2 - 1) + 2) - 2) - 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "140", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -3|(-4(-1|(3|(2sin(1\u03c0x + 2) - 1) + 2| - 2) - 2| - 3)^2 - 1(-1|(3|(2sin(1\u03c0x + 2) - 1) + 2| - 2) - 2| - 3) - 3)| have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -2cos(1\u03c0(3(-2|(1(-3|x + 3| + 3)^2 + 1(-3|x + 3| + 3) - 2) - 3| + 2)^2 - 3(-2|(1(-3|x + 3| + 3)^2 + 1(-3|x + 3| + 3) - 2) - 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": "162", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 2|(-1((1((1(-1x^2 - 3x + 3) + 3)/(3(-1x^2 - 3x + 3) - 1)))/(-2((1(-1x^2 - 3x + 3) + 3)/(3(-1x^2 - 3x + 3) - 1)) - 2))^2 + 4((1((1(-1x^2 - 3x + 3) + 3)/(3(-1x^2 - 3x + 3) - 1)))/(-2((1(-1x^2 - 3x + 3) + 3)/(3(-1x^2 - 3x + 3) - 1)) - 2)) + 3) + 2| - 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = (-2(2cos(1\u03c0(4(-1|(1x + 1) - 3| - 1)^2 - 4(-1|(1x + 1) - 3| - 1) - 1) - 1) + 3) + 3)/(2(2cos(1\u03c0(4(-1|(1x + 1) - 3| - 1)^2 - 4(-1|(1x + 1) - 3| - 1) - 1) - 1) + 3) + 1) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "577", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 4(-2|(5(-3(1|x + 3|)^2 + 4(1|x + 3|) + 4)^2 - 1(-3(1|x + 3|)^2 + 4(1|x + 3|) + 4) - 5)| + 3)^2 - 1(-2|(5(-3(1|x + 3|)^2 + 4(1|x + 3|) + 4)^2 - 1(-3(1|x + 3|)^2 + 4(1|x + 3|) + 4) - 5)| + 3) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -5(-1((2(1(1sin(2\u03c0x - 3) + 1) + 2) - 3)/(-1(1(1sin(2\u03c0x - 3) + 1) + 2) - 2))^2 + 4((2(1(1sin(2\u03c0x - 3) + 1) + 2) - 3)/(-1(1(1sin(2\u03c0x - 3) + 1) + 2) - 2)) - 4)^2 - 4(-1((2(1(1sin(2\u03c0x - 3) + 1) + 2) - 3)/(-1(1(1sin(2\u03c0x - 3) + 1) + 2) - 2))^2 + 4((2(1(1sin(2\u03c0x - 3) + 1) + 2) - 3)/(-1(1(1sin(2\u03c0x - 3) + 1) + 2) - 2)) - 4) + 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 maxima does the function f(x) = 3|(-5(3((-1(1|x - 3| - 3) - 3)/(3(1|x - 3| - 3) + 1))^2 - 1((-1(1|x - 3| - 3) - 3)/(3(1|x - 3| - 3) + 1)) - 4) - 4)| have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 5(-3sin(1\u03c0(2|(5(-5x^2 - 1x + 4)^2 + 4(-5x^2 - 1x + 4) + 5) + 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": "92", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -2|(3|(-3sin(3\u03c0((-2(3|x| - 3) - 2)/(3(3|x| - 3) + 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": "8", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -1|(-3cos(2\u03c0(-1(-1(5x^2 - 5x - 4) + 5)^2 - 4(-1(5x^2 - 5x - 4) + 5) - 2) + 1) + 2) + 1| - 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "90", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -2|((-1(-3cos(3\u03c0((-2(3x^2 - 3x - 3) + 1)/(-2(3x^2 - 3x - 3) - 1)) - 1)) + 3)/(-2(-3cos(3\u03c0((-2(3x^2 - 3x - 3) + 1)/(-2(3x^2 - 3x - 3) - 1)) - 1)) + 1)) + 1| + 1 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|(3|(-3((2(1sin(3\u03c0x + 2) - 3) - 2)/(-2(1sin(3\u03c0x + 2) - 3) + 3))^2 - 4((2(1sin(3\u03c0x + 2) - 3) - 2)/(-2(1sin(3\u03c0x + 2) - 3) + 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": "30", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = (1(3(4(2(3x^2)^2 + 4)^2 - 1(2(3x^2)^2 + 4) - 5)^2 - 1(4(2(3x^2)^2 + 4)^2 - 1(2(3x^2)^2 + 4) - 5) - 3) + 2)/(-3(3(4(2(3x^2)^2 + 4)^2 - 1(2(3x^2)^2 + 4) - 5)^2 - 1(4(2(3x^2)^2 + 4)^2 - 1(2(3x^2)^2 + 4) - 5) - 3) + 4) 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 total count of local extrema points for the function f(x) = (-2(1|(3(-2((1x - 2)/(2x - 3))^2 + 1((1x - 2)/(2x - 3)) + 5)^2 - 4(-2((1x - 2)/(2x - 3))^2 + 1((1x - 2)/(2x - 3)) + 5) - 1) - 1| - 3) - 1)/(-2(1|(3(-2((1x - 2)/(2x - 3))^2 + 1((1x - 2)/(2x - 3)) + 5)^2 - 4(-2((1x - 2)/(2x - 3))^2 + 1((1x - 2)/(2x - 3)) + 5) - 1) - 1| - 3) + 3) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -1(-1|((2(-2(1x - 5)^2 - 2(1x - 5) - 2) - 2)/(1(-2(1x - 5)^2 - 2(1x - 5) - 2) + 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": "5", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -2|(-1(-3(-3cos(2\u03c0((3x - 2)/(-3x - 1))) + 1) - 4) + 4)| have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -1|(3(2|(5(-3x^2 + 1) - 1)| - 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 minima does the function f(x) = 1(-1sin(3\u03c0((3(-3((1x - 2)/(-3x + 4)) + 1) + 2)/(1(-3((1x - 2)/(-3x + 4)) + 1) + 2)) + 1) - 1) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 2|(-2|(3cos(3\u03c0((1(-5x^2 - 5x - 2) + 3)/(-2(-5x^2 - 5x - 2) + 1)) + 1) + 2) - 3| - 2) - 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 total count of local extrema points for the function f(x) = 3(3(-2sin(2\u03c0((-3(-1x^2 + 5x - 5) - 3)/(-1(-1x^2 + 5x - 5) - 1)) - 1) + 3)^2 + 5(-2sin(2\u03c0((-3(-1x^2 + 5x - 5) - 3)/(-1(-1x^2 + 5x - 5) - 1)) - 1) + 3) - 5) - 5 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "151", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -2(1sin(3\u03c0(3|(2(-2x - 3)^2 - 3(-2x - 3) + 2)|) + 3) + 2) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "224", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 2|(-1((3(2e^(-2(2|x|)) - 3) + 1)/(-1(2e^(-2(2|x|)) - 3) - 2)) + 2) - 1| have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = 2|(-2sin(3\u03c0((-1(-1(-3|x - 3| - 2)^2 - 3(-3|x - 3| - 2) - 2) + 2)/(-1(-1(-3|x - 3| - 2)^2 - 3(-3|x - 3| - 2) - 2))) - 3) - 1) - 2| in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -3sin(1\u03c0(-2(-1(-3|(4x^2 - 5x + 2) + 1| + 2)^2 + 2(-3|(4x^2 - 5x + 2) + 1| + 2) + 5) + 1) - 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": "Find the number of local maximum points for f(x) = (1(-3sin(1\u03c0(-3|((2(-3|x + 3|) + 3)/(-2(-3|x + 3|))) + 3| + 1)) - 1) + 1)/(2(-3sin(1\u03c0(-3|((2(-3|x + 3|) + 3)/(-2(-3|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": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 1((1(-5(2sin(3\u03c0(-4x - 1)) + 3)^2 - 4) - 3)/(1(-5(2sin(3\u03c0(-4x - 1)) + 3)^2 - 4) + 3)) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "240", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = (-3(2cos(1\u03c0(-2(1(-2x) + 5)^2 + 1(1(-2x) + 5) + 4) + 3) - 3) - 3)/(-3(2cos(1\u03c0(-2(1(-2x) + 5)^2 + 1(1(-2x) + 5) + 4) + 3) - 3) + 2) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "485", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -4(-3|((3(3sin(2\u03c0(1x^2 + 2x - 1) + 3) - 3) - 1)/(2(3sin(2\u03c0(1x^2 + 2x - 1) + 3) - 3) - 1)) - 3| + 3)^2 - 5(-3|((3(3sin(2\u03c0(1x^2 + 2x - 1) + 3) - 3) - 1)/(2(3sin(2\u03c0(1x^2 + 2x - 1) + 3) - 3) - 1)) - 3| + 3) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "333", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -3((-2(2(-5((2x + 3)/(-1x + 2))^2 - 4((2x + 3)/(-1x + 2)) + 1) + 1) + 1)/(2(2(-5((2x + 3)/(-1x + 2))^2 - 4((2x + 3)/(-1x + 2)) + 1) + 1)))^2 + 5((-2(2(-5((2x + 3)/(-1x + 2))^2 - 4((2x + 3)/(-1x + 2)) + 1) + 1) + 1)/(2(2(-5((2x + 3)/(-1x + 2))^2 - 4((2x + 3)/(-1x + 2)) + 1) + 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 total number of local minima and maxima for f(x) = (1(-3cos(3\u03c0(1(-3((-1x + 1)/(2x)) + 1)^2 + 1(-3((-1x + 1)/(2x)) + 1) - 1) + 3) - 2) - 1)/(2(-3cos(3\u03c0(1(-3((-1x + 1)/(2x)) + 1)^2 + 1(-3((-1x + 1)/(2x)) + 1) - 1) + 3) - 2) + 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "94", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -1|(3sin(1\u03c0((1(2(1x) + 3) - 2)/(1(2(1x) + 3) - 3)) + 1) + 3) - 3| have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "23", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 5(-2((3(5(-2|x + 2| + 3) + 1) + 3)/(1(5(-2|x + 2| + 3) + 1) + 1)) + 5) - 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 total number of local minima and maxima for f(x) = -1(-3(-4(1sin(2\u03c0((3x - 2)/(3x)) - 2) - 3) - 4)^2 - 2(-4(1sin(2\u03c0((3x - 2)/(3x)) - 2) - 3) - 4) + 5) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "23", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = (-3(-2cos(1\u03c0(2|((1(-5x^2 + 3x - 1) - 3)/(1(-5x^2 + 3x - 1) + 3))|) + 1) + 1))/(1(-2cos(1\u03c0(2|((1(-5x^2 + 3x - 1) - 3)/(1(-5x^2 + 3x - 1) + 3))|) + 1) + 1) - 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) = -4(-1(1|(-1(-2|x - 3| - 2)^2 - 2(-2|x - 3| - 2) + 3) - 1| - 3)^2 + 3(1|(-1(-2|x - 3| - 2)^2 - 2(-2|x - 3| - 2) + 3) - 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": "Find the number of local minimum points for f(x) = -3((-2(-2|(-3sin(3\u03c0(1x^2 - 1x) - 2) + 1) - 3| + 2) - 3)/(-2(-2|(-3sin(3\u03c0(1x^2 - 1x) - 2) + 1) - 3| + 2) - 1))^2 + 2((-2(-2|(-3sin(3\u03c0(1x^2 - 1x) - 2) + 1) - 3| + 2) - 3)/(-2(-2|(-3sin(3\u03c0(1x^2 - 1x) - 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": "245", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -2((-3(2|((1((-3x + 2)/(-1x - 1)) - 3)/(2((-3x + 2)/(-1x - 1)) - 1)) + 1| - 2) + 1)/(3(2|((1((-3x + 2)/(-1x - 1)) - 3)/(2((-3x + 2)/(-1x - 1)) - 1)) + 1| - 2) + 2))^2 + 5((-3(2|((1((-3x + 2)/(-1x - 1)) - 3)/(2((-3x + 2)/(-1x - 1)) - 1)) + 1| - 2) + 1)/(3(2|((1((-3x + 2)/(-1x - 1)) - 3)/(2((-3x + 2)/(-1x - 1)) - 1)) + 1| - 2) + 2)) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 2(2cos(1\u03c0(5(-4(3|x + 2| + 1)^2 + 1(3|x + 2| + 1) - 3)^2 + 4(-4(3|x + 2| + 1)^2 + 1(3|x + 2| + 1) - 3) - 4) + 2) + 1) - 2 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) = (-2(-4(1(-3(-1cos(3\u03c0x - 3) + 1) - 2)^2 + 3(-3(-1cos(3\u03c0x - 3) + 1) - 2) + 3)^2 - 5(1(-3(-1cos(3\u03c0x - 3) + 1) - 2)^2 + 3(-3(-1cos(3\u03c0x - 3) + 1) - 2) + 3) - 4) + 3)/(1(-4(1(-3(-1cos(3\u03c0x - 3) + 1) - 2)^2 + 3(-3(-1cos(3\u03c0x - 3) + 1) - 2) + 3)^2 - 5(1(-3(-1cos(3\u03c0x - 3) + 1) - 2)^2 + 3(-3(-1cos(3\u03c0x - 3) + 1) - 2) + 3) - 4) + 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 minima does the function f(x) = 1sin(3\u03c0(-3|(-1|(-3|(-2|x + 1|) + 3| + 1) + 2| - 2) + 3| - 2) + 1) - 2 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": "Determine the count of local maxima for the function f(x) = -5(-2|(5(1sin(1\u03c0(3|x - 2|) + 2) + 3) + 1)| + 3)^2 - 2(-2|(5(1sin(1\u03c0(3|x - 2|) + 2) + 3) + 1)| + 3) + 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) = -4(-2sin(2\u03c0(2|(-1(1x^2 - 4x + 5)^2 - 3(1x^2 - 4x + 5) + 5) + 3| - 1) + 1) - 2) + 4 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "148", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = 3(3(3cos(2\u03c0(1|(-4x^2 - 4x - 1) - 3|)) - 1) - 4) + 4 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "254", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -1|(-3sin(1\u03c0((-1((3(5x + 5) + 3)/(2(5x + 5) - 1)) - 3)/(-1((3(5x + 5) + 3)/(2(5x + 5) - 1)) + 3)) + 1)) - 3| - 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(2|((2(3cos(1\u03c0((-3x + 3)/(-2x + 3))) - 3) - 1)/(-2(3cos(1\u03c0((-3x + 3)/(-2x + 3))) - 3) + 3)) - 2| - 2))/(-2(2|((2(3cos(1\u03c0((-3x + 3)/(-2x + 3))) - 3) - 1)/(-2(3cos(1\u03c0((-3x + 3)/(-2x + 3))) - 3) + 3)) - 2| - 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) = -2|((-2(2sin(2\u03c0((-3((-2x)/(2x - 1)))/(2((-2x)/(2x - 1)) - 1)) - 3) + 2) - 1)/(-2(2sin(2\u03c0((-3((-2x)/(2x - 1)))/(2((-2x)/(2x - 1)) - 1)) - 3) + 2) + 3)) - 2| - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -4(3(1|(-1(-5x^2 + 4x + 4)^2 - 4(-5x^2 + 4x + 4) - 1) + 2| + 1) + 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 maxima does the function f(x) = 2|(-2(-3e^(2(-1|(-4x + 4) + 3| + 3)) + 3) + 4) + 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) = -1(-1(3(1|(-3sin(3\u03c0x + 1)) - 2| - 3)^2 + 1(1|(-3sin(3\u03c0x + 1)) - 2| - 3)) - 3) - 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": "Find the number of local maximum points for f(x) = (1((-1((3(-2|(-1cos(1\u03c0x) - 1) + 1| + 3) - 3)/(1(-2|(-1cos(1\u03c0x) - 1) + 1| + 3) + 3)) - 2)/(3((3(-2|(-1cos(1\u03c0x) - 1) + 1| + 3) - 3)/(1(-2|(-1cos(1\u03c0x) - 1) + 1| + 3) + 3)) + 3)) + 2)/(1((-1((3(-2|(-1cos(1\u03c0x) - 1) + 1| + 3) - 3)/(1(-2|(-1cos(1\u03c0x) - 1) + 1| + 3) + 3)) - 2)/(3((3(-2|(-1cos(1\u03c0x) - 1) + 1| + 3) - 3)/(1(-2|(-1cos(1\u03c0x) - 1) + 1| + 3) + 3)) + 3)) + 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 1cos(3\u03c0(5(3(-3((3x + 2)/(2x + 2))^2 + 1((3x + 2)/(2x + 2)) - 1) - 4)^2 + 1(3(-3((3x + 2)/(2x + 2))^2 + 1((3x + 2)/(2x + 2)) - 1) - 4) - 2) - 1) + 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "443", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -2(1(-3sin(1\u03c0(1(2x^2 + 3) + 2)) - 1)^2 - 3(-3sin(1\u03c0(1(2x^2 + 3) + 2)) - 1) - 5) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "441", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 2cos(3\u03c0(-1|(1(2((1x - 1)/(3x - 1)) + 2)^2 - 3(2((1x - 1)/(3x - 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": "32", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 4(1|(3|(-3(-1cos(1\u03c0x - 1) + 3) - 5)|) + 3| - 1) + 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) = -2|(-1((-1(-1cos(1\u03c0(-2x^2 - 1x - 1) + 1) + 3) + 2)/(2(-1cos(1\u03c0(-2x^2 - 1x - 1) + 1) + 3)))) + 2| + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "169", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = (2(-4(1|(-3e^(-1(-4x + 3)) + 2)|) - 1) - 1)/(2(-4(1|(-3e^(-1(-4x + 3)) + 2)|) - 1)) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = -3(4((3((2((-1x + 2)/(2x)) + 2)/(3((-1x + 2)/(2x)) + 3)))/(1((2((-1x + 2)/(2x)) + 2)/(3((-1x + 2)/(2x)) + 3)) - 2))^2 - 5((3((2((-1x + 2)/(2x)) + 2)/(3((-1x + 2)/(2x)) + 3)))/(1((2((-1x + 2)/(2x)) + 2)/(3((-1x + 2)/(2x)) + 3)) - 2)))^2 + 1 in the interval [-10, 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) = (-2(-2|(1|(-1e^(-1(-3x^2 + 3x + 1))) - 3| + 1) + 2| + 1) + 3)/(-3(-2|(1|(-1e^(-1(-3x^2 + 3x + 1))) - 3| + 1) + 2| + 1) + 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "82", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = (-1(-2sin(1\u03c0(-3|(-2((1x - 1)/(-2x))^2 - 1((1x - 1)/(-2x)) - 4) + 1| + 2) - 2) - 3) + 2)/(-1(-2sin(1\u03c0(-3|(-2((1x - 1)/(-2x))^2 - 1((1x - 1)/(-2x)) - 4) + 1| + 2) - 2) - 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": "Find the number of local minimum points for f(x) = 1(-3cos(3\u03c0(2|(2|(-1x^2 - 1x - 5) - 1| - 3) - 2| - 3) + 2)) + 5 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": "How many local maxima does the function f(x) = -5((2(-2|(3|((2x - 3)/(1x + 2)) + 3| - 3) - 2| + 2) + 2)/(1(-2|(3|((2x - 3)/(1x + 2)) + 3| - 3) - 2| + 2) - 3))^2 - 5((2(-2|(3|((2x - 3)/(1x + 2)) + 3| - 3) - 2| + 2) + 2)/(1(-2|(3|((2x - 3)/(1x + 2)) + 3| - 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": "6", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 2(2|(2sin(2\u03c0(1|(-1x - 5)| + 1) + 2) + 3)| + 2)^2 + 3(2|(2sin(2\u03c0(1|(-1x - 5)| + 1) + 2) + 3)| + 2) - 5 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) = 5(4((-3(3sin(1\u03c0((-3x + 3)/(-3x)) + 3) - 3) + 3)/(2(3sin(1\u03c0((-3x + 3)/(-3x)) + 3) - 3) - 1))^2 + 2((-3(3sin(1\u03c0((-3x + 3)/(-3x)) + 3) - 3) + 3)/(2(3sin(1\u03c0((-3x + 