{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -2cos(1\u03c0(-3(5(3|x - 1| + 2) - 1)^2 + 5(5(3|x - 1| + 2) - 1) - 5) + 2) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "276", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -2cos(3\u03c0(-4(-1|x + 1| - 2)^2 + 4(-1|x + 1| - 2)) + 1) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "234", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -3sin(3\u03c0(-4x - 3) - 1) - 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "240", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = (-2(2sin(3\u03c0(-2|x| + 1) + 2) - 1) + 3)/(-2(2sin(3\u03c0(-2|x| + 1) + 2) - 1) + 1) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = (1(3cos(1\u03c0(-4(-2x - 5)^2 - 2(-2x - 5) - 5) + 2) - 1) - 2)/(-2(3cos(1\u03c0(-4(-2x - 5)^2 - 2(-2x - 5) - 5) + 2) - 1) + 3) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "494", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -1(-2cos(1\u03c0(-3|x + 1|) - 3)) + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = (-1(2(2|(-5x + 2) + 3|)^2 - 3(2|(-5x + 2) + 3|) + 4) + 2)/(3(2(2|(-5x + 2) + 3|)^2 - 3(2|(-5x + 2) + 3|) + 4) + 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = 3(3|x + 1|)^2 - 1(3|x + 1|) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -5((2(-2|x - 3| + 3) + 3)/(1(-2|x - 3| + 3)))^2 - 2((2(-2|x - 3| + 3) + 3)/(1(-2|x - 3| + 3))) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = (-3(-2sin(3\u03c0x - 1) - 3) - 3)/(3(-2sin(3\u03c0x - 1) - 3) - 1) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = (-2(3cos(1\u03c0(-1x^2 - 4x + 1) - 2) - 1) + 1)/(3(3cos(1\u03c0(-1x^2 - 4x + 1) - 2) - 1) - 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "209", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = (-2(-2cos(2\u03c0(2|(1x^2 - 4x - 2) + 3| + 2) - 3) + 1) + 3)/(-1(-2cos(2\u03c0(2|(1x^2 - 4x - 2) + 3| + 2) - 3) + 1) + 2) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "543", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -2(3sin(1\u03c0(4x^2 - 2x + 4) + 1) - 3) - 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "575", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -2sin(2\u03c0(-4(-2|((2x + 1)/(1x - 3)) + 3| - 2)^2 - 3(-2|((2x + 1)/(1x - 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": "235", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 1(-5((-1(-1cos(2\u03c0x - 2) + 1) + 3)/(-2(-1cos(2\u03c0x - 2) + 1)))^2 - 4((-1(-1cos(2\u03c0x - 2) + 1) + 3)/(-2(-1cos(2\u03c0x - 2) + 1))) - 4) + 5 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "79", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 1sin(1\u03c0(5x^2 + 5x - 4) + 2) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "251", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -3|((-3(3x^2 + 3x - 2) - 2)/(2(3x^2 + 3x - 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) = -4(-2|((-3(-2cos(3\u03c0x + 3) - 1) - 2)/(1(-2cos(3\u03c0x + 3) - 1) + 3)) + 3| + 3)^2 - 1(-2|((-3(-2cos(3\u03c0x + 3) - 1) - 2)/(1(-2cos(3\u03c0x + 3) - 1) + 3)) + 3| + 3) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "56", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 1e^(1((-3x - 3)/(-3x + 1))) + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -2cos(2\u03c0((3(1x^2 - 5) - 3)/(-1(1x^2 - 5) + 2)) - 3) - 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 3|((2(-2sin(3\u03c0x - 2)) - 1)/(-1(-2sin(3\u03c0x - 2)) - 1)) + 3| + 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "119", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = (-1(-1(3(1cos(2\u03c0x - 1) + 3))^2 + 1(3(1cos(2\u03c0x - 1) + 3)) - 5) - 2)/(-1(-1(3(1cos(2\u03c0x - 1) + 3))^2 + 1(3(1cos(2\u03c0x - 1) + 3)) - 5) + 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = (1(5(-3(1|x - 1| - 2))^2 + 1(-3(1|x - 1| - 2)) + 4) + 2)/(2(5(-3(1|x - 1| - 2))^2 + 1(-3(1|x - 1| - 2)) + 4) - 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = (3(-1|(-2sin(1\u03c0x - 2) + 3) + 1| - 1) + 1)/(3(-1|(-2sin(1\u03c0x - 2) + 3) + 1| - 1) - 2) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = 1|(3(2sin(1\u03c0(-4x^2 + 3x + 5) + 1) - 1) - 2) - 3| - 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "290", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 1(-1(3sin(1\u03c0x + 1)) - 2)^2 - 3(-1(3sin(1\u03c0x + 1)) - 2) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -1(-3cos(1\u03c0x + 3)) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = -3|(1cos(2\u03c0(1(2x^2 - 2x + 5) - 3) - 3) - 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) = 3sin(2\u03c0(4x^2 - 5x + 5)) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "257", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = (3(-3sin(1\u03c0(1x - 1) - 1) + 1) + 1)/(2(-3sin(1\u03c0(1x - 1) - 1) + 1) + 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 3((-2(3cos(2\u03c0(-2x - 5) - 2) + 2) + 2)/(3(3cos(2\u03c0(-2x - 5) - 2) + 2) - 1))^2 + 1((-2(3cos(2\u03c0(-2x - 5) - 2) + 2) + 2)/(3(3cos(2\u03c0(-2x - 5) - 2) + 2) - 1)) - 4 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": "How many local minima does the function f(x) = 2(2sin(3\u03c0((-1x + 3)/(-2x + 3)) - 3) - 3)^2 - 1(2sin(3\u03c0((-1x + 3)/(-2x + 3)) - 3) - 3) + 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": "How many local extrema (minima and maxima combined) does the function f(x) = (2(3(-1(3|x + 3| + 1) + 1)^2 + 1(-1(3|x + 3| + 1) + 1) - 3))/(-2(3(-1(3|x + 3| + 1) + 1)^2 + 1(-1(3|x + 3| + 1) + 1) - 3) + 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 5(-2sin(1\u03c0(-2|x - 2|) + 3)) - 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": "How many local maxima does the function f(x) = (3(2sin(3\u03c0(2x^2 - 5x - 1) - 2) + 3) - 1)/(-2(2sin(3\u03c0(2x^2 - 5x - 1) - 2) + 3) + 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "297", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 1sin(1\u03c0(2x^2 + 3x) - 1) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "201", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 5(3sin(2\u03c0((3x - 1)/(-2x + 3)) + 3) - 2)^2 + 4(3sin(2\u03c0((3x - 1)/(-2x + 3)) + 3) - 2) - 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = (-2(-2sin(1\u03c0(-2|x + 1| - 1)) + 3) + 3)/(-3(-2sin(1\u03c0(-2|x + 1| - 1)) + 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": "How many local minima does the function f(x) = 3sin(3\u03c0(-2x + 5) + 2) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = (-1(1sin(1\u03c0x + 3) - 2) - 3)/(-3(1sin(1\u03c0x + 3) - 2) + 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -5((2(2cos(3\u03c0x - 3) - 3) + 1)/(-2(2cos(3\u03c0x - 3) - 3) + 1))^2 - 5((2(2cos(3\u03c0x - 3) - 3) + 1)/(-2(2cos(3\u03c0x - 3) - 3) + 1)) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 1|((2(-5(1x + 1)^2 - 5(1x + 1) + 4) + 3)/(-2(-5(1x + 1)^2 - 5(1x + 1) + 4) + 3)) + 3| + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = (2(-3(-1|(1cos(1\u03c0x + 3)) - 1| + 2) - 3) + 1)/(3(-3(-1|(1cos(1\u03c0x + 3)) - 1| + 2) - 3) + 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -5(-1|(-1sin(1\u03c0x + 1) - 1) + 1| - 2) + 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "24", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -1(3|((1(3cos(1\u03c0x - 3) - 3) - 1)/(1(3cos(1\u03c0x - 3) - 3) - 2))| - 2)^2 + 3(3|((1(3cos(1\u03c0x - 3) - 3) - 1)/(1(3cos(1\u03c0x - 3) - 3) - 2))| - 2) - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 2cos(2\u03c0(-5((-1(-1|x + 2|) - 2)/(-1(-1|x + 2|) - 1))^2 - 1((-1(-1|x + 2|) - 2)/(-1(-1|x + 2|) - 1)) + 2) - 3) + 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "98", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -2|(4(-1((-1x - 1)/(2x - 1)) - 2)^2 + 3(-1((-1x - 1)/(2x - 1)) - 2) + 5) - 2| + 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 4(3|(-2sin(2\u03c0x + 2)) + 2| - 3)^2 - 3(3|(-2sin(2\u03c0x + 2)) + 2| - 3) - 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": "Find the number of local maximum points for f(x) = 2(2cos(2\u03c0x + 3) + 1)^2 + 4(2cos(2\u03c0x + 3) + 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 2e^(-1(3|((3x - 3)/(-1x + 2))| + 2)) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 3e^(-2(3(1((-2x + 3)/(-3x - 2))^2 + 3((-2x + 3)/(-3x - 2)) + 2) - 2)) - 2 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) = 1(2cos(2\u03c0(-3x^2 + 3x) - 3) + 1) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "223", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = 5(3|(4((-1x + 3)/(-2x - 2)) + 3) + 1| - 3)^2 - 5(3|(4((-1x + 3)/(-2x - 2)) + 3) + 1| - 3) - 5 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 4(-2sin(3\u03c0x + 3) + 1)^2 - 1(-2sin(3\u03c0x + 3) + 1) + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 2(-2|(-1sin(2\u03c0((1x + 2)/(-1x + 3)) + 3) + 2) + 3|)^2 + 5(-2|(-1sin(2\u03c0((1x + 2)/(-1x + 3)) + 3) + 2) + 3|) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -5(1e^(2(2|((1x - 1)/(3x + 3))| - 1)) - 3)^2 - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -1(4(-2|(2cos(3\u03c0x) - 3) + 1| + 2)^2 - 3(-2|(2cos(3\u03c0x) - 3) + 1| + 2)) - 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "59", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -2cos(3\u03c0(-3|x + 2|) - 2) - 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": "Find the number of local minimum points for f(x) = (-3(-1sin(1\u03c0(4x + 1) + 3) + 2))/(3(-1sin(1\u03c0(4x + 1) + 3) + 2) + 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -1(4(-2cos(1\u03c0((2x + 2)/(-1x + 2)) + 3) - 2) - 5)^2 - 3(4(-2cos(1\u03c0((2x + 2)/(-1x + 2)) + 3) - 2) - 5) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "44", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 1(-2sin(1\u03c0(2|x - 1| + 2)) + 2)^2 - 1(-2sin(1\u03c0(2|x - 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": "Find the number of local minimum points for f(x) = (-1(2sin(3\u03c0x + 1) - 1) + 2)/(-3(2sin(3\u03c0x + 1) - 1) - 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -3e^(-2(-1|(3x^2 + 1x + 2) + 1| + 2)) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -3|(1(1sin(3\u03c0((3x + 3)/(3x + 2)) - 1)) - 2) - 2| + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -3cos(2\u03c0(-3((1(2|x + 2| - 2) - 3)/(1(2|x + 2| - 2) + 3))) + 1) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 2(1cos(3\u03c0(2|(3x^2 - 5) + 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": "256", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 2((3(1|x + 1| - 1) + 2)/(3(1|x + 1| - 1) - 2))^2 - 1((3(1|x + 1| - 1) + 2)/(3(1|x + 1| - 1) - 2)) - 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = 2sin(2\u03c0(2((-1(3x - 3) + 1)/(-2(3x - 3) - 3))^2 + 4((-1(3x - 3) + 1)/(-2(3x - 3) - 3)) + 3) - 3) - 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 3(1cos(3\u03c0((-3x - 3)/(-3x - 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": "Determine the total count of local extrema points for the function f(x) = -1|(-2cos(3\u03c0x - 2) + 1) - 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": "Determine the count of local maxima for the function f(x) = 2sin(1\u03c0(-2|x + 3| + 2) + 1) + 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 1|(-5x^2 + 3x + 2) + 3| + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 2cos(2\u03c0(-1x + 5)) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -3(-1|(2e^(-1x) - 2) - 1| + 1)^2 - 4(-1|(2e^(-1x) - 2) - 1| + 1) - 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -3cos(3\u03c0(2|x + 1|) + 1) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 1(1((-3x + 1)/(1x + 1)) + 4)^2 + 5(1((-3x + 1)/(1x + 1)) + 4) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 3sin(3\u03c0(-2x^2 - 1x - 1) - 2) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "453", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = (3(-2(2sin(3\u03c0x + 3) + 2) - 2) + 1)/(-2(-2(2sin(3\u03c0x + 3) + 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": "Find the number of local maximum points for f(x) = 3|(-1sin(2\u03c0(-5(2x - 1)^2 + 3(2x - 1) - 5)) - 3)| - 1 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": "Find the total number of local minima and maxima for f(x) = -1|(2x^2 - 5x + 1) - 3| - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -5(-3|((-2(-5x - 3) + 2)/(-2(-5x - 3) + 1)) - 2| + 1)^2 - 5(-3|((-2(-5x - 3) + 2)/(-2(-5x - 3) + 1)) - 2| + 1) - 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -3(2|(-2((-3x)/(-3x + 4)) + 4) + 2|)^2 + 2(2|(-2((-3x)/(-3x + 4)) + 4) + 2|) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 3|(2(-1(-3sin(3\u03c0x) + 3) - 1)^2 - 2(-1(-3sin(3\u03c0x) + 3) - 1) - 5) - 2| + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = (-2(-4(-1|(5x^2 + 4x - 4) + 3| + 2) - 4) + 2)/(-3(-4(-1|(5x^2 + 4x - 4) + 3| + 2) - 4) - 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -3((-2(1|x + 1| - 2) + 1)/(1(1|x + 1| - 2)))^2 - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 2|(1e^(2((-2(1x - 4))/(-2(1x - 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": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -1e^(1(1(-1|((-2x + 1)/(-3x + 2)) + 3| + 2) - 2)) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = (-1(-1sin(1\u03c0x + 3)) + 1)/(-2(-1sin(1\u03c0x + 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) = -1|(-2cos(2\u03c0x + 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) = (3(-1(3sin(1\u03c0x + 2) + 1)^2 - 4(3sin(1\u03c0x + 2) + 1) + 3))/(1(-1(3sin(1\u03c0x + 2) + 1)^2 - 4(3sin(1\u03c0x + 2) + 1) + 3) + 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -1sin(1\u03c0(2x^2 + 5x - 5) - 2) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "406", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -2|(3(3cos(1\u03c0x - 1) + 3)^2 + 