3)/(-3x)) + 3) - 3) - 1)) + 5) - 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": "How many local maxima does the function f(x) = 1((2(1|(-2sin(2\u03c0(-1x^2 + 5x + 4))) + 3| + 1) + 1)/(3(1|(-2sin(2\u03c0(-1x^2 + 5x + 4))) + 3| + 1) - 1)) + 5 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": "Determine the count of local maxima for the function f(x) = (3(2cos(1\u03c0((1(-1(2|x + 2|) + 4) - 3)/(-3(-1(2|x + 2|) + 4) + 1)) + 2) + 1) - 1)/(2(2cos(1\u03c0((1(-1(2|x + 2|) + 4) - 3)/(-3(-1(2|x + 2|) + 4) + 1)) + 2) + 1) + 2) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = (2(5((-3(2cos(1\u03c0(-1x^2 + 4) - 3) + 2) - 3)/(-3(2cos(1\u03c0(-1x^2 + 4) - 3) + 2) - 1)) - 1) + 3)/(-2(5((-3(2cos(1\u03c0(-1x^2 + 4) - 3) + 2) - 3)/(-3(2cos(1\u03c0(-1x^2 + 4) - 3) + 2) - 1)) - 1) + 3) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "103", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = 2(-3|((1(-3sin(2\u03c0(-1x^2 - 5x + 2)) + 3))/(2(-3sin(2\u03c0(-1x^2 - 5x + 2)) + 3) + 2)) + 1| + 2)^2 + 5(-3|((1(-3sin(2\u03c0(-1x^2 - 5x + 2)) + 3))/(2(-3sin(2\u03c0(-1x^2 - 5x + 2)) + 3) + 2)) + 1| + 2) + 4 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "107", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 3cos(2\u03c0(-1|(-2(-3|(4x) - 1| + 2) + 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": "469", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -2(-4(4(3sin(1\u03c0(-2x^2 - 2x) + 3) - 2) - 5) - 1)^2 - 5(-4(4(3sin(1\u03c0(-2x^2 - 2x) + 3) - 2) - 5) - 1) + 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "171", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 5((1(-2|(2(3cos(3\u03c0x - 2) - 1)^2 + 4(3cos(3\u03c0x - 2) - 1) + 1) - 2| - 1) - 3)/(-2(-2|(2(3cos(3\u03c0x - 2) - 1)^2 + 4(3cos(3\u03c0x - 2) - 1) + 1) - 2| - 1) + 3))^2 - 5((1(-2|(2(3cos(3\u03c0x - 2) - 1)^2 + 4(3cos(3\u03c0x - 2) - 1) + 1) - 2| - 1) - 3)/(-2(-2|(2(3cos(3\u03c0x - 2) - 1)^2 + 4(3cos(3\u03c0x - 2) - 1) + 1) - 2| - 1) + 3)) + 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "240", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = (-2(3|((-2(-1cos(1\u03c0((-2x + 1)/(-2x + 3)) + 2)) + 2)/(1(-1cos(1\u03c0((-2x + 1)/(-2x + 3)) + 2)) + 2)) - 3| - 3) + 1)/(3(3|((-2(-1cos(1\u03c0((-2x + 1)/(-2x + 3)) + 2)) + 2)/(1(-1cos(1\u03c0((-2x + 1)/(-2x + 3)) + 2)) + 2)) - 3| - 3) + 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = (-1(5(-3(1|(1cos(3\u03c0x + 2) - 1) - 2| - 2))) - 1)/(-3(5(-3(1|(1cos(3\u03c0x + 2) - 1) - 2| - 2))) - 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "166", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = (2(-5(2sin(1\u03c0(2((-2x - 2)/(-3x + 1))^2 + 1((-2x - 2)/(-3x + 1)) - 1) + 2) + 1)^2 + 1(2sin(1\u03c0(2((-2x - 2)/(-3x + 1))^2 + 1((-2x - 2)/(-3x + 1)) - 1) + 2) + 1) + 5))/(-2(-5(2sin(1\u03c0(2((-2x - 2)/(-3x + 1))^2 + 1((-2x - 2)/(-3x + 1)) - 1) + 2) + 1)^2 + 1(2sin(1\u03c0(2((-2x - 2)/(-3x + 1))^2 + 1((-2x - 2)/(-3x + 1)) - 1) + 2) + 1) + 5) + 1) 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": "Find the total number of local minima and maxima for f(x) = 2(4((-3(-2((-1x + 2)/(2x + 3))^2 + 4((-1x + 2)/(2x + 3)) + 5))/(3(-2((-1x + 2)/(2x + 3))^2 + 4((-1x + 2)/(2x + 3)) + 5) - 1))^2 - 5((-3(-2((-1x + 2)/(2x + 3))^2 + 4((-1x + 2)/(2x + 3)) + 5))/(3(-2((-1x + 2)/(2x + 3))^2 + 4((-1x + 2)/(2x + 3)) + 5) - 1)) + 4)^2 + 5(4((-3(-2((-1x + 2)/(2x + 3))^2 + 4((-1x + 2)/(2x + 3)) + 5))/(3(-2((-1x + 2)/(2x + 3))^2 + 4((-1x + 2)/(2x + 3)) + 5) - 1))^2 - 5((-3(-2((-1x + 2)/(2x + 3))^2 + 4((-1x + 2)/(2x + 3)) + 5))/(3(-2((-1x + 2)/(2x + 3))^2 + 4((-1x + 2)/(2x + 3)) + 5) - 1)) + 4) - 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": "Find the total number of local minima and maxima for f(x) = -2cos(3\u03c0(1(1|((2(-4x^2 + 3x - 4) + 3)/(-1(-4x^2 + 3x - 4) + 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": "How many local maxima does the function f(x) = -4(2|(1|(-1sin(2\u03c0(-1x + 2) - 1)) + 2| + 3) - 2| - 1)^2 - 5(2|(1|(-1sin(2\u03c0(-1x + 2) - 1)) + 2| + 3) - 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": "How many local extrema (minima and maxima combined) does the function f(x) = -2(5(-3|(-1sin(1\u03c0(-3x^2 + 3x + 4) + 2) + 3)| + 1)^2 - 3(-3|(-1sin(1\u03c0(-3x^2 + 3x + 4) + 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": "559", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = -5((-1(-5(-3sin(2\u03c0(-1x^2 - 1x + 1) + 3) + 2)^2 + 1(-3sin(2\u03c0(-1x^2 - 1x + 1) + 3) + 2) + 4) + 2)/(-2(-5(-3sin(2\u03c0(-1x^2 - 1x + 1) + 3) + 2)^2 + 1(-3sin(2\u03c0(-1x^2 - 1x + 1) + 3) + 2) + 4) + 3))^2 + 1((-1(-5(-3sin(2\u03c0(-1x^2 - 1x + 1) + 3) + 2)^2 + 1(-3sin(2\u03c0(-1x^2 - 1x + 1) + 3) + 2) + 4) + 2)/(-2(-5(-3sin(2\u03c0(-1x^2 - 1x + 1) + 3) + 2)^2 + 1(-3sin(2\u03c0(-1x^2 - 1x + 1) + 3) + 2) + 4) + 3)) + 4 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "87", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 1|(-2|(3(-4(-1sin(1\u03c0x + 1) - 1) - 3)^2 - 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": "80", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 2(3(1|(-5(-2cos(2\u03c0x - 1) + 3) + 2) - 3|)^2 + 3(1|(-5(-2cos(2\u03c0x - 1) + 3) + 2) - 3|) + 5)^2 + 3(3(1|(-5(-2cos(2\u03c0x - 1) + 3) + 2) - 3|)^2 + 3(1|(-5(-2cos(2\u03c0x - 1) + 3) + 2) - 3|) + 5) + 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = (1(1(2sin(2\u03c0(-3|(-2x^2 - 4x + 2) + 3| + 1) + 1)) - 2) + 3)/(1(1(2sin(2\u03c0(-3|(-2x^2 - 4x + 2) + 3| + 1) + 1)) - 2) + 2) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "495", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = 5(-4((-1(-3(-2x^2 - 4x - 1)^2 - 1(-2x^2 - 4x - 1) + 4) + 3)/(-1(-3(-2x^2 - 4x - 1)^2 - 1(-2x^2 - 4x - 1) + 4) + 2)) + 2)^2 + 4(-4((-1(-3(-2x^2 - 4x - 1)^2 - 1(-2x^2 - 4x - 1) + 4) + 3)/(-1(-3(-2x^2 - 4x - 1)^2 - 1(-2x^2 - 4x - 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": "5", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -1cos(2\u03c0(-2|((-1(2((1x + 1)/(1x - 3))^2 - 5((1x + 1)/(1x - 3)) - 5) - 3)/(2(2((1x + 1)/(1x - 3))^2 - 5((1x + 1)/(1x - 3)) - 5) - 3)) - 1|) + 2) - 3 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) = -2|(-1cos(1\u03c0(4(5(-3x + 1) + 5)^2 + 2(5(-3x + 1) + 5) - 1) + 3) - 3) - 3| + 2 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": "Find the total number of local minima and maxima for f(x) = -2|(2|(-3(-1|(-2x^2 - 5x + 4) - 1|) - 2) - 1| - 2)| - 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": "Find the total number of local minima and maxima for f(x) = 5(-4((1(-1|(1x^2 + 2x - 4) - 2| + 2) - 1)/(1(-1|(1x^2 + 2x - 4) - 2| + 2) + 2)) + 4)^2 + 2(-4((1(-1|(1x^2 + 2x - 4) - 2| + 2) - 1)/(1(-1|(1x^2 + 2x - 4) - 2| + 2) + 2)) + 4) - 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -2e^(2((-3(-3|(4(2|x + 2| - 3)^2 - 3(2|x + 2| - 3)) - 1| - 2) - 3)/(3(-3|(4(2|x + 2| - 3)^2 - 3(2|x + 2| - 3)) - 1| - 2) + 1))) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 1((1((3(4(3sin(1\u03c0x + 3) - 1)^2 + 5(3sin(1\u03c0x + 3) - 1) - 2))/(1(4(3sin(1\u03c0x + 3) - 1)^2 + 5(3sin(1\u03c0x + 3) - 1) - 2))) - 2)/(1((3(4(3sin(1\u03c0x + 3) - 1)^2 + 5(3sin(1\u03c0x + 3) - 1) - 2))/(1(4(3sin(1\u03c0x + 3) - 1)^2 + 5(3sin(1\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": "167", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = -1(2|(3cos(1\u03c0(4(-3x + 4) - 5) - 1) + 1) + 3| + 2)^2 - 3(2|(3cos(1\u03c0(4(-3x + 4) - 5) - 1) + 1) + 3| + 2) - 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": "Find the total number of local minima and maxima for f(x) = -2|(-1(-3|(2sin(2\u03c0((-3x + 1)/(3x - 2)) + 3) + 2) + 3| + 2) + 2) + 3| + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = (-3(1((1(-1cos(2\u03c0(3|x - 3| + 2) - 2)))/(-2(-1cos(2\u03c0(3|x - 3| + 2) - 2)) + 3))^2 - 1((1(-1cos(2\u03c0(3|x - 3| + 2) - 2)))/(-2(-1cos(2\u03c0(3|x - 3| + 2) - 2)) + 3)) + 5) + 2)/(-1(1((1(-1cos(2\u03c0(3|x - 3| + 2) - 2)))/(-2(-1cos(2\u03c0(3|x - 3| + 2) - 2)) + 3))^2 - 1((1(-1cos(2\u03c0(3|x - 3| + 2) - 2)))/(-2(-1cos(2\u03c0(3|x - 3| + 2) - 2)) + 3)) + 5) - 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) = (-2(-2((3(2cos(2\u03c0((2x + 2)/(2x - 3))) - 1) + 3)/(-1(2cos(2\u03c0((2x + 2)/(2x - 3))) - 1) + 2)) + 4) - 1)/(-2(-2((3(2cos(2\u03c0((2x + 2)/(2x - 3))) - 1) + 3)/(-1(2cos(2\u03c0((2x + 2)/(2x - 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": "19", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 3(-2(-2(1cos(2\u03c0((3x + 2)/(-1x - 2)) + 1) + 2)^2 + 2) - 2) - 4 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": "How many local minima does the function f(x) = -1(-3(1(-2cos(1\u03c0(2|x - 3| + 2) - 2) - 2)^2 - 1(-2cos(1\u03c0(2|x - 3| + 2) - 2) - 2) - 4) - 3) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -1(2|(-2(1(1x^2 + 2x - 4) + 1)^2 - 3(1(1x^2 + 2x - 4) + 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": "7", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 2|(-1cos(1\u03c0(2(2|(3x^2 + 5)| + 1)^2 + 2(2|(3x^2 + 5)| + 1) - 4) + 2) - 2)| - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -5(1(3(3(1x^2 + 3x + 2)^2 - 4)^2 + 5(3(1x^2 + 3x + 2)^2 - 4)) + 4)^2 + 5 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 2sin(3\u03c0((-3(2(-2(1x^2 - 2)^2 + 2(1x^2 - 2) + 2) - 2) + 2)/(-2(2(-2(1x^2 - 2)^2 + 2(1x^2 - 2) + 2) - 2) - 3)) + 1) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "47", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 3cos(2\u03c0(-3(5((3(2|x + 2| - 3) - 3)/(-2(2|x + 2| - 3) - 1)) - 5)) - 1) - 1 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 minima does the function f(x) = 1(1cos(2\u03c0(2|(-2((2x + 1)/(1x + 1))^2 + 4((2x + 1)/(1x + 1)) + 2) + 2| + 1) - 2) - 1) - 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "43", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 4(-2|(-1(-3sin(1\u03c0(5x - 5) + 1) - 3)^2 - 2(-3sin(1\u03c0(5x - 5) + 1) - 3)) - 1| - 1) - 2 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": "Find the number of local maximum points for f(x) = 2|(-4(-2(1|(2cos(3\u03c0x - 3) + 1)| + 3) + 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": "111", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 3((-3(-3|(-2cos(2\u03c0(-1x^2 - 4x - 5) - 3) - 1) + 2| + 3) + 1)/(-3(-3|(-2cos(2\u03c0(-1x^2 - 4x - 5) - 3) - 1) + 2| + 3) - 3))^2 + 5((-3(-3|(-2cos(2\u03c0(-1x^2 - 4x - 5) - 3) - 1) + 2| + 3) + 1)/(-3(-3|(-2cos(2\u03c0(-1x^2 - 4x - 5) - 3) - 1) + 2| + 3) - 3)) - 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "319", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -1|(3cos(2\u03c0(-1(-2((1x - 2)/(-3x - 3)) - 4)) - 1) - 1) - 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": "Find the total number of local minima and maxima for f(x) = (3(2sin(2\u03c0(1|(-5(-1|x + 3| + 2)^2 - 4(-1|x + 3| + 2) - 5) - 1|) - 1)) - 3)/(-2(2sin(2\u03c0(1|(-5(-1|x + 3| + 2)^2 - 4(-1|x + 3| + 2) - 5) - 1|) - 1)) - 1) 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) = 2|(1cos(2\u03c0(4(1|(2x - 1)|) - 1) + 3) + 2) - 1| + 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "160", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = 2|(2|(-2cos(1\u03c0(2((-1x + 3)/(1x)) - 1) - 2) + 2) - 1| - 1) - 1| + 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": "Find the number of local maximum points for f(x) = 1((-1(2cos(2\u03c0(4(2|x + 3| + 2) + 2) - 2) - 3) + 1)/(3(2cos(2\u03c0(4(2|x + 3| + 2) + 2) - 2) - 3) - 1))^2 - 3((-1(2cos(2\u03c0(4(2|x + 3| + 2) + 2) - 2) - 3) + 1)/(3(2cos(2\u03c0(4(2|x + 3| + 2) + 2) - 2) - 3) - 1)) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "155", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = -1((1(2(4(3sin(2\u03c0x + 2) - 2) - 3)^2 + 5(4(3sin(2\u03c0x + 2) - 2) - 3) + 1))/(2(2(4(3sin(2\u03c0x + 2) - 2) - 3)^2 + 5(4(3sin(2\u03c0x + 2) - 2) - 3) + 1) - 3))^2 - 4((1(2(4(3sin(2\u03c0x + 2) - 2) - 3)^2 + 5(4(3sin(2\u03c0x + 2) - 2) - 3) + 1))/(2(2(4(3sin(2\u03c0x + 2) - 2) - 3)^2 + 5(4(3sin(2\u03c0x + 2) - 2) - 3) + 1) - 3)) - 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "46", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = (2(1|((-2(2sin(1\u03c0((-2x - 1)/(-1x + 2))) + 3) + 3)/(-1(2sin(1\u03c0((-2x - 1)/(-1x + 2))) + 3))) + 2| - 3) - 3)/(-1(1|((-2(2sin(1\u03c0((-2x - 1)/(-1x + 2))) + 3) + 3)/(-1(2sin(1\u03c0((-2x - 1)/(-1x + 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": "47", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = 5(-1(-5(4(-2cos(3\u03c0x + 1) + 2) + 2) - 4) + 5) + 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -3cos(2\u03c0((-3(5(5(-5x - 5)^2 - 4(-5x - 5) - 4) - 5) + 3)/(-1(5(5(-5x - 5)^2 - 4(-5x - 5) - 4) - 5))) - 3) + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -3(-2(2|(3cos(3\u03c0((3x - 2)/(-2x - 2)) + 2) - 3) - 1| + 2) + 5)^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 total number of local minima and maxima for f(x) = (1((2(-5(1cos(3\u03c0(1x) + 2) + 3)^2 + 5(1cos(3\u03c0(1x) + 2) + 3) + 1) - 2)/(3(-5(1cos(3\u03c0(1x) + 2) + 3)^2 + 5(1cos(3\u03c0(1x) + 2) + 3) + 1))))/(1((2(-5(1cos(3\u03c0(1x) + 2) + 3)^2 + 5(1cos(3\u03c0(1x) + 2) + 3) + 1) - 2)/(3(-5(1cos(3\u03c0(1x) + 2) + 3)^2 + 5(1cos(3\u03c0(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": "60", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = 2|(-1(1(4(-1sin(3\u03c0x) + 3)^2 - 2(-1sin(3\u03c0x) + 3) + 4)^2 + 4(4(-1sin(3\u03c0x) + 3)^2 - 2(-1sin(3\u03c0x) + 3) + 4)) + 4) - 3| - 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|((1(-5(2sin(1\u03c0x - 2) - 2) - 5) - 3)/(-1(-5(2sin(1\u03c0x - 2) - 2) - 5))) + 3| + 2) + 2)/(-2(-2|((1(-5(2sin(1\u03c0x - 2) - 2) - 5) - 3)/(-1(-5(2sin(1\u03c0x - 2) - 2) - 5))) + 3| + 2) + 1) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "56", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 2sin(1\u03c0((1(1|(2(-4x + 4) - 5) + 1| - 2))/(-1(1|(2(-4x + 4) - 5) + 1| - 2) + 3))) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -2((-3(-2(-2e^(-2(-3x^2 + 1x - 3)) - 3) + 1))/(-2(-2(-2e^(-2(-3x^2 + 1x - 3)) - 3) + 1) - 2)) 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": "Find the number of local maximum points for f(x) = -4(3(1(1sin(1\u03c0((3x + 2)/(-1x - 2)) + 1) - 3)^2 + 4(1sin(1\u03c0((3x + 2)/(-1x - 2)) + 1) - 3) - 3)^2 - 5(1(1sin(1\u03c0((3x + 2)/(-1x - 2)) + 1) - 3)^2 + 4(1sin(1\u03c0((3x + 2)/(-1x - 2)) + 1) - 3) - 3) + 4) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 1(3|(-5(5(3sin(3\u03c0x) + 2) - 1)^2 - 2(5(3sin(3\u03c0x) + 2) - 1) - 2) + 3| - 1)^2 - 1(3|(-5(5(3sin(3\u03c0x) + 2) - 1)^2 - 2(5(3sin(3\u03c0x) + 2) - 1) - 2) + 3| - 1) - 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "94", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = 5(-4((2(-1|(-3cos(1\u03c0x + 2) + 1) + 1| + 3) - 1)/(1(-1|(-3cos(1\u03c0x + 2) + 1) + 1| + 3) - 3)))^2 - 4(-4((2(-1|(-3cos(1\u03c0x + 2) + 1) + 1| + 3) - 1)/(1(-1|(-3cos(1\u03c0x + 2) + 