3(3cos(1\u03c0x - 1) + 3) - 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": "Find the number of local minimum points for f(x) = 2(1|(-2sin(1\u03c0x + 2) - 3) - 3| + 2) - 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = 1(5(2|((1x - 1)/(2x)) - 3| - 1) - 5)^2 - 1(5(2|((1x - 1)/(2x)) - 3| - 1) - 5) + 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -4(-3cos(3\u03c0(-4((-1x + 2)/(3x + 3))^2 + 3((-1x + 2)/(3x + 3)) - 3) - 1) + 3) + 5 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = -2cos(2\u03c0((3(-2x + 3))/(2(-2x + 3) - 1)) + 2) + 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 count of local maxima for the function f(x) = -4(-2cos(1\u03c0(5x - 4) - 3) + 3)^2 + 5(-2cos(1\u03c0(5x - 4) - 3) + 3) + 5 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "50", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -1cos(1\u03c0(-2|x + 2| - 2) + 2) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 1|(2((-1(3sin(2\u03c0x + 3) + 3) - 1)/(3(3sin(2\u03c0x + 3) + 3) - 2)) + 4) - 2| - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "79", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 1sin(1\u03c0(1|x - 1| + 3) + 2) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 2((-1x + 2)/(-2x - 3))^2 - 3((-1x + 2)/(-2x - 3)) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = 2sin(2\u03c0(-5x - 1) - 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": "How many local maxima does the function f(x) = -2(-3|(4x - 4)| + 1)^2 + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = (-3(-1sin(3\u03c0(1(-2|x - 2| + 2) + 3) + 2) + 2) + 3)/(-2(-1sin(3\u03c0(1(-2|x - 2| + 2) + 3) + 2) + 2) + 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "61", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 1cos(2\u03c0(1|((3(-4x) + 1)/(-1(-4x) + 3)) + 1| - 3) - 1) - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "47", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = 1sin(3\u03c0(5x^2 - 5x + 1) - 3) - 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "253", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = 2e^(-1(3|(4(1x^2 - 4x + 1)) + 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": "Determine the total count of local extrema points for the function f(x) = -2(4(2sin(3\u03c0(2|x - 2| - 3) + 1))^2 + 4(2sin(3\u03c0(2|x - 2| - 3) + 1)) + 1) + 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "241", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 3sin(1\u03c0((1(-1(-1|x + 2| + 2) - 4) + 2)/(-1(-1(-1|x + 2| + 2) - 4) + 2)) + 3) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 2|(-3e^(1(-4((-3x)/(-1x + 3))^2 + 4((-3x)/(-1x + 3)) + 2)))| where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 1e^(-1(1(-3|x + 3| + 3)^2 - 4)) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -3sin(3\u03c0(-3(-2|((2x - 3)/(3x + 2)) + 3| - 1)^2 + 4(-2|((2x - 3)/(3x + 2)) + 3| - 1)) + 2) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "184", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = -3cos(1\u03c0(-1|(4x^2 + 4x + 3) - 3| + 1) + 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 total number of local minima and maxima for f(x) = -1(-1sin(2\u03c0(-3|(1x^2 - 2x - 2) - 3| - 3) - 3)) - 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "465", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 2(2|(-2sin(1\u03c0x - 2) - 1)| + 1) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 4(2|(4x^2 + 3x - 5) + 3|) - 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 1|(4(-1((3x + 1)/(-2x)))^2 + 4(-1((3x + 1)/(-2x))) - 4) + 1| + 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = (-1(1sin(1\u03c0x + 1) - 2))/(-1(1sin(1\u03c0x + 1) - 2) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 5((-3(2|(1e^(-1x) - 2)| - 3))/(1(2|(1e^(-1x) - 2)| - 3) + 2))^2 - 5((-3(2|(1e^(-1x) - 2)| - 3))/(1(2|(1e^(-1x) - 2)| - 3) + 2)) - 4 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = (1(-3(2(-1cos(1\u03c0x + 2) - 1)^2 + 4(-1cos(1\u03c0x + 2) - 1) + 1) + 4) - 3)/(-2(-3(2(-1cos(1\u03c0x + 2) - 1)^2 + 4(-1cos(1\u03c0x + 2) - 1) + 1) + 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) = -5((-1(-2cos(1\u03c0x - 1) + 2) - 3)/(-1(-2cos(1\u03c0x - 1) + 2) - 2)) + 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": "Determine the count of local minima for the function f(x) = (-3(-1(-2|(3x - 3) - 3| + 2)^2 - 3(-2|(3x - 3) - 3| + 2) + 3) + 1)/(2(-1(-2|(3x - 3) - 3| + 2)^2 - 3(-2|(3x - 3) - 3| + 2) + 3) + 2) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = 1(2cos(3\u03c0x - 1) + 3)^2 + 2(2cos(3\u03c0x - 1) + 3) - 4 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = 1sin(2\u03c0(5x^2 - 4x) - 3) - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "251", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -3cos(2\u03c0(2x^2 - 2x + 2) + 1) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "284", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 2sin(3\u03c0(-2|(1x^2 + 5x - 4) - 2|) - 1) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "515", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = (3(1(2sin(1\u03c0(-1|x - 3| + 1) + 2))^2 - 2(2sin(1\u03c0(-1|x - 3| + 1) + 2)) + 3) + 1)/(-1(1(2sin(1\u03c0(-1|x - 3| + 1) + 2))^2 - 2(2sin(1\u03c0(-1|x - 3| + 1) + 2)) + 3) + 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 maximum points for f(x) = -5(-1cos(1\u03c0x - 3) - 1)^2 + 3(-1cos(1\u03c0x - 3) - 1) - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = 1sin(2\u03c0(1(2|x + 2| + 1)^2 + 4(2|x + 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": "265", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -4((-1(2sin(1\u03c0(4x + 3) - 2) + 2) + 2)/(-1(2sin(1\u03c0(4x + 3) - 2) + 2)))^2 + 2((-1(2sin(1\u03c0(4x + 3) - 2) + 2) + 2)/(-1(2sin(1\u03c0(4x + 3) - 2) + 2))) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "160", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 5(-5(3e^(-2(2|x|)) + 1)^2 - 2(3e^(-2(2|x|)) + 1) + 3) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 3(-1sin(2\u03c0x - 1) + 3)^2 + 5(-1sin(2\u03c0x - 1) + 3) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 2cos(2\u03c0(5x) - 1) - 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": "Determine the total count of local extrema points for the function f(x) = -5(-1|x| + 2)^2 + 5(-1|x| + 2) + 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 2|(1sin(1\u03c0x) - 1) + 3| - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = -3|((-1(3e^(-2(5x + 2)) - 1) - 3)/(1(3e^(-2(5x + 2)) - 1) - 3)) - 2| in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 3|(-1cos(1\u03c0(-2x - 4) - 1) + 2) - 1| - 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -4(2sin(2\u03c0((-1x - 1)/(1x + 2)) + 1) + 1)^2 + 3(2sin(2\u03c0((-1x - 1)/(1x + 2)) + 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 minimum points for f(x) = -3((-1(-2|(1cos(2\u03c0x - 2) - 2) - 1| + 1))/(-2(-2|(1cos(2\u03c0x - 2) - 2) - 1| + 1) + 1)) + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -2((2x - 3)/(3x - 1))^2 - 5((2x - 3)/(3x - 1)) - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 3(-2sin(1\u03c0(-2|x - 1|) - 2) - 2) - 5 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) = -1(-2|((1(3x + 2) - 2)/(-2(3x + 2) - 1)) - 3| + 3)^2 - 5(-2|((1(3x + 2) - 2)/(-2(3x + 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": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 3((-1(-1|(-4x^2 - 1x + 2) + 2| - 2) - 1)/(-2(-1|(-4x^2 - 1x + 2) + 2| - 2))) + 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -4(3cos(2\u03c0(-4x + 5) - 3) + 3)^2 - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "160", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = (-2(-3sin(2\u03c0x - 2) + 2) + 2)/(-2(-3sin(2\u03c0x - 2) + 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": "Find the total number of local minima and maxima for f(x) = 2((2(-2(-2|x| + 3)^2 - 1(-2|x| + 3) - 2) + 2)/(-3(-2(-2|x| + 3)^2 - 1(-2|x| + 3) - 2) + 4)) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = 2sin(3\u03c0((1(1(-3|x - 3| + 3) - 3) + 3)/(2(1(-3|x - 3| + 3) - 3))) - 1) - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 1|(-2sin(2\u03c0(1(2x^2 + 1x - 3) - 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": "286", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -2|(5(2sin(2\u03c0(-3x^2 + 1x - 3) + 2) - 2) - 4) + 2| - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "449", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = (-3(-4(3|x + 1|) + 4))/(-2(-4(3|x + 1|) + 4)) 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(3sin(2\u03c0x - 2) - 2) + 1)/(-1(3sin(2\u03c0x - 2) - 2) + 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -3(1|(-5(2sin(3\u03c0x - 1) + 1)^2 + 2)| + 3) - 5 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "238", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = (-2(-1cos(3\u03c0x + 3) + 2) - 3)/(-2(-1cos(3\u03c0x + 3) + 2) + 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = 2e^(-1(3(-1|((3x - 3)/(2x - 3)) - 3| + 3)^2 + 1(-1|((3x - 3)/(2x - 3)) - 3| + 3) + 4)) + 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -3|(-1x^2 - 5x + 2) - 1| - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -2e^(-1(-4x + 1)) - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -1cos(2\u03c0((3x - 2)/(3x + 3)) + 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": "How many local maxima does the function f(x) = 2cos(3\u03c0(1|((-1x + 1)/(1x + 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": "30", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -3|(-3((3x - 2)/(2x + 1))^2 + 1((3x - 2)/(2x + 1)) + 1) + 1| in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 3(-4(-2|((-2x)/(3x)) - 2| + 2) - 2)^2 - 4(-4(-2|((-2x)/(3x)) - 2| + 2) - 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": "How many local maxima does the function f(x) = -5(-2sin(3\u03c0x + 2) - 3) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = (3(2sin(1\u03c0(3|(5x^2 + 2x + 2) - 3| - 2) - 2) + 1) - 2)/(-2(2sin(1\u03c0(3|(5x^2 + 2x + 2) - 3| - 2) - 2) + 1) + 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "501", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 1sin(3\u03c0(-3|(1(-5x^2 - 1x + 4) + 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": "245", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -4(1cos(2\u03c0(-3|(1x^2 - 1x - 1) + 2| - 3) - 3)) - 5 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "230", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 3sin(1\u03c0(-4(4x^2 + 4x) + 2) - 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) = -3((-1(3cos(3\u03c0x - 1) + 3) - 2)/(-1(3cos(3\u03c0x - 1) + 3) + 2))^2 + 1((-1(3cos(3\u03c0x - 1) + 3) - 2)/(-1(3cos(3\u03c0x - 1) + 3) + 2)) + 4 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "119", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = 1|(-1cos(2\u03c0(2x^2 + 3x + 2) - 2) - 2) + 1| + 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "289", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -1(5(2|(1sin(1\u03c0x) + 2) - 1| + 2)^2 + 4(2|(1sin(1\u03c0x) + 2) - 1| + 2) - 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": "How many local minima does the function f(x) = -3((-2(-2cos(3\u03c0x + 3) + 1))/(2(-2cos(3\u03c0x + 3) + 1) - 1)) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -1sin(2\u03c0(2(3|x + 3| - 3) - 5)) + 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) = 4(2((1x + 3)/(3x + 3)) + 5)^2 - 3(2((1x + 3)/(3x + 3)) + 5) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -2e^(-1(3((1(-3|x - 3| + 3) - 2)/(1(-3|x - 3| + 3)))^2 + 4((1(-3|x - 3| + 3) - 2)/(1(-3|x - 3| + 3))) + 5)) - 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 maxima does the function f(x) = 1sin(2\u03c0((-2(4x^2 + 1x) - 3)/(-2(4x^2 + 1x))) - 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": "Determine the count of local minima for the function f(x) = -2|(2cos(1\u03c0x - 1) - 1) + 2| + 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 1(-3cos(3\u03c0x - 3) + 3) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 1|(1sin(2\u03c0((-3(2x^2 + 4x + 3) + 3)/(-1(2x^2 + 4x + 3) - 3))) + 2) + 2| - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 1sin(3\u03c0((-3(-3x - 2) - 2)/(1(-3x - 2) + 3)) - 3) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "54", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 2sin(2\u03c0(-2|x - 1| + 1)) + 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "81", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 2((-3(2|x - 3| - 3))/(1(2|x - 3| - 3))) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -1(5((-3(-1|x - 1| - 2))/(1(-1|x - 1| - 2))))^2 - 1(5((-3(-1|x - 1| - 2))/(1(-1|x - 1| - 2)))) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "133", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = (-2(1(-1|(-2cos(1\u03c0x - 2) + 3)| - 3) - 2))/(2(1(-1|(-2cos(1\u03c0x - 2) + 3)| - 3) - 2) - 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = 4(3((2x - 1)/(-3x - 1)) + 5)^2 + 5(3((2x - 1)/(-3x - 1)) + 5) - 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = 3|(-1cos(3\u03c0x - 3) - 2) + 3| - 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = -1(-1sin(2\u03c0(-1|x - 3| + 1) + 2) - 3)^2 + 1(-1sin(2\u03c0(-1|x - 3| + 1) + 2) - 3) + 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = (3(-3|(1cos(1\u03c0(4x - 3) - 2) + 1) - 2| + 1) - 3)/(2(-3|(1cos(1\u03c0(4x - 3) - 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": "42", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 3|(-5((3x + 1)/(-2x + 3))^2 + 3)| + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = 2(1|(1((-1x + 2)/(-3x - 3)) - 4)| - 1)^2 + 2(1|(1((-1x + 2)/(-3x - 3)) - 4)| - 1) - 