1) + 1| + 3) - 3))) + 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": "Determine the count of local minima for the function f(x) = (-2(3(2(-3(1sin(3\u03c0x) + 3) + 2) + 3)^2 + 3(2(-3(1sin(3\u03c0x) + 3) + 2) + 3) - 3) - 2)/(-3(3(2(-3(1sin(3\u03c0x) + 3) + 2) + 3)^2 + 3(2(-3(1sin(3\u03c0x) + 3) + 2) + 3) - 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 maxima for the function f(x) = 5(-1|(-2cos(1\u03c0(1|(-2|x| + 2) - 1| + 3) + 1) - 2)|)^2 - 4(-1|(-2cos(1\u03c0(1|(-2|x| + 2) - 1| + 3) + 1) - 2)|) - 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 1(2(4(1sin(3\u03c0(-4x^2 - 2x + 4)) + 1) - 3)^2 - 4(4(1sin(3\u03c0(-4x^2 - 2x + 4)) + 1) - 3) + 5) - 5 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) = 1(3sin(2\u03c0(4(-1|(-1|x| + 1) - 1| + 1) + 5) + 3) - 1)^2 + 5(3sin(2\u03c0(4(-1|(-1|x| + 1) - 1| + 1) + 5) + 3) - 1) + 5 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": "Find the number of local maximum points for f(x) = -1((-2(1|(2|(1x^2 + 4x - 3)| - 2) + 1| + 2) - 1)/(3(1|(2|(1x^2 + 4x - 3)| - 2) + 1| + 2)))^2 + 1((-2(1|(2|(1x^2 + 4x - 3)| - 2) + 1| + 2) - 1)/(3(1|(2|(1x^2 + 4x - 3)| - 2) + 1| + 2))) - 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -1|((1(2(1|(2cos(3\u03c0x + 2) + 3) - 2| - 3)^2 + 4(1|(2cos(3\u03c0x + 2) + 3) - 2| - 3) + 4) + 1)/(3(2(1|(2cos(3\u03c0x + 2) + 3) - 2| - 3)^2 + 4(1|(2cos(3\u03c0x + 2) + 3) - 2| - 3) + 4) - 1)) - 2| where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "86", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 2|(5(2cos(3\u03c0(-1|(5x - 5) + 3|) - 3) + 3) + 2) + 3| + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "150", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -3((-3(-2e^(1(-2|(5x^2 + 1x) + 2|)) + 3) - 1)/(1(-2e^(1(-2|(5x^2 + 1x) + 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 extrema (minima and maxima combined) does the function f(x) = 1(2|(-1sin(1\u03c0(1(2|x + 3| - 1) + 4) + 1) - 2) + 1| - 1) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -4(3sin(2\u03c0((3(-1(-3|x + 2|) - 1) - 1)/(1(-1(-3|x + 2|) - 1))) + 3))^2 - 3(3sin(2\u03c0((3(-1(-3|x + 2|) - 1) - 1)/(1(-1(-3|x + 2|) - 1))) + 3)) - 4 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -1((1(2|(-2(1|x - 3| - 2)^2 + 5(1|x - 3| - 2) - 3) - 3| - 2) + 2)/(1(2|(-2(1|x - 3| - 2)^2 + 5(1|x - 3| - 2) - 3) - 3| - 2) - 3))^2 + 5((1(2|(-2(1|x - 3| - 2)^2 + 5(1|x - 3| - 2) - 3) - 3| - 2) + 2)/(1(2|(-2(1|x - 3| - 2)^2 + 5(1|x - 3| - 2) - 3) - 3| - 2) - 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) = 3(2|(-3cos(2\u03c0(4(-4x^2 - 3x + 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": "8", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -2((-2(2cos(2\u03c0(-3|(-5x) + 2| - 1) + 1)) + 2)/(3(2cos(2\u03c0(-3|(-5x) + 2| - 1) + 1)) + 2)) + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "301", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = 1(3|(4(-2cos(1\u03c0(5x^2 - 4)) + 3)^2 - 2(-2cos(1\u03c0(5x^2 - 4)) + 3) + 2)| + 3) + 4 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "204", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 4((3(4(1((2x - 2)/(-3x - 1))^2 + 3((2x - 2)/(-3x - 1)) - 3)^2 + 3(1((2x - 2)/(-3x - 1))^2 + 3((2x - 2)/(-3x - 1)) - 3) + 2) + 1)/(3(4(1((2x - 2)/(-3x - 1))^2 + 3((2x - 2)/(-3x - 1)) - 3)^2 + 3(1((2x - 2)/(-3x - 1))^2 + 3((2x - 2)/(-3x - 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": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = (-3(-2(2(-3(-3|x - 2| - 2)^2 - 5(-3|x - 2| - 2) + 3)^2 + 2(-3(-3|x - 2| - 2)^2 - 5(-3|x - 2| - 2) + 3) + 3)^2 - 1(2(-3(-3|x - 2| - 2)^2 - 5(-3|x - 2| - 2) + 3)^2 + 2(-3(-3|x - 2| - 2)^2 - 5(-3|x - 2| - 2) + 3) + 3) + 2) + 2)/(-3(-2(2(-3(-3|x - 2| - 2)^2 - 5(-3|x - 2| - 2) + 3)^2 + 2(-3(-3|x - 2| - 2)^2 - 5(-3|x - 2| - 2) + 3) + 3)^2 - 1(2(-3(-3|x - 2| - 2)^2 - 5(-3|x - 2| - 2) + 3)^2 + 2(-3(-3|x - 2| - 2)^2 - 5(-3|x - 2| - 2) + 3) + 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) = -1((3(3|(-2(-1sin(2\u03c0x) - 2)^2 + 5(-1sin(2\u03c0x) - 2) - 3) - 3| + 3))/(-2(3|(-2(-1sin(2\u03c0x) - 2)^2 + 5(-1sin(2\u03c0x) - 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 number of local minimum points for f(x) = -3cos(2\u03c0(2(-2(4(1x^2 + 1x + 3) + 5)^2 + 4(4(1x^2 + 1x + 3) + 5) + 2) + 5) - 3) - 3 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": "Find the number of local minimum points for f(x) = 5(-1(-5(1(2cos(1\u03c0x + 1)) + 4) - 1) + 3)^2 - 1(-1(-5(1(2cos(1\u03c0x + 1)) + 4) - 1) + 3) + 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -3(5(2|(1sin(2\u03c0(-3x^2 - 1x + 3) - 1) + 1) + 3| - 3) + 1)^2 - 2(5(2|(1sin(2\u03c0(-3x^2 - 1x + 3) - 1) + 1) + 3| - 3) + 1) + 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "246", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = (-2(-2|(1|(1(-1x^2 - 5x + 2)^2 - 5(-1x^2 - 5x + 2) + 5) - 1| - 1) + 3| - 3) + 2)/(-3(-2|(1|(1(-1x^2 - 5x + 2)^2 - 5(-1x^2 - 5x + 2) + 5) - 1| - 1) + 3| - 3) - 2) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = 2(-1|(-2sin(3\u03c0(1((-1x + 3)/(3x - 2))^2 + 2((-1x + 3)/(3x - 2)) - 5) + 2)) - 1| + 3)^2 - 4(-1|(-2sin(3\u03c0(1((-1x + 3)/(3x - 2))^2 + 2((-1x + 3)/(3x - 2)) - 5) + 2)) - 1| + 3) 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": "Determine the total count of local extrema points for the function f(x) = -5(-1(-1sin(2\u03c0((-2(1|x - 2| + 2) - 3)/(-1(1|x - 2| + 2) + 3)) - 1) + 2)^2 - 3) - 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "138", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -1((2(-1(-2cos(2\u03c0(-5x^2 + 3x + 3) - 3) - 2) - 3) - 3)/(3(-1(-2cos(2\u03c0(-5x^2 + 3x + 3) - 3) - 2) - 3) - 2))^2 - 1((2(-1(-2cos(2\u03c0(-5x^2 + 3x + 3) - 3) - 2) - 3) - 3)/(3(-1(-2cos(2\u03c0(-5x^2 + 3x + 3) - 3) - 2) - 3) - 2)) - 5 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) = 1|(4(-2cos(1\u03c0(-3|((-1x - 1)/(3x - 2)) - 3| - 3) + 3) - 2)^2 - 4(-2cos(1\u03c0(-3|((-1x - 1)/(3x - 2)) - 3| - 3) + 3) - 2) - 2) + 3| - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "26", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = -1(3(-2sin(2\u03c0((3(3|x + 2| - 1) - 1)/(1(3|x + 2| - 1))) - 3) - 1)^2 + 2(-2sin(2\u03c0((3(3|x + 2| - 1) - 1)/(1(3|x + 2| - 1))) - 3) - 1) + 1)^2 + 2(3(-2sin(2\u03c0((3(3|x + 2| - 1) - 1)/(1(3|x + 2| - 1))) - 3) - 1)^2 + 2(-2sin(2\u03c0((3(3|x + 2| - 1) - 1)/(1(3|x + 2| - 1))) - 3) - 1) + 1) + 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -4(5(3cos(1\u03c0(1(1x^2 - 2x - 4) - 5) + 2)) + 3) - 4 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 count of local maxima for the function f(x) = 4(1cos(3\u03c0(-3|(2|((3x + 3)/(-2x - 3)) - 3|) + 3| - 1) - 1))^2 + 1(1cos(3\u03c0(-3|(2|((3x + 3)/(-2x - 3)) - 3|) + 3| - 1) - 1)) + 1 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 maximum points for f(x) = (2((3(-3(4(1e^(-2x) + 3)^2 + 2(1e^(-2x) + 3) - 3) + 3) - 1)/(1(-3(4(1e^(-2x) + 3)^2 + 2(1e^(-2x) + 3) - 3) + 3) + 3)) - 2)/(2((3(-3(4(1e^(-2x) + 3)^2 + 2(1e^(-2x) + 3) - 3) + 3) - 1)/(1(-3(4(1e^(-2x) + 3)^2 + 2(1e^(-2x) + 3) - 3) + 3) + 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": "Find the total number of local minima and maxima for f(x) = 1cos(2\u03c0(3(-1(1(2|x - 2| - 1))^2 - 3(1(2|x - 2| - 1)) + 1)^2 - 2(-1(1(2|x - 2| - 1))^2 - 3(1(2|x - 2| - 1)) + 1) + 1) + 3) + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "154", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 1((3(1(-1(-1|x - 3| + 2)^2 + 5(-1|x - 3| + 2) + 5)) + 1)/(-1(1(-1(-1|x - 3| + 2)^2 + 5(-1|x - 3| + 2) + 5)) + 2))^2 + 1((3(1(-1(-1|x - 3| + 2)^2 + 5(-1|x - 3| + 2) + 5)) + 1)/(-1(1(-1(-1|x - 3| + 2)^2 + 5(-1|x - 3| + 2) + 5)) + 2)) - 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -1sin(3\u03c0(4(3(-3(-3x + 2) - 2) + 1) + 2) - 2) + 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "486", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 3(3cos(3\u03c0(-5(1(-4x - 2) - 1)^2 - 2(1(-4x - 2) - 1) - 1) + 2) - 1)^2 - 1(3cos(3\u03c0(-5(1(-4x - 2) - 1)^2 - 2(1(-4x - 2) - 1) - 1) + 2) - 1) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "133", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 2cos(1\u03c0((2((1(5(-1x^2 + 2x + 4)^2 - 1(-1x^2 + 2x + 4)) - 2)/(-2(5(-1x^2 + 2x + 4)^2 - 1(-1x^2 + 2x + 4)) - 1)) - 3)/(3((1(5(-1x^2 + 2x + 4)^2 - 1(-1x^2 + 2x + 4)) - 2)/(-2(5(-1x^2 + 2x + 4)^2 - 1(-1x^2 + 2x + 4)) - 1)))) + 1) - 2 where -10 \u2264 x \u2264 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 maxima for the function f(x) = -1(3((2(3|(-2sin(3\u03c0x + 3) - 1)| - 2) + 3)/(3(3|(-2sin(3\u03c0x + 3) - 1)| - 2) + 2))^2 + 3((2(3|(-2sin(3\u03c0x + 3) - 1)| - 2) + 3)/(3(3|(-2sin(3\u03c0x + 3) - 1)| - 2) + 2)) + 5)^2 - 2(3((2(3|(-2sin(3\u03c0x + 3) - 1)| - 2) + 3)/(3(3|(-2sin(3\u03c0x + 3) - 1)| - 2) + 2))^2 + 3((2(3|(-2sin(3\u03c0x + 3) - 1)| - 2) + 3)/(3(3|(-2sin(3\u03c0x + 3) - 1)| - 2) + 2)) + 5) + 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 extrema (minima and maxima combined) does the function f(x) = -5((3(2|(-5((-3x + 3)/(2x - 3))^2 - 2((-3x + 3)/(2x - 3)) + 5)| - 3) + 3)/(2(2|(-5((-3x + 3)/(2x - 3))^2 - 2((-3x + 3)/(2x - 3)) + 5)| - 3) + 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": "How many local extrema (minima and maxima combined) does the function f(x) = 5((2(-1(2|((-2x + 2)/(-2x - 1)) - 2|)^2 - 3(2|((-2x + 2)/(-2x - 1)) - 2|)) + 1)/(-2(-1(2|((-2x + 2)/(-2x - 1)) - 2|)^2 - 3(2|((-2x + 2)/(-2x - 1)) - 2|))))^2 + 4((2(-1(2|((-2x + 2)/(-2x - 1)) - 2|)^2 - 3(2|((-2x + 2)/(-2x - 1)) - 2|)) + 1)/(-2(-1(2|((-2x + 2)/(-2x - 1)) - 2|)^2 - 3(2|((-2x + 2)/(-2x - 1)) - 2|)))) + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 1cos(2\u03c0((1((2(-2((-3x - 1)/(-2x - 2)) - 2) - 3)/(2(-2((-3x - 1)/(-2x - 2)) - 2) + 2)) + 3)/(1((2(-2((-3x - 1)/(-2x - 2)) - 2) - 3)/(2(-2((-3x - 1)/(-2x - 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": "50", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 2(3cos(3\u03c0(5(-3|(-2x + 2) - 1| + 1)^2 + 5(-3|(-2x + 2) - 1| + 1)) + 2) - 3)^2 + 1(3cos(3\u03c0(5(-3|(-2x + 2) - 1| + 1)^2 + 5(-3|(-2x + 2) - 1| + 1)) + 2) - 3) + 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "97", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = -4(-5(-2(-2(2sin(3\u03c0x + 1) + 3) + 5)^2 - 4(-2(2sin(3\u03c0x + 1) + 3) + 5))^2 - 2(-2(-2(2sin(3\u03c0x + 1) + 3) + 5)^2 - 4(-2(2sin(3\u03c0x + 1) + 3) + 5)) - 3)^2 + 4(-5(-2(-2(2sin(3\u03c0x + 1) + 3) + 5)^2 - 4(-2(2sin(3\u03c0x + 1) + 3) + 5))^2 - 2(-2(-2(2sin(3\u03c0x + 1) + 3) + 5)^2 - 4(-2(2sin(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": "106", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = (-3(2|(5(2|(-3x^2 - 5)| + 2)^2 + 3(2|(-3x^2 - 5)| + 2) + 1) - 2| + 3))/(2(2|(5(2|(-3x^2 - 5)| + 2)^2 + 3(2|(-3x^2 - 5)| + 2) + 1) - 2| + 3)) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "191", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = (-3(-5(5(-4(-1sin(3\u03c0x - 2) + 1) + 1) + 1)^2 - 4(5(-4(-1sin(3\u03c0x - 2) + 1) + 1) + 1) + 4) - 3)/(1(-5(5(-4(-1sin(3\u03c0x - 2) + 1) + 1) + 1)^2 - 4(5(-4(-1sin(3\u03c0x - 2) + 1) + 1) + 1) + 4) - 3) 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 total count of local extrema points for the function f(x) = 3(3(-2|(1sin(2\u03c0(-1x + 1)) + 3) - 2| - 2) + 2)^2 - 5(3(-2|(1sin(2\u03c0(-1x + 1)) + 3) - 2| - 2) + 2) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 5(-1(-2|(1(2|x - 2| - 3)^2 - 4(2|x - 2| - 3) - 3) + 3| + 3)^2 - 2(-2|(1(2|x - 2| - 3)^2 - 4(2|x - 2| - 3) - 3) + 3| + 3) + 4) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -1(-2|((1(1|(1x^2 + 5x - 4) + 1| + 1) + 3)/(1(1|(1x^2 + 5x - 4) + 1| + 1) - 3))| + 2)^2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -2(-3(1e^(-1(1(2|x + 3| + 1)^2 - 4(2|x + 3| + 1) - 3)) - 2) - 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": "How many local minima does the function f(x) = 1sin(3\u03c0((1(2|(5(3|x + 2|) - 4) + 1| + 1) - 1)/(-1(2|(5(3|x + 2|) - 4) + 1| + 1) + 2)) - 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = 3sin(2\u03c0(-2((-3(2((1x + 3)/(2x + 1))^2 + 4((1x + 3)/(2x + 1)) - 3))/(3(2((1x + 3)/(2x + 1))^2 + 4((1x + 3)/(2x + 1)) - 3) - 2)) - 4) + 3) + 2 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) = -1(-1(3|(1|(5x - 4) - 3|) - 1| - 3)^2 - 5)^2 - 4(-1(3|(1|(5x - 4) - 3|) - 1| - 3)^2 - 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": "How many local minima does the function f(x) = 2cos(3\u03c0(-5(-1(3|((3x - 3)/(2x + 1)) + 3| - 1) + 1)^2 + 3(-1(3|((3x - 3)/(2x + 1)) + 3| - 1) + 1) - 4)) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "286", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = (1(3|(-1(-2|(1cos(2\u03c0x - 3) + 3) - 1| + 2) + 1) + 2| + 2) - 1)/(2(3|(-1(-2|(1cos(2\u03c0x - 3) + 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": "20", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 5(4(2cos(2\u03c0(-1(-4x + 2) + 5) + 1) - 1)^2 - 5(2cos(2\u03c0(-1(-4x + 2) + 5) + 1) - 1) - 3)^2 + 1(4(2cos(2\u03c0(-1(-4x + 2) + 5) + 1) - 1)^2 - 5(2cos(2\u03c0(-1(-4x + 2) + 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": "243", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -2|((-3(-1cos(2\u03c0((-1(2x + 5) - 3)/(-2(2x + 5) - 3)) - 2) - 2) + 2)/(-2(-1cos(2\u03c0((-1(2x + 5) - 3)/(-2(2x + 5) - 3)) - 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": "18", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -5(-2cos(1\u03c0((1(4((2x + 3)/(1x + 3)) - 1))/(-3(4((2x + 3)/(1x + 3)) - 1))) - 1) + 3)^2 - 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "299", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 5(4(-3|(-1((-2x + 2)/(-3x + 1))^2 + 1) + 1| + 1)^2 - 2(-3|(-1((-2x + 2)/(-3x + 1))^2 + 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": "6", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -3|((-2((-1(3cos(1\u03c0(-1x - 5) - 3) - 3) - 2)/(-3(3cos(1\u03c0(-1x - 5) - 3) - 3) - 2)) + 1)/(-3((-1(3cos(1\u03c0(-1x - 5) - 3) - 3) - 2)/(-3(3cos(1\u03c0(-1x - 5) - 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": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = (-3(-1(-2e^(-1(-1|(5x^2 - 3x) + 1| + 2)) + 2)) - 3)/(-1(-1(-2e^(-1(-1|(5x^2 - 3x) + 1| + 2)) + 2)) + 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = -2(5(3sin(1\u03c0(-3|(4x + 2) + 3| - 3) + 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) = -2(-1|(1sin(2\u03c0(3(3x + 1) - 3) - 2)) - 2| + 3)^2 + 4(-1|(1sin(2\u03c0(3(3x + 1) - 3) - 2)) - 2| + 3) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "720", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = -4(-3(1(2cos(2\u03c0(-4x + 3) + 3) + 3)^2 - 4)^2 - 1(1(2cos(2\u03c0(-4x + 3) + 3) + 3)^2 - 4) - 3) - 5 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "157", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = 1(1cos(1\u03c0(-1(-2((-1x + 1)/(2x + 2)) + 1) + 5) - 3) + 2)^2 + 4 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((-3((-2(3(-1x)^2 + 1(-1x) - 4) + 3)/(3(3(-1x)^2 + 1(-1x) - 4) - 1)))/(-1((-2(3(-1x)^2 + 1(-1x) - 4) + 3)/(3(3(-1x)^2 + 1(-1x) - 4) - 1)) + 2))^2 + 4((-3((-2(3(-1x)^2 + 1(-1x) - 4) + 3)/(3(3(-1x)^2 + 1(-1x) - 4) - 1)))/(-1((-2(3(-1x)^2 + 1(-1x) - 4) + 3)/(3(3(-1x)^2 + 1(-1x) - 4) - 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": "Determine the total count of local extrema points for the function f(x) = 1sin(1\u03c0(5(4(-1|(3|x - 3| + 3) - 3|)^2 - 5(-1|(3|x - 3| + 3) - 3|) - 1)^2 + 5(4(-1|(3|x - 3| + 3) - 3|)^2 - 5(-1|(3|x - 3| + 3) - 3|) - 1) + 4) - 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": "How many local maxima does the function f(x) = (-2(-2((-2(-2cos(1\u03c0(1x + 2) + 1) + 2) - 3)/(3(-2cos(1\u03c0(1x + 2) + 1) + 2) - 2)) + 2))/(-1(-2((-2(-2cos(1\u03c0(1x + 2) + 1) + 2) - 3)/(3(-2cos(1\u03c0(1x + 2) + 1) + 2) - 2)) + 2) - 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = 4(1((2(2(-2cos(2\u03c0x - 1) + 1) - 4) + 3)/(3(2(-2cos(2\u03c0x - 1) + 1) - 4) + 2))^2 + 5((2(2(-2cos(2\u03c0x - 1) + 1) - 4) + 3)/(3(2(-2cos(2\u03c0x - 1) + 1) - 4) + 2)) + 2)^2 - 2(1((2(2(-2cos(2\u03c0x - 1) + 1) - 4) + 3)/(3(2(-2cos(2\u03c0x - 1) + 1) - 4) + 2))^2 + 5((2(2(-2cos(2\u03c0x - 1) + 1) - 4) + 3)/(3(2(-2cos(2\u03c0x - 1) + 1) - 4) + 2)) + 2) - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "71", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = (-2(1((3(1cos(3\u03c0(1|x - 2| - 3) - 1) + 2) + 2)/(1(1cos(3\u03c0(1|x - 2| - 3) - 1) + 2) + 1))) + 2)/(1(1((3(1cos(3\u03c0(1|x - 2| - 3) - 1) + 2) + 2)/(1(1cos(3\u03c0(1|x - 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": "31", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -2(1(-2|(-1cos(1\u03c0((3x)/(1x - 3)) + 1) - 2) - 2| + 1) + 4)^2 - 3(1(-2|(-1cos(1\u03c0((3x)/(1x - 3)) + 1) - 2) - 2| + 1) + 4) + 4 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": "Find the number of local minimum points for f(x) = -1(-5((-2((1(4x^2 + 2x + 2) + 2)/(-1(4x^2 + 2x + 2) + 2)) - 2)/(3((1(4x^2 + 2x + 2) + 2)/(-1(4x^2 + 2x + 2) + 2)) + 3))^2 + 1((-2((1(4x^2 + 2x + 2) + 2)/(-1(4x^2 + 2x + 2) + 2)) - 2)/(3((1(4x^2 + 2x + 2) + 2)/(-1(4x^2 + 2x + 2) + 2)) + 3)) - 4)^2 - 1(-5((-2((1(4x^2 + 2x + 2) + 2)/(-1(4x^2 + 2x + 2) + 2)) - 2)/(3((1(4x^2 + 2x + 2) + 2)/(-1(4x^2 + 2x + 2) + 2)) + 3))^2 + 1((-2((1(4x^2 + 2x + 2) + 2)/(-1(4x^2 + 2x + 2) + 2)) - 2)/(3((1(4x^2 + 2x + 2) + 2)/(-1(4x^2 + 2x + 2) + 2)) + 3)) - 4) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "149", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 1|(-1((1((-3(3sin(2\u03c0x - 2) + 2))/(1(3sin(2\u03c0x - 2) + 2) + 2)) + 1)/(3((-3(3sin(2\u03c0x - 2) + 2))/(1(3sin(2\u03c0x - 2) + 2) + 2)) - 1))^2 - 1((1((-3(3sin(2\u03c0x - 2) + 2))/(1(3sin(2\u03c0x - 2) + 2) + 2)) + 1)/(3((-3(3sin(2\u03c0x - 2) + 2))/(1(3sin(2\u03c0x - 2) + 2) + 2)) - 1)) - 5) - 1| + 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) = -2((-3(4(2sin(2\u03c0((1x)/(-3x + 4)) - 2))^2 + 4(2sin(2\u03c0((1x)/(-3x + 4)) - 2)) - 5) + 2)/(-1(4(2sin(2\u03c0((1x)/(-3x + 4)) - 2))^2 + 4(2sin(2\u03c0((1x)/(-3x + 4)) - 2)) - 5) - 2)) + 5 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": "Find the number of local minimum points for f(x) = (2(-5((-1(-2(1|x - 3| - 2)^2 + 1) - 1)/(-3(-2(1|x - 3| - 2)^2 + 1) - 2))^2 + 2((-1(-2(1|x - 3| - 2)^2 + 1) - 1)/(-3(-2(1|x - 3| - 2)^2 + 1) - 2)) + 4) + 1)/(-3(-5((-1(-2(1|x - 3| - 2)^2 + 1) - 1)/(-3(-2(1|x - 3| - 2)^2 + 1) - 2))^2 + 2((-1(-2(1|x - 3| - 2)^2 + 1) - 1)/(-3(-2(1|x - 3| - 2)^2 + 1) - 2)) + 4) + 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": "How many local maxima does the function f(x) = -2(-5(-3sin(3\u03c0(4(-4x^2 - 3x + 5)^2 - 2) - 1) - 3)^2 - 1(-3sin(3\u03c0(4(-4x^2 - 3x + 5)^2 - 2) - 1) - 3) - 3)^2 - 4(-5(-3sin(3\u03c0(4(-4x^2 - 3x + 5)^2 - 2) - 1) - 3)^2 - 1(-3sin(3\u03c0(4(-4x^2 - 3x + 5)^2 - 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": "31", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 4(-2|(2|((-2(3cos(1\u03c0x + 1) - 1) + 3)/(-1(3cos(1\u03c0x + 1) - 1) - 1))| + 2) + 1| - 1)^2 - 5(-2|(2|((-2(3cos(1\u03c0x + 1) - 1) + 3)/(-1(3cos(1\u03c0x + 1) - 1) - 1))| + 2) + 1| - 1) - 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 number of local maximum points for f(x) = -5(1cos(2\u03c0(4(3|(3x^2 + 2x - 3) + 1| + 2)^2 - 2(3|(3x^2 + 2x - 3) + 1| + 2) + 2) + 1) - 3)^2 + 2(1cos(2\u03c0(4(3|(3x^2 + 2x - 3) + 1| + 2)^2 - 2(3|(3x^2 + 2x - 3) + 1| + 2) + 2) + 1) - 3) - 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "55", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = (-2(-1|(3|(2cos(2\u03c0(-2|x - 3|) + 1) + 2) + 3|) + 3| + 3) + 3)/(-2(-1|(3|(2cos(2\u03c0(-2|x - 3|) + 1) + 2) + 3|) + 3| + 3)) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "81", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -3(5(-2e^(2(-5(1|x + 3| - 2)^2 + 5(1|x + 3| - 2) + 5)) + 1)^2 + 2(-2e^(2(-5(1|x + 3| - 2)^2 + 5(1|x + 3| - 2) + 5)) + 1) + 3)^2 + 5(5(-2e^(2(-5(1|x + 3| - 2)^2 + 5(1|x + 3| - 2) + 5)) + 1)^2 + 2(-2e^(2(-5(1|x + 3| - 2)^2 + 5(1|x + 3| - 2) + 5)) + 1) + 3) - 4 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = -1(1|((3(3(3x^2 - 4x + 5)^2 + 2(3x^2 - 4x + 5) + 2) + 3)/(-1(3(3x^2 - 4x + 5)^2 + 2(3x^2 - 4x + 5) + 2) - 1)) - 1| - 2)^2 + 1(1|((3(3(3x^2 - 4x + 5)^2 + 2(3x^2 - 4x + 5) + 2) + 3)/(-1(3(3x^2 - 4x + 5)^2 + 2(3x^2 - 4x + 5) + 2) - 1)) - 1| - 2) + 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "25", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = (1(5((-1(-2cos(1\u03c0(4x^2 + 4x) + 3) - 1) + 3)/(2(-2cos(1\u03c0(4x^2 + 4x) + 3) - 1) - 1))^2 - 3((-1(-2cos(1\u03c0(4x^2 + 4x) + 3) - 1) + 3)/(2(-2cos(1\u03c0(4x^2 + 4x) + 3) - 1) - 1)) - 2) - 1)/(-3(5((-1(-2cos(1\u03c0(4x^2 + 4x) + 3) - 1) + 3)/(2(-2cos(1\u03c0(4x^2 + 4x) + 3) - 1) - 1))^2 - 3((-1(-2cos(1\u03c0(4x^2 + 4x) + 3) - 1) + 3)/(2(-2cos(1\u03c0(4x^2 + 4x) + 3) - 1) - 1)) - 2) - 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "385", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = 3|(5(5(1(-5x^2 - 1x)^2 + 5(-5x^2 - 1x)) + 2)^2 + 1(5(1(-5x^2 - 1x)^2 + 5(-5x^2 - 1x)) + 2) + 5) - 2| + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 1cos(2\u03c0((-2(5(1((2x + 2)/(-3x + 4))) - 4) - 2)/(-1(5(1((2x + 2)/(-3x + 4))) - 4) + 3)) - 3) + 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 3cos(2\u03c0(1|((-3(-3(-3|x + 3| - 1)^2 - 3(-3|x + 3| - 1) + 4) + 1)/(-1(-3(-3|x + 3| - 1)^2 - 3(-3|x + 3| - 1) + 4) - 1)) - 1| + 3) - 1) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = 3cos(1\u03c0((-2(-4(-1(-3x - 5) - 2) + 4))/(-1(-4(-1(-3x - 5) - 2) + 4) - 2)) - 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 3(3|((-3((2(2sin(1\u03c0x - 2)) - 1)/(-3(2sin(1\u03c0x - 2)) - 3)) - 1)/(2((2(2sin(1\u03c0x - 2)) - 1)/(-3(2sin(1\u03c0x - 2)) - 3)) + 3)) - 2|) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = (-2(-1cos(1\u03c0((-1(-4(-3|x - 2| + 1) + 1) + 3)/(-2(-4(-3|x - 2| + 1) + 1) - 2)) + 1) + 3) + 3)/(2(-1cos(1\u03c0((-1(-4(-3|x - 2| + 1) + 1) + 3)/(-2(-4(-3|x - 2| + 1) + 1) - 2)) + 1) + 3) - 1) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 2(2(2sin(1\u03c0(2|(3|x + 1| - 2) + 3| + 2) - 3) + 3)^2 - 5(2sin(1\u03c0(2|(3|x + 1| - 2) + 3| + 2) - 3) + 3) - 1) - 5 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 count of local maxima for the function f(x) = -3sin(2\u03c0(-1(1|((2(1x - 1))/(-3(1x - 1) + 1)) - 2| + 3) - 1) - 1) + 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 1(-5(2(1(1|x + 2| + 3)^2 - 5(1|x + 2| + 3) + 5)^2 + 1(1(1|x + 2| + 3)^2 - 5(1|x + 2| + 3) + 5))^2 + 4(2(1(1|x + 2| + 3)^2 - 5(1|x + 2| + 3) + 5)^2 + 1(1(1|x + 2| + 3)^2 - 5(1|x + 2| + 3) + 5)) - 1) - 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 extrema (minima and maxima combined) does the function f(x) = (-2(4(-2|(-1|(1x^2 + 5x + 3) + 2| + 1) + 1|)^2 + 4(-2|(-1|(1x^2 + 5x + 3) + 2| + 1) + 1|) + 4) - 2)/(-1(4(-2|(-1|(1x^2 + 5x + 3) + 2| + 1) + 1|)^2 + 4(-2|(-1|(1x^2 + 5x + 3) + 2| + 1) + 1|) + 4) - 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -1sin(2\u03c0(-2(3((2((1x - 2)/(-3x - 1)))/(1((1x - 2)/(-3x - 1)) - 2))^2 + 2((2((1x - 2)/(-3x - 1)))/(1((1x - 2)/(-3x - 1)) - 2))) - 2) - 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": "How many local minima does the function f(x) = -1((3(-2|(-3|(-1sin(2\u03c0x + 1) - 3) + 2| + 1)| + 1) + 2)/(1(-2|(-3|(-1sin(2\u03c0x + 1) - 3) + 2| + 1)| + 1) - 2))^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": "Determine the count of local minima for the function f(x) = -1(-1(3sin(1\u03c0(1(5x^2 + 2x + 3)^2 - 5) + 1) + 2)^2 + 5(3sin(1\u03c0(1(5x^2 + 2x + 3)^2 - 5) + 1) + 2) + 2)^2 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 maxima for the function f(x) = -1(-1sin(1\u03c0(3(-5(3|x - 3|) + 3))) + 1) - 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "451", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -1sin(1\u03c0(-2(5((-3(4x^2 + 4x + 5) - 2)/(-2(4x^2 + 4x + 5) + 3)) + 4)^2 + 2) + 1) - 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "102", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -2sin(2\u03c0(1|(-3|((1((-3x + 3)/(-2x - 1)))/(-3((-3x + 3)/(-2x - 1)) + 2)) - 3| + 3) - 3| + 2) - 2) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -1|((-2(3sin(3\u03c0(-4(-2x^2 - 3)^2 - 1(-2x^2 - 3) + 5) - 3) + 2) - 3)/(-2(3sin(3\u03c0(-4(-2x^2 - 3)^2 - 1(-2x^2 - 3) + 5) - 3) + 2) - 2)) - 2| - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "174", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -2cos(3\u03c0((-2(-3((-2(1x^2 + 4x + 4) + 1)/(-3(1x^2 + 4x + 4) - 1))^2 + 1((-2(1x^2 + 4x + 4) + 1)/(-3(1x^2 + 4x + 4) - 1))) - 3)/(-3(-3((-2(1x^2 + 4x + 4) + 1)/(-3(1x^2 + 4x + 4) - 1))^2 + 1((-2(1x^2 + 4x + 4) + 1)/(-3(1x^2 + 4x + 4) - 1))) + 4)) - 3) - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 3sin(3\u03c0(-2|((1(4(2|x| - 1) - 1) - 3)/(2(4(2|x| - 1) - 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": "27", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -1(-2|(-1e^(-2((-2(1x^2 + 3x - 3) - 1)/(-2(1x^2 + 3x - 3) + 1))) + 2) + 2| + 2) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -1cos(2\u03c0(4(3|(-4((2x - 3)/(3x - 1))^2 - 5((2x - 3)/(3x - 1)) + 5) - 3| + 3)^2 + 2(3|(-4((2x - 3)/(3x - 1))^2 - 5((2x - 3)/(3x - 1)) + 5) - 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": "246", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = -2(3|(-2cos(2\u03c0((1((2x + 3)/(2x + 1)) + 2)/(-2((2x + 3)/(2x + 1)) + 1)) + 3)) - 2| + 3)^2 + 4(3|(-2cos(2\u03c0((1((2x + 3)/(2x + 1)) + 2)/(-2((2x + 3)/(2x + 1)) + 1)) + 3)) - 2| + 3) + 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "25", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = (2(2sin(1\u03c0(-2(-2(3x + 4)^2 + 1(3x + 4) + 5) + 5) + 3) + 3) + 1)/(-3(2sin(1\u03c0(-2(-2(3x + 4)^2 + 1(3x + 4) + 5) + 5) + 3) + 3)) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "377", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -2cos(3\u03c0(3|(2((-2((-2x - 2)/(-2x - 1)))/(3((-2x - 2)/(-2x - 1)) + 2))^2 + 3((-2((-2x - 2)/(-2x - 1)))/(3((-2x - 2)/(-2x - 1)) + 2)) + 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": "How many local extrema (minima and maxima combined) does the function f(x) = (3(2sin(2\u03c0(-2(4((3x + 3)/(1x + 3))^2 + 5((3x + 3)/(1x + 3)) + 4)^2 - 1) + 2) + 2) + 2)/(-1(2sin(2\u03c0(-2(4((3x + 3)/(1x + 3))^2 + 5((3x + 3)/(1x + 3)) + 4)^2 - 1) + 2) + 2) - 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "355", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 3(-5(1cos(1\u03c0(-4(3|x + 2| - 3) - 1) - 2) - 3) + 3)^2 + 1(-5(1cos(1\u03c0(-4(3|x + 2| - 3) - 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": "241", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -4(1|((3(1|(-3|x + 2| + 3) + 3| + 1) - 3)/(-2(1|(-3|x + 2| + 3) + 3| + 1) + 3)) - 1| - 1)^2 + 5(1|((3(1|(-3|x + 2| + 3) + 3| + 1) - 3)/(-2(1|(-3|x + 2| + 3) + 3| + 1) + 3)) - 1| - 1) - 5 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 minimum points for f(x) = -2|(-2(2cos(2\u03c0(-2((2x - 2)/(-3x - 1))^2 + 5((2x - 2)/(-3x - 1)) - 1) - 1) - 2)^2 - 1(2cos(2\u03c0(-2((2x - 2)/(-3x - 1))^2 + 5((2x - 2)/(-3x - 1)) - 1) - 1) - 2) - 1) + 3| - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "85", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 1sin(1\u03c0(-1|(-2(-4((-3x - 3)/(2x - 1))^2 - 2((-3x - 3)/(2x - 1)) - 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": "60", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = 4(3(-2(-3|((-2x + 1)/(2x + 2)) + 2| + 3) + 4)^2 - 4(-2(-3|((-2x + 1)/(2x + 2)) + 2| + 3) + 4) + 3)^2 - 2(3(-2(-3|((-2x + 1)/(2x + 2)) + 2| + 3) + 4)^2 - 4(-2(-3|((-2x + 1)/(2x + 2)) + 2| + 3) + 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": "Determine the total count of local extrema points for the function f(x) = 2(3(-1sin(3\u03c0(-1((-1x - 1)/(-3x + 1))) + 1))^2 - 4(-1sin(3\u03c0(-1((-1x - 1)/(-3x + 1))) + 1)) + 5)^2 - 2(3(-1sin(3\u03c0(-1((-1x - 1)/(-3x + 1))) + 1))^2 - 4(-1sin(3\u03c0(-1((-1x - 1)/(-3x + 1))) + 1)) + 5) - 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 5((1(1(-3cos(2\u03c0((-2x + 2)/(2x + 3))) + 3)^2 + 4(-3cos(2\u03c0((-2x + 2)/(2x + 3))) + 3) - 2) - 3)/(3(1(-3cos(2\u03c0((-2x + 2)/(2x + 3))) + 3)^2 + 4(-3cos(2\u03c0((-2x + 2)/(2x + 3))) + 3) - 2) + 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": "Determine the total count of local extrema points for the function f(x) = 2sin(2\u03c0((2(-3(3(-1x + 2)^2 + 5(-1x + 2) - 1) - 5) - 1)/(-1(-3(3(-1x + 2)^2 + 5(-1x + 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": "30", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -3sin(1\u03c0(-3|(1(3|(-2|x + 2| - 3) + 1| - 1)) - 1| + 3)) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "181", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -3sin(1\u03c0(-5(-3(4((-3x + 2)/(-3x - 3))^2 - 5((-3x + 2)/(-3x - 3)) + 5)^2 - 5(4((-3x + 2)/(-3x - 3))^2 - 5((-3x + 2)/(-3x - 3)) + 5) + 1) + 2) + 2) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "154", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -4(-2cos(2\u03c0(-1|(4((-3x + 2)/(-1x + 2))^2 + 4((-3x + 2)/(-1x + 2)) + 4) + 1| + 2) + 3) + 2) + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -1cos(2\u03c0(2(4(2|(3|x| + 2) - 1| - 3)^2 + 5(2|(3|x| + 2) - 1| - 3) + 5) - 2) + 3) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "169", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -1((3(-3(1|(2x^2 - 5x + 2) + 2|)^2 + 5) - 3)/(2(-3(1|(2x^2 - 5x + 2) + 2|)^2 + 5)))^2 - 2((3(-3(1|(2x^2 - 5x + 2) + 2|)^2 + 5) - 3)/(2(-3(1|(2x^2 - 5x + 2) + 2|)^2 + 5))) - 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": "How many local maxima does the function f(x) = -5(3cos(1\u03c0(3(2(5x^2 + 5x - 3) - 4)^2 - 2(2(5x^2 + 5x - 3) - 4) - 3) + 2) - 1)^2 - 3(3cos(1\u03c0(3(2(5x^2 + 5x - 3) - 4)^2 - 2(2(5x^2 + 5x - 3) - 4) - 3) + 2) - 1) - 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 number of local maximum points for f(x) = 5(-3|(1sin(3\u03c0(-5(-4x^2 - 5x)^2 - 3(-4x^2 - 5x) - 3) + 1) - 2)| + 3)^2 - 1(-3|(1sin(3\u03c0(-5(-4x^2 - 5x)^2 - 3(-4x^2 - 5x) - 3) + 1) - 2)| + 3) + 5 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": "Determine the count of local maxima for the function f(x) = -1(-4(1(-1(1cos(3\u03c0x + 3))^2 + 2(1cos(3\u03c0x + 3)) - 4)^2 + 2(-1(1cos(3\u03c0x + 3))^2 + 2(1cos(3\u03c0x + 3)) - 4) - 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 extrema (minima and maxima combined) does the function f(x) = 3|(2(1sin(1\u03c0(-1|(5x + 4) + 3|) + 3) - 2) + 2) - 3| - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "101", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = (3(3sin(1\u03c0(-4(5(-2|x + 3| + 1)^2 + 5(-2|x + 3| + 1) + 2) - 3) + 1) + 1) + 3)/(-1(3sin(1\u03c0(-4(5(-2|x + 3| + 1)^2 + 5(-2|x + 3| + 1) + 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": "333", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = (-3(2(4(-1|((-2x - 2)/(-3x + 4)) - 3| + 1) + 3)))/(-1(2(4(-1|((-2x - 2)/(-3x + 4)) - 3| + 1) + 3))) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -1|(-3sin(1\u03c0(2(4(1x - 5)^2 - 1(1x - 5) - 4)) + 3) + 2) + 3| - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "508", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -1(1|(-2|(5(3sin(3\u03c0x - 1) - 3)^2 - 1(3sin(3\u03c0x - 1) - 3) + 1) + 3|) - 2| - 2) + 4 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) = -5((1((-2(2sin(3\u03c0((3x - 3)/(1x)) + 1) + 1) - 1)/(-2(2sin(3\u03c0((3x - 3)/(1x)) + 1) + 1))) - 3)/(-1((-2(2sin(3\u03c0((3x - 3)/(1x)) + 1) + 1) - 1)/(-2(2sin(3\u03c0((3x - 3)/(1x)) + 1) + 1))))) - 1 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(3cos(1\u03c0(4(-2|((-1x)/(3x + 1))| + 2)^2 - 3(-2|((-1x)/(3x + 1))| + 2) - 5) + 2) + 2))/(-2(3cos(1\u03c0(4(-2|((-1x)/(3x + 1))| + 2)^2 - 3(-2|((-1x)/(3x + 1))| + 2) - 5) + 2) + 2) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -5(-5(2|(2(1sin(3\u03c0x + 1) + 3)^2 + 2(1sin(3\u03c0x + 1) + 3) - 5)| + 3)^2 + 1(2|(2(1sin(3\u03c0x + 1) + 3)^2 + 2(1sin(3\u03c0x + 1) + 3) - 5)| + 3) - 5)^2 + 2(-5(2|(2(1sin(3\u03c0x + 1) + 3)^2 + 2(1sin(3\u03c0x + 1) + 3) - 5)| + 3)^2 + 1(2|(2(1sin(3\u03c0x + 1) + 3)^2 + 2(1sin(3\u03c0x + 1) + 3) - 5)| + 3) - 5) - 1 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 minima does the function f(x) = 5(-1sin(1\u03c0(-4(2|(3x^2 - 1x) - 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": "65", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -1cos(1\u03c0(1(-2|((1(-1|x - 1| + 3))/(3(-1|x - 1| + 3) + 2)) - 2| + 1) + 5) - 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 2|(1cos(3\u03c0(-2|(-4(4x^2 + 4x + 4) + 1) + 1| + 3))) + 2| + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "445", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 5(3(1cos(2\u03c0(-2|(-1x - 5) + 3| + 2) + 3) + 1)^2 - 1(1cos(2\u03c0(-2|(-1x - 5) + 3| + 2) + 3) + 1) - 4) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "161", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -5(-3(-2cos(3\u03c0((-3((-3x)/(-1x - 1)) + 3)/(2((-3x)/(-1x - 1)) + 1)) + 3) - 2) + 3) + 4 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 1(2(-3(1(-1cos(2\u03c0x - 1))^2 - 4(-1cos(2\u03c0x - 1)) + 2)^2 + 2(1(-1cos(2\u03c0x - 1))^2 - 4(-1cos(2\u03c0x - 1)) + 2))^2 - 2(-3(1(-1cos(2\u03c0x - 1))^2 - 4(-1cos(2\u03c0x - 1)) + 2)^2 + 2(1(-1cos(2\u03c0x - 1))^2 - 4(-1cos(2\u03c0x - 1)) + 2))) + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 4((1((-3(2|(3|x - 3| - 2) + 2| + 1))/(-2(2|(3|x - 3| - 2) + 2| + 1))) + 3)/(2((-3(2|(3|x - 3| - 2) + 2| + 1))/(-2(2|(3|x - 3| - 2) + 2| + 1))) + 1))^2 + 5((1((-3(2|(3|x - 3| - 2) + 2| + 1))/(-2(2|(3|x - 3| - 2) + 2| + 1))) + 3)/(2((-3(2|(3|x - 3| - 2) + 2| + 1))/(-2(2|(3|x - 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": "99", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 1(-4(-1(-1sin(2\u03c0(4x) + 2) - 3) - 3) - 4)^2 + 5(-4(-1(-1sin(2\u03c0(4x) + 2) - 3) - 3) - 4) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "320", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = 1|(-4(3(1sin(2\u03c0(1x^2 + 5x + 2)) - 1) + 1)^2 + 2(3(1sin(2\u03c0(1x^2 + 5x + 2)) - 1) + 1) - 3) - 2| - 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "197", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 2cos(2\u03c0(2(-3|(3((-2x - 1)/(3x - 2))) - 3| + 2)^2 + 1(-3|(3((-2x - 1)/(3x - 2))) - 3| + 2) + 4) - 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 extrema (minima and maxima combined) does the function f(x) = 3(1((-2(-2(5x - 2)^2 + 2(5x - 2)) - 2)/(1(-2(5x - 2)^2 + 2(5x - 2)) + 3)) - 1)^2 - 1(1((-2(-2(5x - 2)^2 + 2(5x - 2)) - 2)/(1(-2(5x - 2)^2 + 2(5x - 2)) + 3)) - 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 maxima does the function f(x) = -2|((-1((1(3|(-5x^2 - 3x + 4)| - 3) - 3)/(-2(3|(-5x^2 - 3x + 4)| - 3) + 3)) - 2)/(1((1(3|(-5x^2 - 3x + 4)| - 3) - 3)/(-2(3|(-5x^2 - 3x + 4)| - 3) + 3)) + 1)) + 3| - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 1|(1((-1(2|(5x) + 3| + 1) - 1)/(1(2|(5x) + 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": "4", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -3(-5(2|(2cos(3\u03c0(-3x^2 + 5x - 2) + 3) - 2) - 1| + 1)^2 - 4(2|(2cos(3\u03c0(-3x^2 + 5x - 2) + 3) - 2) - 1| + 1) + 5) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "483", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -4(3(-1cos(1\u03c0(3(-1|x - 3| - 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": "61", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 5(-2|((-3(2sin(3\u03c0(3x^2 - 2x - 1) + 1) + 2) - 2)/(3(2sin(3\u03c0(3x^2 - 2x - 1) + 1) + 2) - 2)) + 3|) + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "496", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -1(1(-1((-2(-4x^2 + 3x - 2) + 2)/(2(-4x^2 + 3x - 2) + 3)) + 2) - 3)^2 + 5(1(-1((-2(-4x^2 + 3x - 2) + 2)/(2(-4x^2 + 3x - 2) + 3)) + 2) - 3) - 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 2((1((-3(-3(2sin(1\u03c0x + 1) - 3)) - 1)/(-2(-3(2sin(1\u03c0x + 1) - 3)) + 1)) + 3)/(-2((-3(-3(2sin(1\u03c0x + 1) - 3)) - 1)/(-2(-3(2sin(1\u03c0x + 1) - 3)) + 1))))^2 - 2((1((-3(-3(2sin(1\u03c0x + 1) - 3)) - 1)/(-2(-3(2sin(1\u03c0x + 1) - 3)) + 1)) + 3)/(-2((-3(-3(2sin(1\u03c0x + 1) - 3)) - 1)/(-2(-3(2sin(1\u03c0x + 1) - 3)) + 1)))) - 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = (-3(1(3(3(-5x^2 + 3x - 1)^2 - 3) - 1)^2 + 2(3(3(-5x^2 + 3x - 1)^2 - 3) - 1) + 2) - 2)/(3(1(3(3(-5x^2 + 3x - 1)^2 - 3) - 1)^2 + 2(3(3(-5x^2 + 3x - 1)^2 - 3) - 1) + 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": "How many local minima does the function f(x) = -3sin(3\u03c0(3(-2(-1|(-3x^2 - 4x - 2) + 3|) + 1) - 5) + 1) - 3 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 total count of local extrema points for the function f(x) = -2|(2(-1(2(4x^2 - 3x - 4)^2 + 1(4x^2 - 3x - 4) - 1) + 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": "Determine the total count of local extrema points for the function f(x) = 1|(1|(-1(5(1cos(1\u03c0x)) - 3)^2 - 3(5(1cos(1\u03c0x)) - 3) - 5) + 1| + 2) - 2| + 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = 1(3sin(3\u03c0(-2(5(4x^2 + 3x + 1) + 1) + 4) - 1) + 3)^2 - 1(3sin(3\u03c0(-2(5(4x^2 + 3x + 1) + 1) + 4) - 1) + 3) + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "49", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -1|(3|(-2|(-3cos(1\u03c0(1x^2 + 5x - 3))) + 2| - 1) + 3| - 3) - 2| - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "412", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -2(1(-3(3(2cos(1\u03c0x - 3) - 3) - 4) - 1) - 1)^2 + 2(1(-3(3(2cos(1\u03c0x - 3) - 3) - 4) - 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": "Find the total number of local minima and maxima for f(x) = -3sin(1\u03c0(-3|(4((3((1x - 3)/(-2x + 3)) - 1)/(-2((1x - 3)/(-2x + 3)) - 1))^2 - 5((3((1x - 3)/(-2x + 3)) - 1)/(-2((1x - 3)/(-2x + 3)) - 1)) - 4) + 2| - 1) + 2) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "488", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -4(-2sin(1\u03c0((-1(4(-2|x - 1| + 3) + 3) + 2)/(-2(4(-2|x - 1| + 3) + 3) - 3)) + 1)) - 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 1(1|((3(-3(1x - 5)^2 + 3(1x - 5)) + 1)/(2(-3(1x - 5)^2 + 3(1x - 5)))) - 2|)^2 - 5(1|((3(-3(1x - 5)^2 + 3(1x - 5)) + 1)/(2(-3(1x - 5)^2 + 3(1x - 5)))) - 2|) + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -2sin(2\u03c0((2(-4((-3(-1x^2 - 5x + 2) - 3)/(1(-1x^2 - 5x + 2)))^2 + 4) - 3)/(-2(-4((-3(-1x^2 - 5x + 2) - 3)/(1(-1x^2 - 5x + 2)))^2 + 4) - 1)) + 1) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = (-1(-1((1(1(3cos(2\u03c0x) - 2)^2 + 2) - 1)/(-1(1(3cos(2\u03c0x) - 2)^2 + 2) - 1)) - 2) + 1)/(-3(-1((1(1(3cos(2\u03c0x) - 2)^2 + 2) - 1)/(-1(1(3cos(2\u03c0x) - 2)^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 minima does the function f(x) = -3(-1(5(2e^(-2(-2x^2 + 5)) - 1)^2 + 3(2e^(-2(-2x^2 + 5)) - 1))^2 + 2(5(2e^(-2(-2x^2 + 5)) - 1)^2 + 3(2e^(-2(-2x^2 + 5)) - 1)) - 5) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 4(3cos(2\u03c0(1(-1(1x + 5) - 1) - 1) - 2) - 2) - 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 2|((1(1cos(3\u03c0(2(1|x + 1| - 1)^2 - 5(1|x + 1| - 1) - 4)) + 3) + 3)/(-3(1cos(3\u03c0(2(1|x + 1| - 1)^2 - 5(1|x + 1| - 1) - 4)) + 3) - 3)) + 1| have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "191", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 2(5(3|(-5(-3cos(3\u03c0x - 2) + 1) - 5) - 2| - 1)^2 - 4(3|(-5(-3cos(3\u03c0x - 2) + 1) - 5) - 2| - 1) + 2)^2 - 5(5(3|(-5(-3cos(3\u03c0x - 2) + 1) - 5) - 2| - 1)^2 - 4(3|(-5(-3cos(3\u03c0x - 2) + 1) - 5) - 2| - 1) + 2) + 5 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": "Find the number of local minimum points for f(x) = 1(1cos(1\u03c0(-4(1(2x^2 - 4x)^2 + 5(2x^2 - 4x) + 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": "113", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = 2|((1(5(-3((1x)/(-3x + 1))^2 - 4((1x)/(-3x + 1)) - 3)^2 + 1(-3((1x)/(-3x + 1))^2 - 4((1x)/(-3x + 1)) - 3) + 4) + 1)/(3(5(-3((1x)/(-3x + 1))^2 - 4((1x)/(-3x + 1)) - 3)^2 + 1(-3((1x)/(-3x + 1))^2 - 4((1x)/(-3x + 1)) - 3) + 4) + 3))| + 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "104", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = 4(-2(-3cos(1\u03c0(1|((-3x - 2)/(1x)) - 2| + 3))) - 4) - 4 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = (1(-2sin(2\u03c0(2|(-2((3x + 1)/(-3x + 4)) + 5)|) + 2) + 2) - 1)/(-1(-2sin(2\u03c0(2|(-2((3x + 1)/(-3x + 4)) + 5)|) + 2) + 2) + 2) 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) = (-1(5((-3(2|(-1sin(1\u03c0x - 2) - 2)| + 1) + 2)/(-2(2|(-1sin(1\u03c0x - 2) - 2)| + 1) + 3)) + 4) - 3)/(3(5((-3(2|(-1sin(1\u03c0x - 2) - 2)| + 1) + 2)/(-2(2|(-1sin(1\u03c0x - 2) - 2)| + 1) + 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) = -1(3cos(1\u03c0(1(-1(-2|x - 2| - 1)^2 + 2(-2|x - 2| - 1)) + 2) + 1) + 2) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "571", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -2|(-3cos(1\u03c0((-1((1((2x - 2)/(-2x + 3)))/(1((2x - 2)/(-2x + 3)) - 3)) - 3)/(2((1((2x - 2)/(-2x + 3)))/(1((2x - 2)/(-2x + 3)) - 3)) - 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": "45", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 2(1(-1((-2(-1sin(2\u03c0x - 2) - 3) + 2)/(-1(-1sin(2\u03c0x - 2) - 3) - 1))^2 + 3((-2(-1sin(2\u03c0x - 2) - 3) + 2)/(-1(-1sin(2\u03c0x - 2) - 3) - 1)) - 2)^2 + 1)^2 - 5(1(-1((-2(-1sin(2\u03c0x - 2) - 3) + 2)/(-1(-1sin(2\u03c0x - 2) - 3) - 1))^2 + 3((-2(-1sin(2\u03c0x - 2) - 3) + 2)/(-1(-1sin(2\u03c0x - 2) - 3) - 1)) - 2)^2 + 1) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -4(-2|(1((2(3cos(1\u03c0x + 1)) - 3)/(-1(3cos(1\u03c0x + 1)) - 1)) + 2) - 1| - 2)^2 + 1(-2|(1((2(3cos(1\u03c0x + 1)) - 3)/(-1(3cos(1\u03c0x + 1)) - 1)) + 2) - 1| - 2) - 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -5(-3cos(3\u03c0(3(-1(2|x + 2| - 1) + 2)^2 - 5(-1(2|x + 2| - 1) + 2) + 5) - 1) + 1) - 1 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": "Find the total number of local minima and maxima for f(x) = (-3(2|(2e^(-1(-3(-5x^2 - 1)^2 + 5(-5x^2 - 1) + 3)) - 1) + 3| - 3) + 1)/(2(2|(2e^(-1(-3(-5x^2 - 1)^2 + 5(-5x^2 - 1) + 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": "7", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 5(-2(4((-1(2sin(2\u03c0x - 3) + 2) + 3)/(2(2sin(2\u03c0x - 3) + 2) + 1))^2 - 4)^2 - 1(4((-1(2sin(2\u03c0x - 3) + 2) + 3)/(2(2sin(2\u03c0x - 3) + 2) + 1))^2 - 4) - 5)^2 - 2(-2(4((-1(2sin(2\u03c0x - 3) + 2) + 3)/(2(2sin(2\u03c0x - 3) + 2) + 1))^2 - 4)^2 - 1(4((-1(2sin(2\u03c0x - 3) + 2) + 3)/(2(2sin(2\u03c0x - 3) + 2) + 1))^2 - 4) - 5) + 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "57", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = 5((3(-2|(1e^(-1(-5x^2 + 3x - 4))) + 2| + 2) + 1)/(2(-2|(1e^(-1(-5x^2 + 3x - 4))) + 2| + 2) - 1))^2 + 4((3(-2|(1e^(-1(-5x^2 + 3x - 4))) + 2| + 2) + 1)/(2(-2|(1e^(-1(-5x^2 + 3x - 4))) + 2| + 2) - 1)) + 5 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -2(-4(1sin(1\u03c0(-3|(-5x + 2) + 1| - 1) + 1) - 1) - 2) - 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "301", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -2|(1|(3|((1(2|x| - 3) - 2)/(2(2|x| - 3) + 3)) - 3| + 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": "9", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -1(-1((1(-2cos(1\u03c0(1|x + 1| + 3)) - 1) + 3)/(2(-2cos(1\u03c0(1|x + 1| + 3)) - 1) - 1)) - 1) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -1|(-5(4(1((3x - 1)/(-2x + 3)) + 5) + 4)^2 - 4(4(1((3x - 1)/(-2x + 3)) + 5) + 4) + 3) + 3| + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = 2(2|(-3(1sin(3\u03c0(1x^2 - 4x + 5) + 2)) + 3)| + 1) - 1 where -10 \u2264 x \u2264 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) = (-3(-2sin(3\u03c0((3(2(5x - 1)^2 + 3(5x - 1) + 2) + 3)/(2(2(5x - 1)^2 + 3(5x - 1) + 2) - 1)) + 3) - 2) + 3)/(1(-2sin(3\u03c0((3(2(5x - 1)^2 + 3(5x - 1) + 2) + 3)/(2(2(5x - 1)^2 + 3(5x - 1) + 2) - 1)) + 3) - 2) - 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": "Determine the total count of local extrema points for the function f(x) = -1|((3(-3|(2|(3cos(3\u03c0x - 3) - 1) + 1|)| + 3) + 1)/(1(-3|(2|(3cos(3\u03c0x - 3) - 1) + 1|)| + 3) + 2)) + 3| - 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": "Determine the count of local maxima for the function f(x) = (3(2|(4(-1sin(3\u03c0(1|x - 3| + 3)) - 1) - 4) + 3|) - 2)/(-1(2|(4(-1sin(3\u03c0(1|x - 3| + 3)) - 1) - 4) + 3|) + 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": "Find the number of local minimum points for f(x) = 1e^(1(-1|(-2(1(2|x - 2| - 3) + 