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = 3|(-5(-2cos(3\u03c0x - 2) + 1)^2 - 2(-2cos(3\u03c0x - 2) + 1)) - 3| + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 5(3sin(2\u03c0(1((1x - 2)/(1x + 2)) - 4)) - 3)^2 + 5(3sin(2\u03c0(1((1x - 2)/(1x + 2)) - 4)) - 3) - 5 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) = 3|(-1cos(1\u03c0(4x^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": "292", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -3e^(-2(-3x^2 - 2x + 1)) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = (2(1|(-2sin(2\u03c0(5x - 3) + 3)) + 3| - 1) + 2)/(2(1|(-2sin(2\u03c0(5x - 3) + 3)) + 3| - 1) + 1) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "100", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = -1(-2cos(3\u03c0x - 2) - 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 count of local maxima for the function f(x) = 3e^(1(-2x^2 - 1x)) + 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -5(-1|(-2cos(1\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": "20", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 2(1cos(3\u03c0x + 1) - 1) + 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": "Determine the total count of local extrema points for the function f(x) = 1(-1sin(3\u03c0x - 2) + 2) - 5 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 1|(2sin(3\u03c0x - 1) - 1) - 3| + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = 2|(-1sin(3\u03c0((-3(1x) - 3)/(1(1x))) + 1) - 3) - 2| + 3 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": "Find the number of local maximum points for f(x) = 1(-2cos(2\u03c0(4x^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": "261", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 3|(3(-5((-3x + 2)/(3x + 3)) - 2)^2 - 3(-5((-3x + 2)/(3x + 3)) - 2) - 3)| - 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 2sin(2\u03c0((1(-2|x + 1| + 2) - 1)/(-3(-2|x + 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": "13", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -2cos(3\u03c0(-2|(4((2x + 2)/(1x))^2 + 4((2x + 2)/(1x)) - 4) + 2| + 3) + 3) - 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": "Find the total number of local minima and maxima for f(x) = 3cos(3\u03c0(-2|(-5x + 1) + 3| - 1) + 3) + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "601", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = (-2(-1(-2cos(3\u03c0x - 1) + 2) - 4) - 3)/(-1(-1(-2cos(3\u03c0x - 1) + 2) - 4) + 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 extrema (minima and maxima combined) does the function f(x) = -1(-1cos(3\u03c0x - 1) - 3) + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 1|(-2cos(2\u03c0(2x + 3) + 2) - 1) + 2| - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "160", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -1cos(3\u03c0(4((2x - 1)/(1x + 2))^2 - 4((2x - 1)/(1x + 2)) + 1) - 2) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "110", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = 1((3(-5x - 5) - 3)/(1(-5x - 5) + 1))^2 - 1((3(-5x - 5) - 3)/(1(-5x - 5) + 1)) + 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = (-2(-2sin(2\u03c0(1x + 3) + 3) - 1) + 3)/(-2(-2sin(2\u03c0(1x + 3) + 3) - 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) = -3|(2cos(3\u03c0((3(-5x + 3) + 1)/(2(-5x + 3) - 3)) + 3) - 1) - 3| where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -5(-1((2x + 3)/(-1x - 1))^2 + 3((2x + 3)/(-1x - 1)) + 4) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 2|(2sin(1\u03c0x - 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": "Find the total number of local minima and maxima for f(x) = 3((-3(1cos(2\u03c0x - 3) + 1) - 2)/(-1(1cos(2\u03c0x - 3) + 1) + 3))^2 - 4((-3(1cos(2\u03c0x - 3) + 1) - 2)/(-1(1cos(2\u03c0x - 3) + 1) + 3)) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 1|(4(-1cos(1\u03c0x + 2) - 1) - 5) + 1| - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = (-2(1cos(1\u03c0(3|x + 1| - 3) - 3) - 3) + 3)/(1(1cos(1\u03c0(3|x + 1| - 3) - 3) - 3)) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -1(-2cos(2\u03c0(2x)) - 1)^2 + 3(-2cos(2\u03c0(2x)) - 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 total count of local extrema points for the function f(x) = 1|((-2(1e^(-1(3x^2 + 1x - 3)) - 1))/(-1(1e^(-1(3x^2 + 1x - 3)) - 1) - 2))| + 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = 1cos(2\u03c0(1|((-1x + 1)/(2x + 2)) + 2| + 3) + 2) - 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -3(-1cos(3\u03c0((2(1x - 4) + 3)/(-2(1x - 4) + 3)) + 3) - 2)^2 - 3(-1cos(3\u03c0((2(1x - 4) + 3)/(-2(1x - 4) + 3)) + 3) - 2) - 4 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = 3(2|(-1(3cos(3\u03c0x + 3) + 2) + 2) + 1| + 3)^2 + 5(2|(-1(3cos(3\u03c0x + 3) + 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": "45", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -5((-3(-3|(-5x + 1) - 2| + 1) + 1)/(-1(-3|(-5x + 1) - 2| + 1) + 2))^2 + 5((-3(-3|(-5x + 1) - 2| + 1) + 1)/(-1(-3|(-5x + 1) - 2| + 1) + 2)) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -1|(1cos(2\u03c0x + 3) + 3) + 1| have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = 3(3((3(3cos(1\u03c0x - 2) + 2) - 1)/(-1(3cos(1\u03c0x - 2) + 2) + 2)) + 4)^2 + 3(3((3(3cos(1\u03c0x - 2) + 2) - 1)/(-1(3cos(1\u03c0x - 2) + 2) + 2)) + 4) - 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -3cos(3\u03c0(-5((2x)/(3x))) - 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": "How many local maxima does the function f(x) = -1e^(-1(-4((-2(4x + 5) + 1)/(3(4x + 5) - 2))^2 + 1((-2(4x + 5) + 1)/(3(4x + 5) - 2)) - 3)) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 3|(-3((1(1x^2 - 1x - 2) + 1)/(1(1x^2 - 1x - 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": "5", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 1|(1sin(1\u03c0x - 1) - 3) + 1| + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -4((2(-1cos(3\u03c0x)) - 2)/(2(-1cos(3\u03c0x)) - 1)) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -1(1(3cos(2\u03c0x + 3) + 3) + 5)^2 - 2(1(3cos(2\u03c0x + 3) + 3) + 5) + 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -2e^(-2(3|x + 1|)) - 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = 2|(2(-3cos(3\u03c0x) + 3) + 4) + 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 total number of local minima and maxima for f(x) = 4(-3|((2(-1x - 5) - 1)/(3(-1x - 5) + 3)) + 3| + 2)^2 - 2(-3|((2(-1x - 5) - 1)/(3(-1x - 5) + 3)) + 3| + 2) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -1|(-1((-3(-5x^2 + 3) - 2)/(2(-5x^2 + 3) - 1)) - 2)| + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 1(-2(3|x - 1| - 2)^2 - 3(3|x - 1| - 2) - 3) + 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -5(-1cos(3\u03c0x - 3) + 2) - 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -1sin(2\u03c0(-2((1(4x^2 - 1x + 4) + 