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": "5", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = 2cos(2\u03c0(-2|((-3(-4((-2x - 2)/(1x))^2 - 4((-2x - 2)/(1x)) + 5) + 1)/(-1(-4((-2x - 2)/(1x))^2 - 4((-2x - 2)/(1x)) + 5) + 2)) + 3|) + 2) - 3 in the interval [-10, 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) = 1cos(2\u03c0(-2|((2(-1(-3|x + 1| + 1) - 2) - 2)/(3(-1(-3|x + 1| + 1) - 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": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -3((-2(3|(-2e^(-2(-2|x - 1| - 1)) - 2) - 2| + 3) - 1)/(-3(3|(-2e^(-2(-2|x - 1| - 1)) - 2) - 2| + 3) + 2))^2 + 2((-2(3|(-2e^(-2(-2|x - 1| - 1)) - 2) - 2| + 3) - 1)/(-3(3|(-2e^(-2(-2|x - 1| - 1)) - 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": "31", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = -1((-2((2(-2(-1sin(1\u03c0x + 3) + 2) + 2))/(-1(-2(-1sin(1\u03c0x + 3) + 2) + 2) - 1)) + 1)/(1((2(-2(-1sin(1\u03c0x + 3) + 2) + 2))/(-1(-2(-1sin(1\u03c0x + 3) + 2) + 2) - 1)) + 1))^2 - 3((-2((2(-2(-1sin(1\u03c0x + 3) + 2) + 2))/(-1(-2(-1sin(1\u03c0x + 3) + 2) + 2) - 1)) + 1)/(1((2(-2(-1sin(1\u03c0x + 3) + 2) + 2))/(-1(-2(-1sin(1\u03c0x + 3) + 2) + 2) - 1)) + 1)) + 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -3|(3sin(1\u03c0(1((3(5x - 1) - 3)/(-1(5x - 1) + 2))^2 + 5((3(5x - 1) - 3)/(-1(5x - 1) + 2)) - 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": "27", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = (1(-2|(-2|(-1cos(1\u03c0((-1x + 1)/(-3x + 4)) + 1) - 2)|) + 3| - 3) - 3)/(1(-2|(-2|(-1cos(1\u03c0((-1x + 1)/(-3x + 4)) + 1) - 2)|) + 3| - 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": "Find the number of local maximum points for f(x) = 2e^(1(5(-1|((-3((1x + 3)/(2x - 3)) - 2)/(2((1x + 3)/(2x - 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 maxima does the function f(x) = -3(2(1(-2(2cos(1\u03c0x) - 2) + 1)^2 - 5(-2(2cos(1\u03c0x) - 2) + 1) - 1)^2 - 1(1(-2(2cos(1\u03c0x) - 2) + 1)^2 - 5(-2(2cos(1\u03c0x) - 2) + 1) - 1) - 4) - 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -2(-1|(2|(3sin(3\u03c0((-1x + 3)/(3x - 2)) + 2) + 1) + 1| - 3) + 2| + 1)^2 - 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -1|((-2(-1(1(-1cos(1\u03c0x + 2)) + 3)^2 + 3(1(-1cos(1\u03c0x + 2)) + 3) - 5) + 2)/(2(-1(1(-1cos(1\u03c0x + 2)) + 3)^2 + 3(1(-1cos(1\u03c0x + 2)) + 3) - 5) - 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) = 3sin(2\u03c0(5(-2|(1(-1x + 2) + 2) - 2| + 3) + 2) - 3) - 1 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 minima does the function f(x) = -3(-1|(4(1(3sin(1\u03c0x + 2) + 2) + 4)^2 - 4(1(3sin(1\u03c0x + 2) + 2) + 4) + 1) - 1|) - 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": "Determine the total count of local extrema points for the function f(x) = (2(1(2(3(3x^2 + 2) + 1)^2 - 4(3(3x^2 + 2) + 1) - 3)^2 + 2) - 2)/(1(1(2(3(3x^2 + 2) + 1)^2 - 4(3(3x^2 + 2) + 1) - 3)^2 + 2) + 3) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 2e^(2(1|(2|(-1(5x - 3) + 4) - 1| - 3)| - 3)) - 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -2|(-1|((-1(-1(2x^2 - 2x - 5)^2 - 2(2x^2 - 2x - 5) + 2) - 3)/(1(-1(2x^2 - 2x - 5)^2 - 2(2x^2 - 2x - 5) + 2))) - 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": "How many local minima does the function f(x) = 2cos(3\u03c0((-2(-5(1(2|x + 3|)^2 - 2(2|x + 3|))^2 + 1(1(2|x + 3|)^2 - 2(2|x + 3|)) - 1) + 2)/(-1(-5(1(2|x + 3|)^2 - 2(2|x + 3|))^2 + 1(1(2|x + 3|)^2 - 2(2|x + 3|)) - 1) + 2)) - 3) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 1|(1(-1(-2cos(1\u03c0(3|x + 2| + 3) + 2) - 1)^2 - 2(-2cos(1\u03c0(3|x + 2| + 3) + 2) - 1) - 4)^2 + 5(-1(-2cos(1\u03c0(3|x + 2| + 3) + 2) - 1)^2 - 2(-2cos(1\u03c0(3|x + 2| + 3) + 2) - 1) - 4) - 2) + 3| - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "241", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 2|(-2|(-1|(-1(-1sin(2\u03c0x - 1) + 3)^2 + 1(-1sin(2\u03c0x - 1) + 3) - 4) + 3| - 3) - 2| - 1) + 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": "Find the number of local maximum points for f(x) = -4(-1(-3(-2cos(1\u03c0(1x^2 - 2x)) + 2)^2 + 5)) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "101", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = 2|(-3(3(-3sin(1\u03c0(2|x - 2| + 1) - 3) - 1) - 4) + 4)| - 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "81", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = (-2(-1cos(3\u03c0(1|(3(4x + 3) - 1) - 2| + 2) - 3) + 3))/(-3(-1cos(3\u03c0(1|(3(4x + 3) - 1) - 2| + 2) - 3) + 3) + 4) 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 minima does the function f(x) = -1sin(2\u03c0(-4((2(-2|(-5x - 1) - 1| + 1) + 3)/(1(-2|(-5x - 1) - 1| + 1) + 2)) + 1) - 3) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -2(1(-3(-3(2|x - 1|)^2 + 2(2|x - 1|) + 1)^2 - 3(-3(2|x - 1|)^2 + 2(2|x - 1|) + 1) - 2) + 3) - 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 number of local minimum points for f(x) = 4(2|((2(-2e^(-1(-3|x - 2| - 2)) + 2) - 3)/(3(-2e^(-1(-3|x - 2| - 2)) + 2) + 1))| + 3)^2 + 5(2|((2(-2e^(-1(-3|x - 2| - 2)) + 2) - 3)/(3(-2e^(-1(-3|x - 2| - 2)) + 2) + 1))| + 3) - 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 3(-2|((1(3e^(-1((-1x + 3)/(2x)))) - 1)/(1(3e^(-1((-1x + 3)/(2x)))) - 3)) + 3| + 2)^2 + 3(-2|((1(3e^(-1((-1x + 3)/(2x)))) - 1)/(1(3e^(-1((-1x + 3)/(2x)))) - 3)) + 3| + 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = (-2(3(3(-2cos(3\u03c0((-2x + 2)/(-1x + 2)) + 3)) + 2)^2 + 3(3(-2cos(3\u03c0((-2x + 2)/(-1x + 2)) + 3)) + 2) - 1) + 3)/(3(3(3(-2cos(3\u03c0((-2x + 2)/(-1x + 2)) + 3)) + 2)^2 + 3(3(-2cos(3\u03c0((-2x + 2)/(-1x + 2)) + 3)) + 2) - 1) - 2) 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) = -1sin(3\u03c0(-1(-2|(3|(-3x + 3)| + 2)| - 2)^2 + 2) - 1) - 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "110", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = (-2(-1|(2e^(1(-5(5x^2 + 3x - 5) - 1)) - 2) + 2| + 2))/(3(-1|(2e^(1(-5(5x^2 + 3x - 5) - 1)) - 2) + 2| + 2) + 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = (1((3(-1(2|(-1sin(3\u03c0x) + 2)| - 2)^2 - 3(2|(-1sin(3\u03c0x) + 2)| - 2) + 1) + 3)/(3(-1(2|(-1sin(3\u03c0x) + 2)| - 2)^2 - 3(2|(-1sin(3\u03c0x) + 2)| - 2) + 1) - 1)) + 3)/(1((3(-1(2|(-1sin(3\u03c0x) + 2)| - 2)^2 - 3(2|(-1sin(3\u03c0x) + 2)| - 2) + 1) + 3)/(3(-1(2|(-1sin(3\u03c0x) + 2)| - 2)^2 - 3(2|(-1sin(3\u03c0x) + 2)| - 2) + 1) - 1)) - 3) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = 1|((-3(5(2sin(1\u03c0(-1x - 5) + 2) + 2)^2 - 3(2sin(1\u03c0(-1x - 5) + 2) + 2) + 3) + 3)/(-2(5(2sin(1\u03c0(-1x - 5) + 2) + 2)^2 - 3(2sin(1\u03c0(-1x - 5) + 2) + 2) + 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 minima for the function f(x) = -1|(1(1sin(2\u03c0(-3(3|x - 1| - 1)^2) + 2) + 2)^2 + 2(1sin(2\u03c0(-3(3|x - 1| - 1)^2) + 2) + 2) - 2) - 2| - 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "456", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 1(-1(4((2((-2x + 3)/(1x)) - 1)/(-1((-2x + 3)/(1x)) - 2))^2 - 5((2((-2x + 3)/(1x)) - 1)/(-1((-2x + 3)/(1x)) - 2)) + 4)^2 + 5(4((2((-2x + 3)/(1x)) - 1)/(-1((-2x + 3)/(1x)) - 2))^2 - 5((2((-2x + 3)/(1x)) - 1)/(-1((-2x + 3)/(1x)) - 2)) + 4) + 4)^2 + 1(-1(4((2((-2x + 3)/(1x)) - 1)/(-1((-2x + 3)/(1x)) - 2))^2 - 5((2((-2x + 3)/(1x)) - 1)/(-1((-2x + 3)/(1x)) - 2)) + 4)^2 + 5(4((2((-2x + 3)/(1x)) - 1)/(-1((-2x + 3)/(1x)) - 2))^2 - 5((2((-2x + 3)/(1x)) - 1)/(-1((-2x + 3)/(1x)) - 2)) + 4) + 4) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 5(-1((1(3sin(1\u03c0(4x - 2) - 1) - 2) + 3)/(2(3sin(1\u03c0(4x - 2) - 1) - 2) - 3))^2 + 4)^2 + 1(-1((1(3sin(1\u03c0(4x - 2) - 1) - 2) + 3)/(2(3sin(1\u03c0(4x - 2) - 1) - 2) - 3))^2 + 4) - 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": "Find the total number of local minima and maxima for f(x) = -4(1(-2|((-2(2sin(3\u03c0x) - 2))/(1(2sin(3\u03c0x) - 2) + 3)) + 2| + 3)^2 - 3(-2|((-2(2sin(3\u03c0x) - 2))/(1(2sin(3\u03c0x) - 2) + 3)) + 2| + 3) + 3) + 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "119", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -5(4(-1|(-2sin(2\u03c0(1|x - 2|) - 1) - 3) + 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": "78", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = 2(-1|(4(1(3|x - 2| + 1) - 3) - 4) + 1| + 1)^2 + 2(-1|(4(1(3|x - 2| + 1) - 3) - 4) + 1| + 1) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = (3((-1((-1((1(-1cos(1\u03c0x - 1) + 2) - 3)/(1(-1cos(1\u03c0x - 1) + 2) - 2)) - 1)/(-2((1(-1cos(1\u03c0x - 1) + 2) - 3)/(1(-1cos(1\u03c0x - 1) + 2) - 2)) - 1)) + 3)/(2((-1((1(-1cos(1\u03c0x - 1) + 2) - 3)/(1(-1cos(1\u03c0x - 1) + 2) - 2)) - 1)/(-2((1(-1cos(1\u03c0x - 1) + 2) - 3)/(1(-1cos(1\u03c0x - 1) + 2) - 2)) - 1)) + 2)))/(-3((-1((-1((1(-1cos(1\u03c0x - 1) + 2) - 3)/(1(-1cos(1\u03c0x - 1) + 2) - 2)) - 1)/(-2((1(-1cos(1\u03c0x - 1) + 2) - 3)/(1(-1cos(1\u03c0x - 1) + 2) - 2)) - 1)) + 3)/(2((-1((1(-1cos(1\u03c0x - 1) + 2) - 3)/(1(-1cos(1\u03c0x - 1) + 2) - 2)) - 1)/(-2((1(-1cos(1\u03c0x - 1) + 2) - 3)/(1(-1cos(1\u03c0x - 1) + 2) - 2)) - 1)) + 2)) - 2) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -3sin(3\u03c0((3(1|(-2(-2x))| - 1) + 1)/(2(1|(-2(-2x))| - 1) + 1))) + 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": "Find the number of local minimum points for f(x) = 3(1|(2cos(1\u03c0(4((2x - 3)/(-3x)) - 2) + 2) - 2) + 2|)^2 - 3(1|(2cos(1\u03c0(4((2x - 3)/(-3x)) - 2) + 2) - 2) + 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 number of local maximum points for f(x) = -2|(3(-1(-2sin(1\u03c0(2|x + 1|))) + 4) + 2) + 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 minima for the function f(x) = (-1(-2(-1|(-1e^(-2(1|x - 2| + 1))) - 2| - 1)^2 + 3(-1|(-1e^(-2(1|x - 2| + 1))) - 2| - 1) - 5) - 2)/(2(-2(-1|(-1e^(-2(1|x - 2| + 1))) - 2| - 1)^2 + 3(-1|(-1e^(-2(1|x - 2| + 1))) - 2| - 1) - 5)) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 3(-2sin(2\u03c0(3(-5((1x - 2)/(1x))^2 - 3((1x - 2)/(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": "199", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -3cos(2\u03c0(1(5(1((1x - 2)/(-3x))^2 - 5((1x - 2)/(-3x)) + 3) - 4)^2 + 5(5(1((1x - 2)/(-3x))^2 - 5((1x - 2)/(-3x)) + 3) - 4) - 4) + 2) - 1 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": "Determine the total count of local extrema points for the function f(x) = 5(1sin(3\u03c0(4(1|(2|x| - 1) - 3| - 1)^2 - 2(1|(2|x| - 1) - 3| - 1)) + 2) + 3) + 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "499", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -5(-1|((2(1cos(3\u03c0((-1x + 2)/(3x + 2)) + 3) + 2) + 2)/(-2(1cos(3\u03c0((-1x + 2)/(3x + 2)) + 3) + 2) + 3)) + 3| - 1)^2 + 5(-1|((2(1cos(3\u03c0((-1x + 2)/(3x + 2)) + 3) + 2) + 2)/(-2(1cos(3\u03c0((-1x + 2)/(3x + 2)) + 3) + 2) + 3)) + 3| - 1) + 4 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 total number of local minima and maxima for f(x) = 1(1((-1(-5(1|x + 3| - 1)^2 - 4(1|x + 3| - 1) + 1) - 1)/(-1(-5(1|x + 3| - 1)^2 - 4(1|x + 3| - 1) + 1))) - 3)^2 - 2(1((-1(-5(1|x + 3| - 1)^2 - 4(1|x + 3| - 1) + 1) - 1)/(-1(-5(1|x + 3| - 1)^2 - 4(1|x + 3| - 1) + 1))) - 3) - 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -1cos(2\u03c0(1(3|(3|((1x + 1)/(2x - 1)) - 3| - 2) - 3| + 1)^2 + 5(3|(3|((1x + 1)/(2x - 1)) - 3| - 2) - 3| + 1) + 4) - 1) - 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "291", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -2|(-5(2|(1(-2sin(3\u03c0x + 3))^2 + 3(-2sin(3\u03c0x + 3)) - 1) - 3| + 1)^2 + 5(2|(1(-2sin(3\u03c0x + 3))^2 + 3(-2sin(3\u03c0x + 3)) - 1) - 3| + 1))| + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "90", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = (-2(2|(-2e^(-1(-1|(-3x^2 - 2x + 1) + 3| - 1))) + 2| + 3) - 1)/(3(2|(-2e^(-1(-1|(-3x^2 - 2x + 1) + 3| - 1))) + 2| + 3)) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "50", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = -3|(-3sin(1\u03c0(-3|(-4(1x + 5)^2 - 2(1x + 5))| - 2) + 1) - 1) + 3| - 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "463", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = (3(-4(-3cos(3\u03c0(2(-5x^2 + 2x - 2) - 2) + 2)) - 1) - 2)/(1(-4(-3cos(3\u03c0(2(-5x^2 + 2x - 2) - 2) + 2)) - 1) - 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 maxima does the function f(x) = -1|(3cos(2\u03c0(3(5(1|x - 2| + 3) - 2) + 5)) + 3) + 1| - 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) = -3cos(1\u03c0(1|(-3|((-1(-1x^2 - 3x + 1) - 2)/(-3(-1x^2 - 3x + 1))) + 1| - 3) + 2| - 2) - 3) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 1|(-5(2|((3((2x - 1)/(-3x - 1)) - 3)/(1((2x - 1)/(-3x - 1)) + 2)) - 1| - 1)^2 + 3(2|((3((2x - 1)/(-3x - 1)) - 3)/(1((2x - 1)/(-3x - 1)) + 2)) - 1| - 1) - 4) - 2| - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -3sin(3\u03c0(5((-1((3((-3x - 2)/(-1x + 2)) + 1)/(-1((-3x - 2)/(-1x + 2)) - 1)))/(-1((3((-3x - 2)/(-1x + 2)) + 1)/(-1((-3x - 2)/(-1x + 2)) - 1)) - 3))^2 - 2((-1((3((-3x - 2)/(-1x + 2)) + 1)/(-1((-3x - 2)/(-1x + 2)) - 1)))/(-1((3((-3x - 2)/(-1x + 2)) + 1)/(-1((-3x - 2)/(-1x + 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": "252", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = (3(-1((3(-4(-1sin(1\u03c0x + 3) - 2) + 1) + 3)/(-1(-4(-1sin(1\u03c0x + 3) - 2) + 1) + 2))^2 + 1((3(-4(-1sin(1\u03c0x + 3) - 2) + 1) + 3)/(-1(-4(-1sin(1\u03c0x + 3) - 2) + 1) + 2)) - 5) - 1)/(2(-1((3(-4(-1sin(1\u03c0x + 3) - 2) + 1) + 3)/(-1(-4(-1sin(1\u03c0x + 3) - 2) + 1) + 2))^2 + 1((3(-4(-1sin(1\u03c0x + 3) - 2) + 1) + 3)/(-1(-4(-1sin(1\u03c0x + 3) - 2) + 1) + 2)) - 5) + 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) = -5(-4(-2(-1e^(1(-2x^2 + 5x + 5)) + 2) + 5) + 5)^2 + 2(-4(-2(-1e^(1(-2x^2 + 5x + 5)) + 2) + 5) + 5) + 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|(-4(2|(-2e^(2((2x + 1)/(-3x))) + 1) + 2| - 1)^2 + 1(2|(-2e^(2((2x + 1)/(-3x))) + 1) + 2| - 1) + 5) + 3| + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -2|(-2((-3(3(1e^(2x) - 3)^2 + 3(1e^(2x) - 3) + 5))/(1(3(1e^(2x) - 3)^2 + 3(1e^(2x) - 3) + 5) + 3))^2 - 4((-3(3(1e^(2x) - 3)^2 + 3(1e^(2x) - 3) + 5))/(1(3(1e^(2x) - 3)^2 + 3(1e^(2x) - 3) + 5) + 3)) - 4) - 2| + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "43", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 1(-3(2|(-3((-1x - 3)/(-2x - 1))^2 + 2((-1x - 3)/(-2x - 1)) + 5)| - 2) - 2)^2 - 2(-3(2|(-3((-1x - 3)/(-2x - 1))^2 + 2((-1x - 3)/(-2x - 1)) + 5)| - 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": "How many local minima does the function f(x) = (1(3|(1(1cos(3\u03c0((1x)/(-2x - 2)) + 2) - 3) + 5) + 3| - 2) - 2)/(-3(3|(1(1cos(3\u03c0((1x)/(-2x - 2)) + 2) - 3) + 5) + 3| - 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": "Determine the count of local minima for the function f(x) = 1e^(2(-2|((-1(2(-5x^2 - 4x - 5)^2 - 2) + 3)/(2(2(-5x^2 - 4x - 5)^2 - 2) - 3)) - 3| - 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": "Determine