3)/(2(4x^2 - 1x + 4) + 1)) + 1) + 1) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = (-3(2sin(1\u03c0(5x + 3)) - 3) + 3)/(3(2sin(1\u03c0(5x + 3)) - 3) - 2) 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) = -1cos(2\u03c0(-4(-3x^2 - 2x + 1) - 3) + 3) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "252", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -4(-3sin(1\u03c0x - 1))^2 + 2(-3sin(1\u03c0x - 1)) + 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": "Find the number of local maximum points for f(x) = -4(-3cos(2\u03c0x - 2) + 3)^2 - 1(-3cos(2\u03c0x - 2) + 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": "Find the number of local minimum points for f(x) = -1(1cos(3\u03c0x) - 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 maxima does the function f(x) = 2cos(3\u03c0((3x + 2)/(-3x + 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) = 3e^(-2(2|(-2x + 1)| + 1)) + 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -2cos(2\u03c0(-2(4x + 2)^2 - 5(4x + 2) - 5) + 2) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "233", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = (-3(-1(2sin(3\u03c0x + 1) - 3) + 2) - 3)/(-1(-1(2sin(3\u03c0x + 1) - 3) + 2) + 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = (-2(-1|(3(1x - 1)^2 - 1(1x - 1)) - 3|) - 3)/(-2(-1|(3(1x - 1)^2 - 1(1x - 1)) - 3|) + 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -2(-1|(-1(1sin(2\u03c0x + 2) + 3)^2 - 2(1sin(2\u03c0x + 2) + 3))| - 1) - 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": "How many local minima does the function f(x) = -3cos(1\u03c0(2|((3x - 3)/(-1x - 2))| + 2) - 1) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "43", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 1(5((-2x + 3)/(2x - 1)) + 3)^2 + 1(5((-2x + 3)/(2x - 1)) + 3) + 5 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -1(3cos(1\u03c0(1((1x + 3)/(-3x + 2)) - 5) - 3) - 1)^2 - 2(3cos(1\u03c0(1((1x + 3)/(-3x + 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": "32", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 2(-2sin(3\u03c0x + 3) - 1) - 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": "Determine the count of local maxima for the function f(x) = (-3(2cos(2\u03c0x) + 3))/(-2(2cos(2\u03c0x) + 3) - 1) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = (-2(-1e^(-1(1x^2 + 5x - 3)) + 3) + 1)/(-3(-1e^(-1(1x^2 + 5x - 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": "How many local maxima does the function f(x) = 1sin(1\u03c0((-2x + 3)/(-1x - 1)) - 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": "Find the number of local minimum points for f(x) = -5(-3(2|((1x + 1)/(2x + 1)) + 1| - 3)^2 - 3(2|((1x + 1)/(2x + 1)) + 1| - 3) + 3) + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -1(-2sin(3\u03c0x - 1) + 2)^2 + 5(-2sin(3\u03c0x - 1) + 2) + 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 minima does the function f(x) = 3e^(1(1(-3(-3|x + 2| + 2) + 3)^2 + 3(-3(-3|x + 2| + 2) + 3) - 1)) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = (-3(-3cos(3\u03c0x + 2) + 3) - 2)/(2(-3cos(3\u03c0x + 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": "Find the total number of local minima and maxima for f(x) = 1sin(2\u03c0(-1x^2 + 3x - 5) - 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "411", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = (1(-3sin(3\u03c0x - 2) - 2) + 3)/(2(-3sin(3\u03c0x - 2) - 2) + 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = (-1(-2|(3x^2 - 3x - 3) + 1| + 3) - 2)/(1(-2|(3x^2 - 3x - 3) + 1| + 3)) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = (2(-2(2(-1|x - 2| + 3)^2 + 3(-1|x - 2| + 3) - 2) - 1) + 1)/(2(-2(2(-1|x - 2| + 3)^2 + 3(-1|x - 2| + 3) - 2) - 1) - 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -3|(-5(-1cos(1\u03c0x - 1) + 3)^2) - 2| + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -4(3cos(3\u03c0((2(1x^2 + 1x - 2))/(-1(1x^2 + 1x - 2) - 1))) - 3) - 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 4((-2(-2|x - 3| + 3))/(1(-2|x - 3| + 3) - 3))^2 - 4((-2(-2|x - 3| + 3))/(1(-2|x - 3| + 3) - 3)) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 3(-1cos(1\u03c0(-2x^2 + 5x + 4) - 2) - 1) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "407", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -1cos(2\u03c0(1|(1(4x^2 + 1x - 2) + 5) - 1| - 2)) - 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "262", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -1(2|x + 1|)^2 + 5(2|x + 1|) + 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -1|((2(4(-1x + 2)^2 - 2(-1x + 2) - 2) + 2)/(-1(4(-1x + 2)^2 - 2(-1x + 2) - 2))) + 3| + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -5(-1cos(1\u03c0x + 2) + 2)^2 + 4(-1cos(1\u03c0x + 2) + 2) - 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": "Find the total number of local minima and maxima for f(x) = 2cos(2\u03c0(2(-2|x + 2| - 3)^2 - 5(-2|x + 2| - 3) + 4) + 2) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "468", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -3cos(3\u03c0(-2x^2 + 4) - 3) - 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "224", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = (1(1(-5(1sin(2\u03c0x - 2) - 3) + 2)^2 - 5(-5(1sin(2\u03c0x - 2) - 3) + 2)) + 2)/(1(1(-5(1sin(2\u03c0x - 2) - 3) + 2)^2 - 5(-5(1sin(2\u03c0x - 2) - 3) + 2))) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = 1(1(-1|x + 3| + 1) - 3)^2 + 5(1(-1|x + 3| + 1) - 3) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -1cos(3\u03c0((2x - 3)/(3x - 1)) + 1) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -2sin(3\u03c0(-3x - 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 maxima does the function f(x) = -5(-2|(2sin(2\u03c0x) - 3) - 3| + 2)^2 - 4(-2|(2sin(2\u03c0x) - 3) - 3| + 2) - 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": "How many local maxima does the function f(x) = 2cos(1\u03c0((2x + 1)/(-3x + 4)) - 1) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 1|(5(2sin(1\u03c0((-1x - 2)/(-1x + 2)) - 2) - 2)^2 + 4(2sin(1\u03c0((-1x - 2)/(-1x + 2)) - 2) - 2) + 5) + 1| + 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "48", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = 2(3(-2sin(2\u03c0x - 1) - 2) - 4)^2 - 2(3(-2sin(2\u03c0x - 1) - 2) - 4) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -5(-2|(-3x + 5) - 3| + 1)^2 - 1(-2|(-3x + 5) - 3| + 1) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = (-1(-1(1sin(2\u03c0x - 2) - 2)^2 - 2(1sin(2\u03c0x - 2) - 2) - 3) + 3)/(-1(-1(1sin(2\u03c0x - 2) - 2)^2 - 2(1sin(2\u03c0x - 2) - 2) - 3) - 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 maximum points for f(x) = -5(-1|(-2cos(3\u03c0x + 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": "114", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -3(-1((-1x + 3)/(-2x - 3))^2 + 4((-1x + 3)/(-2x - 3)) - 2) - 5 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -1sin(3\u03c0(2|((1(4x^2 + 2x + 5) + 2)/(-1(4x^2 + 2x + 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": "10", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = 1(1sin(2\u03c0((-2x)/(-1x - 2)) - 2)) - 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 2(1sin(3\u03c0x + 1) + 3)^2 + 2(1sin(3\u03c0x + 1) + 3) + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 1(-2((-2(-2cos(1\u03c0x - 3) - 1) - 3)/(3(-2cos(1\u03c0x - 3) - 1) + 3))^2 + 4((-2(-2cos(1\u03c0x - 3) - 1) - 3)/(3(-2cos(1\u03c0x - 3) - 1) + 3)) - 5) - 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "59", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -1|((2(-5(4x^2 - 1x - 1)) + 1)/(-1(-5(4x^2 - 1x - 1)) - 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": "Find the number of local minimum points for f(x) = 4(5(-1cos(3\u03c0(2|x - 2| + 3) + 1) - 3)^2 - 5(-1cos(3\u03c0(2|x - 2| + 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": "61", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -1sin(2\u03c0(5x + 1) + 1) + 1 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 count of local maxima for the function f(x) = -1(-3|(-3x + 2) + 2| - 1)^2 - 3(-3|(-3x + 2) + 2| - 1) + 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = 1sin(3\u03c0(-1(1|x| - 3)^2 - 3(1|x| - 3) - 4) - 3) - 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "229", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = (2(-2(2(2cos(1\u03c0x - 3) + 2)^2 - 5)) - 3)/(-1(-2(2(2cos(1\u03c0x - 3) + 2)^2 - 5)) - 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -1|(-3(1cos(3\u03c0x + 3) + 3) + 4) - 3| - 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -3(1cos(1\u03c0(-2|(3x^2 - 5x + 5) - 2| - 3) - 1) + 2) + 4 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "459", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 4(4((-2x)/(3x - 2)) - 4)^2 + 2(4((-2x)/(3x - 2)) - 4) - 4 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -2|(1(-4x + 1)^2 - 5(-4x + 1) - 4)| + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = (-3(2sin(2\u03c0x) - 2) + 3)/(-2(2sin(2\u03c0x) - 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": "Determine the total count of local extrema points for the function f(x) = 1|((-1(-3(-2x + 4)^2 - 1(-2x + 4) + 1) - 3)/(3(-3(-2x + 4)^2 - 1(-2x + 4) + 1) + 2))| in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -1(-2cos(3\u03c0x))^2 - 4(-2cos(3\u03c0x)) + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = (2(1(-2|(-4x^2 - 4x + 1) + 3| - 2) + 5) - 1)/(3(1(-2|(-4x^2 - 4x + 1) + 3| - 2) + 5) - 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = 3sin(3\u03c0(-1|(-5x^2 + 2x - 4) - 1| + 1) + 2) - 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "253", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = 3sin(1\u03c0(-4((-3(-2|x - 3| + 2))/(-3(-2|x - 3| + 2) + 2)) - 1)) + 2 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) = (-3(-2cos(2\u03c0(3|x - 3| + 3) - 2) - 2) + 1)/(-3(-2cos(2\u03c0(3|x - 3| + 3) - 2) - 2) - 3) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "66", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 2(1e^(2(-2x^2 + 4x + 4)) + 3) + 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -4((-1(-2|(-1x^2 + 2x)| + 2) + 3)/(2(-2|(-1x^2 + 2x)| + 2) + 3)) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -2|(-1(3((2x + 1)/(3x)) + 3)^2 + 3(3((2x + 1)/(3x)) + 3) + 1) + 3| + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 2(-2sin(3\u03c0(3|x - 1| + 3) - 3) - 1)^2 + 5(-2sin(3\u03c0(3|x - 1| + 3) - 3) - 1) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "180", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 2cos(3\u03c0((-1x - 2)/(1x)) - 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 extrema (minima and maxima combined) does the function f(x) = -2|(2cos(2\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": "79", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = (1(4(3|x - 2| - 3)^2 + 5(3|x - 2| - 3) + 5) - 2)/(3(4(3|x - 2| - 3)^2 + 5(3|x - 2| - 3) + 5) - 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = (-3(-2(3sin(3\u03c0(5x^2 - 5x + 2) - 3) + 3) - 2) + 2)/(-3(-2(3sin(3\u03c0(5x^2 - 5x + 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": "411", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 2cos(2\u03c0((1(-1x - 3) - 1)/(3(-1x - 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": "Determine the count of local maxima for the function f(x) = 3(-1e^(-1(-5x^2 + 5)) + 2) + 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -2|(1(-1((-3x - 3)/(-2x - 3)) - 4)^2 + 5(-1((-3x - 3)/(-2x - 3)) - 4) + 3) - 2| + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 2|(-2((2(2x^2 + 4x))/(-1(2x^2 + 4x) + 2)) + 5) - 1| + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 2(-1cos(2\u03c0(1|x| - 1) - 1) - 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": "Determine the total count of local extrema points for the function f(x) = 2(-1e^(2(-2x - 4)) - 2)^2 - 5(-1e^(2(-2x - 4)) - 2) - 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -4(-3|x - 2|)^2 - 2(-3|x - 2|) + 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = 2e^(2(2(-5x - 5)^2 - 5(-5x - 5) + 3)) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 3e^(1((2x)/(2x - 1))) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = -4(3sin(2\u03c0((-3(2|x + 1|) + 2)/(1(2|x + 1|) - 3)) + 1) - 3)^2 + 4(3sin(2\u03c0((-3(2|x + 1|) + 2)/(1(2|x + 1|) - 3)) + 1) - 3) - 1 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|(2cos(1\u03c0x - 3) + 3)| + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -1|((3(-5(-1x^2 - 5x + 5)) - 3)/(1(-5(-1x^2 - 5x + 5)))) - 3| - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 2sin(2\u03c0(5x^2 + 5x - 4) - 2) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "254", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -1(-2e^(2(-3|x + 3| + 1)) + 1) - 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = (-2(2|(-1sin(2\u03c0x - 2) + 2) - 3| + 1) - 1)/(-1(2|(-1sin(2\u03c0x - 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": "21", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 2cos(3\u03c0((2x - 2)/(3x + 1)) - 1) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -2|((-1(-2sin(3\u03c0(-4x^2 - 4x - 2) - 3) + 3) - 1)/(-1(-2sin(3\u03c0(-4x^2 - 4x - 2) - 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": "317", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 2(-1(-1|((2x + 3)/(-1x + 3)) + 3| - 1)^2 - 5(-1|((2x + 3)/(-1x + 3)) + 3| - 1) - 5) + 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -1((1(-2|x - 3| + 2) - 3)/(3(-2|x - 3| + 2) + 3))^2 - 5((1(-2|x - 3| + 2) - 3)/(3(-2|x - 3| + 2) + 3)) - 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": "Determine the total count of