the total count of local extrema points for the function f(x) = -5(3(2(3sin(1\u03c0(-3x - 2) - 3) + 1) - 2)^2 + 2)^2 + 4(3(2(3sin(1\u03c0(-3x - 2) - 3) + 1) - 2)^2 + 2) - 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "117", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = (2(-2sin(1\u03c0(4(3(3x + 2)^2 - 2(3x + 2) + 2)^2 - 3(3(3x + 2)^2 - 2(3x + 2) + 2) - 4)) + 3) + 1)/(-2(-2sin(1\u03c0(4(3(3x + 2)^2 - 2(3x + 2) + 2)^2 - 3(3(3x + 2)^2 - 2(3x + 2) + 2) - 4)) + 3) - 2) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "57", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = (-3(-2sin(3\u03c0((3(-4(2x + 4)^2 + 2(2x + 4) - 5) - 2)/(-1(-4(2x + 4)^2 + 2(2x + 4) - 5) - 3)) + 1) - 2) - 3)/(-1(-2sin(3\u03c0((3(-4(2x + 4)^2 + 2(2x + 4) - 5) - 2)/(-1(-4(2x + 4)^2 + 2(2x + 4) - 5) - 3)) + 1) - 2) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "103", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = 2|(-1|(3sin(3\u03c0(1(4x + 4) + 3) - 1) - 1)| - 1)| + 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "471", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -1sin(3\u03c0(-1(-1(-5(-1x - 5)^2 - 4(-1x - 5) - 2)^2 + 5(-5(-1x - 5)^2 - 4(-1x - 5) - 2) - 4) - 5) + 2) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "190", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 5(-3sin(2\u03c0(-3|(-4(4x)^2 - 4(4x) + 3) + 2| + 2) - 1) - 2) + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "145", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -1(-3|(3|(-3cos(2\u03c0(-1x - 2) - 3)) - 3| + 3) - 3|) - 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = 1|(5(1cos(2\u03c0(-1(3x^2 - 1x - 1) + 1) - 1) - 1) + 3) - 3| - 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "225", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = (-3(4(2(-1|(3sin(1\u03c0x + 1) + 3)| + 3)) - 4) + 2)/(-1(4(2(-1|(3sin(1\u03c0x + 1) + 3)| + 3)) - 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": "How many local extrema (minima and maxima combined) does the function f(x) = 2(-3|(2(3e^(1(5x^2 - 1x - 1)))^2 - 4(3e^(1(5x^2 - 1x - 1))) - 1) + 1| + 3) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 3|(1((2(5(-1cos(2\u03c0x + 2) - 1) + 5) + 3)/(3(5(-1cos(2\u03c0x + 2) - 1) + 5) + 2))^2 - 2((2(5(-1cos(2\u03c0x + 2) - 1) + 5) + 3)/(3(5(-1cos(2\u03c0x + 2) - 1) + 5) + 2)) - 2) + 1| + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = 1(1((-2(-1|(-3cos(3\u03c0x + 1) + 1) - 3| + 3) + 2)/(2(-1|(-3cos(3\u03c0x + 1) + 1) - 3| + 3)))^2 - 5((-2(-1|(-3cos(3\u03c0x + 1) + 1) - 3| + 3) + 2)/(2(-1|(-3cos(3\u03c0x + 1) + 1) - 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": "Find the number of local minimum points for f(x) = 4(-5(-1((2(-1e^(2x) - 2) + 3)/(1(-1e^(2x) - 2) + 3))^2 - 2((2(-1e^(2x) - 2) + 3)/(1(-1e^(2x) - 2) + 3)))^2 - 5(-1((2(-1e^(2x) - 2) + 3)/(1(-1e^(2x) - 2) + 3))^2 - 2((2(-1e^(2x) - 2) + 3)/(1(-1e^(2x) - 2) + 3))) + 2)^2 + 1(-5(-1((2(-1e^(2x) - 2) + 3)/(1(-1e^(2x) - 2) + 3))^2 - 2((2(-1e^(2x) - 2) + 3)/(1(-1e^(2x) - 2) + 3)))^2 - 5(-1((2(-1e^(2x) - 2) + 3)/(1(-1e^(2x) - 2) + 3))^2 - 2((2(-1e^(2x) - 2) + 3)/(1(-1e^(2x) - 2) + 3))) + 2) - 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 number of local maximum points for f(x) = (1(-2(4(1|(-2cos(2\u03c0x) - 3) - 1| - 3)^2 - 4(1|(-2cos(2\u03c0x) - 3) - 1| - 3) + 1)^2 + 5(4(1|(-2cos(2\u03c0x) - 3) - 1| - 3)^2 - 4(1|(-2cos(2\u03c0x) - 3) - 1| - 3) + 1) + 1) - 1)/(-3(-2(4(1|(-2cos(2\u03c0x) - 3) - 1| - 3)^2 - 4(1|(-2cos(2\u03c0x) - 3) - 1| - 3) + 1)^2 + 5(4(1|(-2cos(2\u03c0x) - 3) - 1| - 3)^2 - 4(1|(-2cos(2\u03c0x) - 3) - 1| - 3) + 1) + 1) + 4) 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) = -1|((2(-3|(-1|(5x^2 + 4x + 5) - 1| + 1) + 3| + 2) - 2)/(1(-3|(-1|(5x^2 + 4x + 5) - 1| + 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": "7", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -2|((-3(5(1(1sin(1\u03c0x - 1))^2 - 4(1sin(1\u03c0x - 1)) - 4) - 3) + 3)/(-2(5(1(1sin(1\u03c0x - 1))^2 - 4(1sin(1\u03c0x - 1)) - 4) - 3) + 3)) - 1| + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = 5((1(-2cos(1\u03c0((-3(-3x) + 3)/(-1(-3x) - 1)))) + 1)/(-2(-2cos(1\u03c0((-3(-3x) + 3)/(-1(-3x) - 1)))) - 1)) + 5 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) = -3((2(-5(1((1x)/(3x + 1))^2 + 4((1x)/(3x + 1)) - 4)^2 - 1(1((1x)/(3x + 1))^2 + 4((1x)/(3x + 1)) - 4) - 5) + 2)/(3(-5(1((1x)/(3x + 1))^2 + 4((1x)/(3x + 1)) - 4)^2 - 1(1((1x)/(3x + 1))^2 + 4((1x)/(3x + 1)) - 4) - 5) + 3))^2 + 4((2(-5(1((1x)/(3x + 1))^2 + 4((1x)/(3x + 1)) - 4)^2 - 1(1((1x)/(3x + 1))^2 + 4((1x)/(3x + 1)) - 4) - 5) + 2)/(3(-5(1((1x)/(3x + 1))^2 + 4((1x)/(3x + 1)) - 4)^2 - 1(1((1x)/(3x + 1))^2 + 4((1x)/(3x + 1)) - 4) - 5) + 3)) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "183", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -1(-2|(-2sin(2\u03c0(1(2x^2 - 5x - 3)) + 1)) - 3| - 1) - 4 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": "Find the number of local maximum points for f(x) = (-2(-4(-5(-2e^(1(-3|x| - 1)) - 2) - 3) + 2))/(-2(-4(-5(-2e^(1(-3|x| - 1)) - 2) - 3) + 2) - 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -3sin(1\u03c0(-3(3(-1|(4x - 3) + 3| + 3)^2 + 4(-1|(4x - 3) + 3| + 3) - 3)^2 + 5(3(-1|(4x - 3) + 3| + 3)^2 + 4(-1|(4x - 3) + 3| + 3) - 3) - 1)) - 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "101", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -2|(-1sin(3\u03c0(-4(-2((-1x - 3)/(-3x - 1)) - 4) + 4) + 3) + 2) - 3| - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "46", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -3(1sin(2\u03c0(1(1(2|x - 1| + 2) - 3)^2 + 3(1(2|x - 1| + 2) - 3) - 1) - 3) - 1) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "528", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = 5(1cos(3\u03c0(-2|(5((2x + 1)/(-3x))^2 - 5((2x + 1)/(-3x)) - 5) + 1| - 2)) - 2) - 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "51", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 1(3(-1sin(2\u03c0(3((-3x)/(1x - 2))^2 - 1((-3x)/(1x - 2)))) - 3) + 5) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "106", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = 5(-4(3(2(1cos(1\u03c0x - 2))^2 - 1(1cos(1\u03c0x - 2)) - 5)^2 + 5(2(1cos(1\u03c0x - 2))^2 - 1(1cos(1\u03c0x - 2)) - 5) + 4) - 3)^2 - 5(-4(3(2(1cos(1\u03c0x - 2))^2 - 1(1cos(1\u03c0x - 2)) - 5)^2 + 5(2(1cos(1\u03c0x - 2))^2 - 1(1cos(1\u03c0x - 2)) - 5) + 4) - 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 count of local minima for the function f(x) = 2cos(1\u03c0(2|(-4(4(4x)^2 - 4(4x)) + 1) - 3| - 3) + 1) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "135", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 3sin(2\u03c0(-2|((-3(-2(1x^2 + 3x - 1)^2 + 4(1x^2 + 3x - 1) - 2) + 3)/(-3(-2(1x^2 + 3x - 1)^2 + 4(1x^2 + 3x - 1) - 2) - 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": "17", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -5(-1|(1e^(-2(-2(-1x^2 + 4x + 5)^2 + 2(-1x^2 + 4x + 5))) - 1)| + 1)^2 + 5(-1|(1e^(-2(-2(-1x^2 + 4x + 5)^2 + 2(-1x^2 + 4x + 5))) - 1)| + 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": "Find the number of local maximum points for f(x) = -5(-5(-3sin(1\u03c0(2|(-2|x + 2| + 3) + 1| - 1) - 3) + 2)^2 + 5)^2 - 4(-5(-3sin(1\u03c0(2|(-2|x + 2| + 3) + 1| - 1) - 3) + 2)^2 + 5) + 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "115", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -1sin(2\u03c0(-2(1|(-1|(-1x^2 - 4)| + 1) - 3| - 2)^2 - 3(1|(-1|(-1x^2 - 4)| + 1) - 3| - 2) + 2) + 1) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "175", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -1cos(2\u03c0((-1(1(3(3|x + 1| - 2) + 1)^2 + 1(3(3|x + 1| - 2) + 1) + 3))/(-3(1(3(3|x + 1| - 2) + 1)^2 + 1(3(3|x + 1| - 2) + 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": "7", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -3(1|((-2(-1(1x^2 + 3x - 5) + 2) + 1)/(-3(-1(1x^2 + 3x - 5) + 2) + 4)) - 3| + 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": "How many local minima does the function f(x) = -3(-2sin(3\u03c0(3(-1(-1x^2 + 3x + 5)^2 + 1(-1x^2 + 3x + 5)) - 5)) + 1)^2 - 3(-2sin(3\u03c0(3(-1(-1x^2 + 3x + 5)^2 + 1(-1x^2 + 3x + 5)) - 5)) + 1) + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "149", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 2|((-1(-1|(3(3|x - 3| - 1)^2 - 2(3|x - 3| - 1) - 2)| + 3) + 1)/(2(-1|(3(3|x - 3| - 1)^2 - 2(3|x - 3| - 1) - 2)| + 3) + 2)) + 2| have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -2sin(3\u03c0(5((1(-3|(1x - 1) + 1| + 2) + 1)/(1(-3|(1x - 1) + 1| + 2) - 2))^2 - 5((1(-3|(1x - 1) + 1| + 2) + 1)/(1(-3|(1x - 1) + 1| + 2) - 2)) + 3) - 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 2sin(3\u03c0(-1(-3(2((3x)/(-2x + 3))^2 - 1((3x)/(-2x + 3)) + 5)^2 - 5(2((3x)/(-2x + 3))^2 - 1((3x)/(-2x + 3)) + 5) + 5)^2 - 3(-3(2((3x)/(-2x + 3))^2 - 1((3x)/(-2x + 3)) + 5)^2 - 5(2((3x)/(-2x + 3))^2 - 1((3x)/(-2x + 3)) + 5) + 5)) + 1) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 5(-5(-3sin(1\u03c0(1((2x - 1)/(3x + 3)) + 4) + 2))^2 + 5(-3sin(1\u03c0(1((2x - 1)/(3x + 3)) + 4) + 2)) + 3)^2 + 5(-5(-3sin(1\u03c0(1((2x - 1)/(3x + 3)) + 4) + 2))^2 + 5(-3sin(1\u03c0(1((2x - 1)/(3x + 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": "33", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -2(3|(-1(1|(5x - 3)|)^2 - 1(1|(5x - 3)|) + 5) + 1| - 2)^2 - 3(3|(-1(1|(5x - 3)|)^2 - 1(1|(5x - 3)|) + 5) + 1| - 2) + 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = 3|(4(5(-1|(-5x^2 - 1x + 2) + 1| + 2)^2 + 1(-1|(-5x^2 - 1x + 2) + 1| + 2) - 1)^2 + 2(5(-1|(-5x^2 - 1x + 2) + 1| + 2)^2 + 1(-1|(-5x^2 - 1x + 2) + 1| + 2) - 1) - 3) - 3| + 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -2|(3cos(3\u03c0(4(2(5x)^2 + 4(5x) + 4)^2 - 4(2(5x)^2 + 4(5x) + 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": "28", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -3((2(2e^(1(4(1|x - 3| - 1) - 5)) - 2) + 2)/(3(2e^(1(4(1|x - 3| - 1) - 5)) - 2) - 2))^2 + 3((2(2e^(1(4(1|x - 3| - 1) - 5)) - 2) + 2)/(3(2e^(1(4(1|x - 3| - 1) - 5)) - 2) - 2)) - 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "63", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 2(3(3|(-3sin(2\u03c0(-3|x - 2| + 1) - 1) - 1)| + 1)^2 + 4(3|(-3sin(2\u03c0(-3|x - 2| + 1) - 1) - 1)| + 1) - 2)^2 + 5(3(3|(-3sin(2\u03c0(-3|x - 2| + 1) - 1) - 1)| + 1)^2 + 4(3|(-3sin(2\u03c0(-3|x - 2| + 1) - 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": "171", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 4(1|(-2|(-3cos(1\u03c0(-2|x + 3| + 3) + 3) - 3)| + 1) - 2| + 1)^2 + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = -2(1sin(3\u03c0(1((2(-1|x + 2| + 1) - 3)/(3(-1|x + 2| + 1) + 2))^2 - 2((2(-1|x + 2| + 1) - 3)/(3(-1|x + 2| + 1) + 2)) - 4) - 3) - 1) + 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "58", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -3|((1((-2(3sin(2\u03c0(2x^2 - 1x + 5) + 3) - 2))/(1(3sin(2\u03c0(2x^2 - 1x + 5) + 3) - 2) + 2)))/(-1((-2(3sin(2\u03c0(2x^2 - 1x + 5) + 3) - 2))/(1(3sin(2\u03c0(2x^2 - 1x + 5) + 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": "288", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -3|(-3|(-3|(1(-2x^2 + 5x + 5)^2 + 3(-2x^2 + 5x + 5)) - 2|) + 1| + 2) - 1| - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 2|(-3sin(3\u03c0(1((-3((-1x - 3)/(1x + 1)) - 1)/(-1((-1x - 3)/(1x + 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": "53", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = (3(-1cos(1\u03c0(5((-2((2x + 3)/(-1x + 2)) - 3)/(1((2x + 3)/(-1x + 2)) + 3))^2 + 1((-2((2x + 3)/(-1x + 2)) - 3)/(1((2x + 3)/(-1x + 2)) + 3)) - 4)) - 3) + 3)/(-3(-1cos(1\u03c0(5((-2((2x + 3)/(-1x + 2)) - 3)/(1((2x + 3)/(-1x + 2)) + 3))^2 + 1((-2((2x + 3)/(-1x + 2)) - 3)/(1((2x + 3)/(-1x + 2)) + 3)) - 4)) - 3)) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "110", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = (1(-1cos(3\u03c0(-1((2(-1|x - 2| + 1) - 1)/(1(-1|x - 2| + 1) - 2))^2 + 5((2(-1|x - 2| + 1) - 1)/(1(-1|x - 2| + 1) - 2)) - 5) + 2)) + 2)/(-1(-1cos(3\u03c0(-1((2(-1|x - 2| + 1) - 1)/(1(-1|x - 2| + 1) - 2))^2 + 5((2(-1|x - 2| + 1) - 1)/(1(-1|x - 2| + 1) - 2)) - 5) + 2)) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "69", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = (3(1((2(-4(1|x - 2| - 3)^2 - 4(1|x - 2| - 3)) + 3)/(-1(-4(1|x - 2| - 3)^2 - 4(1|x - 2| - 3))))^2 + 4((2(-4(1|x - 2| - 3)^2 - 4(1|x - 2| - 3)) + 3)/(-1(-4(1|x - 2| - 3)^2 - 4(1|x - 2| - 3)))) - 1) - 3)/(2(1((2(-4(1|x - 2| - 3)^2 - 4(1|x - 2| - 3)) + 3)/(-1(-4(1|x - 2| - 3)^2 - 4(1|x - 2| - 3))))^2 + 4((2(-4(1|x - 2| - 3)^2 - 4(1|x - 2| - 3)) + 3)/(-1(-4(1|x - 2| - 3)^2 - 4(1|x - 2| - 3)))) - 1) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -2|((-1(-2(-2((1x - 3)/(1x + 3))^2 + 4((1x - 3)/(1x + 3)) + 2)^2 - 4(-2((1x - 3)/(1x + 3))^2 + 4((1x - 3)/(1x + 3)) + 2) + 2) - 2)/(3(-2(-2((1x - 3)/(1x + 3))^2 + 4((1x - 3)/(1x + 3)) + 2)^2 - 4(-2((1x - 3)/(1x + 3))^2 + 4((1x - 3)/(1x + 3)) + 2) + 2) - 1)) - 2| + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = (2((2((-1(-2cos(3\u03c0(-1x + 3) - 1) - 3) + 1)/(-1(-2cos(3\u03c0(-1x + 3) - 1) - 3) - 1)) - 1)/(1((-1(-2cos(3\u03c0(-1x + 3) - 1) - 3) + 1)/(-1(-2cos(3\u03c0(-1x + 3) - 1) - 3) - 1)))) - 2)/(1((2((-1(-2cos(3\u03c0(-1x + 3) - 1) - 3) + 1)/(-1(-2cos(3\u03c0(-1x + 3) - 1) - 3) - 1)) - 1)/(1((-1(-2cos(3\u03c0(-1x + 3) - 1) - 3) + 1)/(-1(-2cos(3\u03c0(-1x + 3) - 1) - 3) - 1)))) - 2) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "57", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -4(-1(2(-1(3sin(2\u03c0x) + 2) + 5)^2 + 1(-1(3sin(2\u03c0x) + 2) + 5) - 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": "How many local extrema (minima and maxima combined) does the function f(x) = 5(-3(-1((3(1|x - 2| - 2) - 1)/(3(1|x - 2| - 2)))^2 + 5((3(1|x - 2| - 2) - 1)/(3(1|x - 2| - 2))) - 1)^2 + 4(-1((3(1|x - 2| - 2) - 1)/(3(1|x - 2| - 2)))^2 + 5((3(1|x - 2| - 2) - 1)/(3(1|x - 2| - 2))) - 1) + 4) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 2cos(3\u03c0(-4(1|((3(4x + 4) + 2)/(-2(4x + 4) + 1)) + 1| - 1)^2 - 5(1|((3(4x + 4) + 2)/(-2(4x + 4) + 1)) + 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": "25", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = 1(-1|(-5((1(-3sin(2\u03c0x + 2) - 2) + 2)/(-2(-3sin(2\u03c0x + 2) - 2) + 3)) - 2) - 2| - 3) + 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 count of local minima for the function f(x) = -4(1sin(3\u03c0((3(-3(2x^2 - 5x - 1) - 2) - 2)/(1(-3(2x^2 - 5x - 1) - 2) + 1)) - 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 extrema (minima and maxima combined) does the function f(x) = -2(-5(-2sin(3\u03c0(3|((-3x)/(-1x - 2))| - 2) + 1) - 3)^2 + 4(-2sin(3\u03c0(3|((-3x)/(-1x - 2))| - 2) + 1) - 3))^2 - 4(-5(-2sin(3\u03c0(3|((-3x)/(-1x - 2))| - 2) + 1) - 3)^2 + 4(-2sin(3\u03c0(3|((-3x)/(-1x - 2))| - 2) + 1) - 3)) - 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "129", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 1(3sin(3\u03c0(4(-1(-5x - 4) + 1)^2 + 1(-1(-5x - 4) + 1) - 4) - 2) + 3)^2 - 5(3sin(3\u03c0(4(-1(-5x - 4) + 1)^2 + 1(-1(-5x - 4) + 1) - 4) - 2) + 3) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "44", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -2|(-1((3(-3|(-1x^2 + 4x + 3)| + 2) - 2)/(2(-3|(-1x^2 + 4x + 3)| + 2) + 2)) - 2) + 1| - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -3|((-3(-2cos(1\u03c0((1(-1|x - 3| + 3) - 1)/(-2(-1|x - 3| + 3))) - 1) + 2) + 3)/(2(-2cos(1\u03c0((1(-1|x - 3| + 3) - 1)/(-2(-1|x - 3| + 3))) - 1) + 2) - 1)) + 2| - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = (2(1|(-3e^(-1(-3|(4x^2 - 3x - 1)| - 1)) - 1) - 2| + 2) - 1)/(-2(1|(-3e^(-1(-3|(4x^2 - 3x - 1)| - 1)) - 1) - 2| + 2) - 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -4(3|((-3(4(-2cos(1\u03c0x + 1) - 3)^2 + 3) + 2)/(-3(4(-2cos(1\u03c0x + 1) - 3)^2 + 3) - 3)) - 1| - 1)^2 + 1(3|((-3(4(-2cos(1\u03c0x + 1) - 3)^2 + 3) + 2)/(-3(4(-2cos(1\u03c0x + 1) - 3)^2 + 3) - 3)) - 1| - 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": "Find the number of local minimum points for f(x) = 2cos(2\u03c0(2(-2|(-1(-5x + 2) + 4)| + 3) + 2) + 3) - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "401", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -3|(-1|(5((1(-2cos(3\u03c0x + 1) + 2))/(1(-2cos(3\u03c0x + 1) + 2) + 2))^2 + 3((1(-2cos(3\u03c0x + 1) + 2))/(1(-2cos(3\u03c0x + 1) + 2) + 2)) + 5) + 3| - 2) + 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) = 4(2((-1(3|(-2sin(2\u03c0x)) + 1| - 3) - 1)/(3(3|(-2sin(2\u03c0x)) + 1| - 3) - 2))^2 - 4((-1(3|(-2sin(2\u03c0x)) + 1| - 3) - 1)/(3(3|(-2sin(2\u03c0x)) + 1| - 3) - 2)) + 5)^2 + 2(2((-1(3|(-2sin(2\u03c0x)) + 1| - 3) - 1)/(3(3|(-2sin(2\u03c0x)) + 1| - 3) - 2))^2 - 4((-1(3|(-2sin(2\u03c0x)) + 1| - 3) - 1)/(3(3|(-2sin(2\u03c0x)) + 1| - 3) - 2)) + 5) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "74", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = 1|((-1(4(2cos(3\u03c0((1x - 3)/(-3x - 2)) - 3))))/(-2(4(2cos(3\u03c0((1x - 3)/(-3x - 2)) - 3))) - 1)) + 2| + 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "24", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 1((-2(2cos(1\u03c0(2((1x - 1)/(-1x - 3))^2 - 1) - 3)))/(1(2cos(1\u03c0(2((1x - 1)/(-1x - 3))^2 - 1) - 3)) - 3)) + 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "99", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = (-1(1(1cos(1\u03c0(-3|(1|x - 2| - 3) - 3| + 3) + 3) + 1)^2 + 5(1cos(1\u03c0(-3|(1|x - 2| - 3) - 3| + 3) + 3) + 1) + 5))/(-3(1(1cos(1\u03c0(-3|(1|x - 2| - 3) - 3| + 3) + 3) + 1)^2 + 5(1cos(1\u03c0(-3|(1|x - 2| - 3) - 3| + 3) + 3) + 1) + 5) - 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "63", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = (-3(3(-2|((1((3x)/(1x)) + 3)/(-1((3x)/(1x)))) + 1| - 3)^2 - 1(-2|((1((3x)/(1x)) + 3)/(-1((3x)/(1x)))) + 1| - 3)) + 2)/(2(3(-2|((1((3x)/(1x)) + 3)/(-1((3x)/(1x)))) + 1| - 3)^2 - 1(-2|((1((3x)/(1x)) + 3)/(-1((3x)/(1x)))) + 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": "How many local extrema (minima and maxima combined) does the function f(x) = 3(-5(5(2cos(1\u03c0(-1x - 5) - 3) + 2)^2 + 3(2cos(1\u03c0(-1x - 5) - 3) + 2) - 2) - 2)^2 + 3(-5(5(2cos(1\u03c0(-1x - 5) - 3) + 2)^2 + 3(2cos(1\u03c0(-1x - 5) - 3) + 2) - 2) - 2) - 1 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 maxima does the function f(x) = 1(-1sin(1\u03c0(5(-1(1x + 1)^2 - 1(1x + 1) - 4) - 2) - 3)) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "250", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -2|(-2(-1(-3cos(3\u03c0((1x - 3)/(-3x - 2)) - 1) - 2) - 4)^2 + 5) - 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": "How many local minima does the function f(x) = 3cos(1\u03c0(2(-2(-5(2x^2 + 1x - 3) + 2) - 1)^2 + 3(-2(-5(2x^2 + 1x - 3) + 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": "45", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = (-1(-2e^(1(3(-3(-1x^2 - 1x + 1) + 3) - 3)) - 2) + 2)/(-2(-2e^(1(3(-3(-1x^2 - 1x + 1) + 3) - 3)) - 2) + 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -5(2cos(1\u03c0(-3(-4(-4x + 3)^2 - 2(-4x + 3) + 2)^2 - 3(-4(-4x + 3)^2 - 2(-4x + 3) + 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": "17", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 1(2(4(1sin(2\u03c0(5x - 4)) - 1) - 3)^2 - 2(4(1sin(2\u03c0(5x - 4)) - 1) - 3) + 3) + 3 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": "How many local extrema (minima and maxima combined) does the function f(x) = 3(-3sin(3\u03c0(-2(5(-2|x| - 3) - 2)^2 + 3(5(-2|x| - 3) - 2) - 1)) + 3)^2 + 2(-3sin(3\u03c0(-2(5(-2|x| - 3) - 2)^2 + 3(5(-2|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": "109", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 1((-2((2(1cos(2\u03c0(2|x| + 1) + 2) - 2) + 2)/(-2(1cos(2\u03c0(2|x| + 1) + 2) - 2) + 3)))/(2((2(1cos(2\u03c0(2|x| + 1) + 2) - 2) + 2)/(-2(1cos(2\u03c0(2|x| + 1) + 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": "40", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = (2((-2(-1(-2cos(2\u03c0(-2x + 4) - 2) - 1)^2 - 5) - 1)/(3(-1(-2cos(2\u03c0(-2x + 4) - 2) - 1)^2 - 5) + 3)) + 2)/(-3((-2(-1(-2cos(2\u03c0(-2x + 4) - 2) - 1)^2 - 5) - 1)/(3(-1(-2cos(2\u03c0(-2x + 4) - 2) - 1)^2 - 5) + 3)) - 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": "How many local maxima does the function f(x) = 3|(-1e^(-2(3|(2|(-5x^2 - 2x + 2)| - 2) + 2| + 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": "Find the total number of local minima and maxima for f(x) = -2|((3((-3(-2cos(1\u03c0(5x - 4) + 1) - 1) - 2)/(2(-2cos(1\u03c0(5x - 4) + 1) - 1))) - 1)/(1((-3(-2cos(1\u03c0(5x - 4) + 1) - 1) - 2)/(2(-2cos(1\u03c0(5x - 4) + 1) - 1))))) + 1| - 3 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": "Find the number of local minimum points for f(x) = -1|(-4(-4(-5(4x^2 + 1x - 5)^2 + 1(4x^2 + 1x - 5) + 1)^2 + 1(-5(4x^2 + 1x - 5)^2 + 1(4x^2 + 1x - 5) + 1) + 5) + 5) + 2| - 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 count of local minima for the function f(x) = -1|(-1|(-2sin(1\u03c0(-4(-1x - 2) + 5) + 3) - 2) - 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": "How many local extrema (minima and maxima combined) does the function f(x) = (-2(2(1(1(2sin(1\u03c0x - 2) - 3)^2 + 5(2sin(1\u03c0x - 2) - 3) - 2))^2 + 3(1(1(2sin(1\u03c0x - 2) - 3)^2 + 5(2sin(1\u03c0x - 2) - 3) - 2)) - 2) + 2)/(2(2(1(1(2sin(1\u03c0x - 2) - 3)^2 + 5(2sin(1\u03c0x - 2) - 3) - 2))^2 + 3(1(1(2sin(1\u03c0x - 2) - 3)^2 + 5(2sin(1\u03c0x - 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": "40", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -3cos(1\u03c0(-1|(4((-3(1x + 4) + 3)/(-2(1x + 4) - 3)) - 1) + 1| + 2) + 1) + 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": "How many local maxima does the function f(x) = 2|(-1|(4(3(1|x - 3|)^2 + 1(1|x - 3|) - 2) - 4) + 3| + 1) + 2| - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -1((-2(2(2(3|x + 1| - 1)^2 - 1(3|x + 1| - 1) - 3)^2 - 5(2(3|x + 1| - 1)^2 - 1(3|x + 1| - 1) - 3) + 2) - 1)/(-1(2(2(3|x + 1| - 1)^2 - 1(3|x + 1| - 1) - 3)^2 - 5(2(3|x + 1| - 1)^2 - 1(3|x + 1| - 1) - 3) + 2) - 1))^2 + 2((-2(2(2(3|x + 1| - 1)^2 - 1(3|x + 1| - 1) - 3)^2 - 5(2(3|x + 1| - 1)^2 - 1(3|x + 1| - 1) - 3) + 2) - 1)/(-1(2(2(3|x + 1| - 1)^2 - 1(3|x + 1| - 1) - 3)^2 - 5(2(3|x + 1| - 1)^2 - 1(3|x + 1| - 1) - 3) + 2) - 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": "How many local extrema (minima and maxima combined) does the function f(x) = 3(-2cos(3\u03c0((-3(2(-2|x|)^2 + 3(-2|x|) + 1))/(-2(2(-2|x|)^2 + 3(-2|x|) + 1) + 3))) - 2)^2 - 4(-2cos(3\u03c0((-3(2(-2|x|)^2 + 3(-2|x|) + 1))/(-2(2(-2|x|)^2 + 3(-2|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": "49", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 4(-4(1|(2|(-3x^2 - 4x + 5) + 2| - 3) - 2| - 3)^2 - 3(1|(2|(-3x^2 - 4x + 5) + 2| - 3) - 2| - 3) + 3)^2 - 2(-4(1|(2|(-3x^2 - 4x + 5) + 2| - 3) - 2| - 3)^2 - 3(1|(2|(-3x^2 - 4x + 5) + 2| - 3) - 2| - 3) + 3) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = (1(4(-1sin(2\u03c0(-1(-2x + 1)^2 - 1(-2x + 1) + 5) + 1)) + 1) - 3)/(-3(4(-1sin(2\u03c0(-1(-2x + 1)^2 - 1(-2x + 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": "225", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 2((-1(-2cos(1\u03c0(1(-2x)^2 + 4(-2x) - 1) - 3) + 1) - 1)/(3(-2cos(1\u03c0(1(-2x)^2 + 4(-2x) - 1) - 3) + 1) - 1))^2 + 1((-1(-2cos(1\u03c0(1(-2x)^2 + 4(-2x) - 1) - 3) + 1) - 1)/(3(-2cos(1\u03c0(1(-2x)^2 + 4(-2x) - 1) - 3) + 1) - 1)) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "518", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = (3(-1(4(1cos(1\u03c0(-4x^2 + 4x + 3) + 2) + 1) - 4)^2 + 5(4(1cos(1\u03c0(-4x^2 + 4x + 3) + 2) + 1) - 4) - 2) - 1)/(-2(-1(4(1cos(1\u03c0(-4x^2 + 4x + 3) + 2) + 1) - 4)^2 + 5(4(1cos(1\u03c0(-4x^2 + 4x + 3) + 2) + 1) - 4) - 2) - 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "345", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -4(3|(3((-2(3cos(3\u03c0x + 2) - 3) + 3)/(3(3cos(3\u03c0x + 2) - 3) - 2))^2 - 1((-2(3cos(3\u03c0x + 2) - 3) + 3)/(3(3cos(3\u03c0x + 2) - 3) - 2)) + 2) + 1| + 3)^2 - 2(3|(3((-2(3cos(3\u03c0x + 2) - 3) + 3)/(3(3cos(3\u03c0x + 2) - 3) - 2))^2 - 1((-2(3cos(3\u03c0x + 2) - 3) + 3)/(3(3cos(3\u03c0x + 2) - 3) - 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": "60", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -2(-1cos(1\u03c0(2|(1((-3x - 3)/(1x + 3)) - 2)| - 2) + 3) - 3)^2 - 4(-1cos(1\u03c0(2|(1((-3x - 3)/(1x + 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": "38", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -3(-5(1((-2(-1|x - 3| + 3) + 1)/(-3(-1|x - 3| + 3) + 2))^2 + 5((-2(-1|x - 3| + 3) + 1)/(-3(-1|x - 3| + 3) + 2)) - 5) + 4)^2 - 2(-5(1((-2(-1|x - 3| + 3) + 1)/(-3(-1|x - 3| + 3) + 2))^2 + 5((-2(-1|x - 3| + 3) + 1)/(-3(-1|x - 3| + 3) + 2)) - 5) + 4) - 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": "How many local extrema (minima and maxima combined) does the function f(x) = 4((3(-2cos(2\u03c0(4((3x - 1)/(2x - 1))^2 - 5((3x - 1)/(2x - 1)) - 5) + 2) + 2) + 2)/(-2(-2cos(2\u03c0(4((3x - 1)/(2x - 1))^2 - 5((3x - 1)/(2x - 1)) - 5) + 2) + 2) - 2))^2 - 3((3(-2cos(2\u03c0(4((3x - 1)/(2x - 1))^2 - 5((3x - 1)/(2x - 1)) - 5) + 2) + 2) + 2)/(-2(-2cos(2\u03c0(4((3x - 1)/(2x - 1))^2 - 5((3x - 1)/(2x - 1)) - 5) + 2) + 2) - 2)) + 1 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(-2|((-3((-2(3|x|) + 1)/(2(3|x|) + 2)) + 2)/(1((-2(3|x|) + 1)/(2(3|x|) + 2)) - 2)) - 2| + 3)) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -5(-4(-5(1cos(1\u03c0(2x) + 2) + 2)^2 + 3(1cos(1\u03c0(2x) + 2) + 2) - 2)^2 + 5(-5(1cos(1\u03c0(2x) + 2) + 2)^2 + 3(1cos(1\u03c0(2x) + 2) + 2) - 2) - 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": "Determine the count of local minima for the function f(x) = (-3(-2|(-1cos(2\u03c0(-1(-1|x + 2| - 2)^2 + 1(-1|x + 2| - 2) - 1) - 3) - 3) - 3|))/(-1(-2|(-1cos(2\u03c0(-1(-1|x + 2| - 2)^2 + 1(-1|x + 2| - 2) - 1) - 3) - 3) - 3|)) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "75", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 3(-1sin(2\u03c0(-3|(-3(-5x^2 - 5x + 2) + 4) - 1| + 2) + 1) + 3)^2 - 5(-1sin(2\u03c0(-3|(-3(-5x^2 - 5x + 2) + 4) - 1| + 2) + 1) + 3) - 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "169", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = 4(4(-1|(1|(3sin(3\u03c0x - 1) + 2) - 3| + 2) - 3|)^2 - 4(-1|(1|(3sin(3\u03c0x - 1) + 2) - 3| + 2) - 3|) - 5)^2 + 4(4(-1|(1|(3sin(3\u03c0x - 1) + 2) - 3| + 2) - 3|)^2 - 4(-1|(1|(3sin(3\u03c0x - 1) + 2) - 3| + 2) - 3|) - 5) + 4 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "102", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 1(-1(1cos(2\u03c0(-2|(-5x^2 - 5x - 5)| + 3) - 1)) + 4)^2 - 1(-1(1cos(2\u03c0(-2|(-5x^2 - 5x - 5)| + 3) - 1)) + 4) - 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "263", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 2cos(1\u03c0(-3((1(-2((3x + 2)/(-2x - 3))) - 2)/(-3(-2((3x + 2)/(-2x - 3)))))^2 + 1((1(-2((3x + 2)/(-2x - 3))) - 2)/(-3(-2((3x + 2)/(-2x - 3))))) - 2) + 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": "How many local extrema (minima and maxima combined) does the function f(x) = 2((-2(-1|((3((2x - 3)/(-3x - 2)) - 1)/(1((2x - 3)/(-3x - 2)) - 3)) + 1| + 2) - 3)/(1(-1|((3((2x - 3)/(-3x - 2)) - 1)/(1((2x - 3)/(-3x - 2)) - 3)) + 1| + 2) + 2))^2 + 2((-2(-1|((3((2x - 3)/(-3x - 2)) - 1)/(1((2x - 3)/(-3x - 2)) - 3)) + 1| + 2) - 3)/(1(-1|((3((2x - 3)/(-3x - 2)) - 1)/(1((2x - 3)/(-3x - 2)) - 3)) + 1| + 2) + 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": "Determine the total count of local extrema points for the function f(x) = -1cos(1\u03c0(-1(1(-4(-3|x - 1| + 1)^2 + 5(-3|x - 1| + 1) + 2)^2 + 1(-4(-3|x - 1| + 1)^2 + 5(-3|x - 1| + 1) + 2) - 2) - 4)) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "102", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 2(-2sin(3\u03c0((1((-1(5x^2 + 3x - 2) - 2)/(-1(5x^2 + 3x - 2) + 3)) - 2)/(-1((-1(5x^2 + 3x - 2) - 2)/(-1(5x^2 + 3x - 2) + 3)) - 1)) + 1))^2 + 4(-2sin(3\u03c0((1((-1(5x^2 + 3x - 2) - 2)/(-1(5x^2 + 3x - 2) + 3)) - 2)/(-1((-1(5x^2 + 3x - 2) - 2)/(-1(5x^2 + 3x - 2) + 3)) - 1)) + 1)) + 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "58", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -3(-2e^(-2(2(1(1x^2 + 3x - 3) - 3)^2 + 2(1(1x^2 + 3x - 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": "7", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 1sin(3\u03c0(2|(5(5(3|x + 2| + 1) + 5) - 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": "974", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -1(1(2(-4(-3x^2 + 2x + 2)^2 - 3(-3x^2 + 2x + 2) + 2)^2 - 4(-4(-3x^2 + 2x + 2)^2 - 3(-3x^2 + 2x + 2) + 2))^2 + 5(2(-4(-3x^2 + 2x + 2)^2 - 3(-3x^2 + 2x + 2) + 2)^2 - 4(-4(-3x^2 + 2x + 2)^2 - 3(-3x^2 + 2x + 2) + 2)) + 3)^2 + 4(1(2(-4(-3x^2 + 2x + 2)^2 - 3(-3x^2 + 2x + 2) + 2)^2 - 4(-4(-3x^2 + 2x + 2)^2 - 3(-3x^2 + 2x + 2) + 2))^2 + 5(2(-4(-3x^2 + 2x + 2)^2 - 3(-3x^2 + 2x + 2) + 2)^2 - 4(-4(-3x^2 + 2x + 2)^2 - 3(-3x^2 + 2x + 2) + 2)) + 3) - 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = 1((1(4(-1(-1|x - 1| + 2)^2 - 5(-1|x - 1| + 2) - 3)^2 - 2(-1(-1|x - 1| + 2)^2 - 5(-1|x - 1| + 2) - 3) + 2) - 1)/(-2(4(-1(-1|x - 1| + 2)^2 - 5(-1|x - 1| + 2) - 3)^2 - 2(-1(-1|x - 1| + 2)^2 - 5(-1|x - 1| + 2) - 3) + 2) + 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": "How many local minima does the function f(x) = -4(2sin(3\u03c0((-2(2|(1x + 4) + 2| - 2) + 3)/(2(2|(1x + 4) + 2| - 2) + 1))) - 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "27", "dataset": "MATH"}