local extrema points for the function f(x) = -3|(-2((1(1cos(2\u03c0x - 3)) - 1)/(2(1cos(2\u03c0x - 3)) - 3))^2 - 1((1(1cos(2\u03c0x - 3)) - 1)/(2(1cos(2\u03c0x - 3)) - 3)) - 5)| + 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 1|((1(3(-4x^2 + 1x + 1) - 1) - 2)/(2(3(-4x^2 + 1x + 1) - 1) + 1)) - 1| + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -3e^(-2(-4(-2(-1|x - 3|)^2 + 2(-1|x - 3|) + 4) - 3)) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 5(-3(-3|((3x)/(2x + 2)) - 2|)^2 + 2(-3|((3x)/(2x + 2)) - 2|) + 4) + 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -5((-2(-1|(-1x - 5)| + 2) - 3)/(-1(-1|(-1x - 5)| + 2) - 1))^2 + 3((-2(-1|(-1x - 5)| + 2) - 3)/(-1(-1|(-1x - 5)| + 2) - 1)) - 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -1(2e^(-1((-2x - 3)/(-2x - 1))) - 3) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 1(-3(3cos(3\u03c0(-2|x + 1| + 2) - 1) + 1)^2 + 5(3cos(3\u03c0(-2|x + 1| + 2) - 1) + 1) - 2) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "241", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -3(-2cos(1\u03c0x - 1))^2 - 5(-2cos(1\u03c0x - 1)) + 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = 1|(-2sin(1\u03c0x + 1) - 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": "Determine the count of local minima for the function f(x) = (1(-3sin(3\u03c0x) + 2))/(-1(-3sin(3\u03c0x) + 2) - 1) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 2sin(3\u03c0(1|(-3x + 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": "89", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -1sin(3\u03c0(-3x^2 + 2x - 2) + 3) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "533", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = (-3(2cos(2\u03c0x - 1) + 1) - 3)/(-1(2cos(2\u03c0x - 1) + 1) - 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "126", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 1|(5(-5x + 1)^2 - 1(-5x + 1) - 4)| + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 2(4((3(-3cos(3\u03c0x + 3) - 3) + 2)/(1(-3cos(3\u03c0x + 3) - 3) + 3)) + 4)^2 - 5(4((3(-3cos(3\u03c0x + 3) - 3) + 2)/(1(-3cos(3\u03c0x + 3) - 3) + 3)) + 4) + 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) = -2sin(2\u03c0(4x^2 + 5x + 2) + 1) - 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "260", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -2|(-4x^2 - 5x + 1) + 2| + 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -2cos(3\u03c0((3x - 2)/(3x)) - 3) - 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": "Find the number of local maximum points for f(x) = 1(-2cos(1\u03c0(1|x + 2| - 2)) + 3) - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -3(-3((-1(2|x + 1| + 1) + 2)/(2(2|x + 1| + 1) - 1)) - 1)^2 + 1(-3((-1(2|x + 1| + 1) + 2)/(2(2|x + 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": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = (-2(-5(-2|(-2e^(-2x) + 1)| + 3)^2 - 4(-2|(-2e^(-2x) + 1)| + 3) - 5) - 1)/(1(-5(-2|(-2e^(-2x) + 1)| + 3)^2 - 4(-2|(-2e^(-2x) + 1)| + 3) - 5) - 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) = -3(-1|((-2(3cos(1\u03c0x - 1) + 3))/(2(3cos(1\u03c0x - 1) + 3) + 1)) + 2| + 3) + 5 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -3(3sin(2\u03c0(1|x - 2| - 3) + 1) - 3) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -1e^(1(3|(3((-3x - 2)/(-2x + 3))^2 + 5((-3x - 2)/(-2x + 3)) + 4)|)) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -2(-1|(1x^2 + 4x - 4) - 2| + 3) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 3(-1|(-1sin(3\u03c0x + 3) - 3) + 2|) - 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": "Find the number of local minimum points for f(x) = -3sin(2\u03c0(2|x| - 1) - 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": "Determine the total count of local extrema points for the function f(x) = 1sin(2\u03c0(-1x + 5) - 3) - 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 5(2sin(3\u03c0(-1|(-5x + 1)| - 3) + 2) - 2)^2 + 4(2sin(3\u03c0(-1|(-5x + 1)| - 3) + 2) - 2) + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "201", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -1(1cos(2\u03c0x + 2) - 3) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -3|(-3sin(3\u03c0x - 1) + 2) - 2| + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -1|(-3cos(1\u03c0(3(-1x^2 + 2x + 5) + 4) - 2) + 2)| + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "527", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 3((-3(1|(-3x^2 - 3x + 3) - 2|) + 1)/(-2(1|(-3x^2 - 3x + 3) - 2|) + 3)) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = -3|(3sin(1\u03c0((-2x + 2)/(-3x + 2)) - 2) + 2) + 3| in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -3((-1x + 3)/(2x - 1))^2 + 2((-1x + 3)/(2x - 1)) + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -1((1(-2|(-3x^2 + 4x + 4) + 2| + 2))/(2(-2|(-3x^2 + 4x + 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": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -2cos(1\u03c0(2|(-2(1x - 5)^2 + 2(1x - 5) + 5)| + 1) - 1) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "431", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 2e^(1(-1(-2(1|x + 2| - 1) - 5)^2 + 4(-2(1|x + 2| - 1) - 5))) - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = 1(-2sin(1\u03c0x) + 1) + 5 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 1(-2|(1x + 1)| + 3)^2 - 2(-2|(1x + 1)| + 3) - 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -2e^(-2(-4x - 1)) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -1(-2((1(3|x + 3| - 3) + 2)/(2(3|x + 3| - 3)))^2 + 2((1(3|x + 3| - 3) + 2)/(2(3|x + 3| - 3))) - 1) + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -1sin(3\u03c0(4x + 2) + 1) - 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "240", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = (-3(1e^(-1(3|x + 2| - 3)) - 2))/(-2(1e^(-1(3|x + 2| - 3)) - 2) + 3) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 3(2cos(1\u03c0x + 2) - 3)^2 + 5(2cos(1\u03c0x + 2) - 3) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = 3cos(1\u03c0((-2x)/(1x - 2)) - 3) + 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) = (-1(2|(-3(-2x^2 - 5x) - 4) + 3| - 1) + 2)/(2(2|(-3(-2x^2 - 5x) - 4) + 3| - 1) - 1) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -2(-1sin(2\u03c0x + 2) + 1) + 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -2|(3x^2 - 2x + 3) - 3| - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -5(5(3sin(1\u03c0x + 2) + 3)^2 + 2(3sin(1\u03c0x + 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": "Find the total number of local minima and maxima for f(x) = (3(-4(-1(-2|x - 2| + 3)^2 - 3(-2|x - 2| + 3) + 3) + 4) - 2)/(-2(-4(-1(-2|x - 2| + 3)^2 - 3(-2|x - 2| + 3) + 3) + 4)) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = (-3(-1(-1e^(2(-2|x - 1| + 1)) - 1) - 3) - 1)/(-3(-1(-1e^(2(-2|x - 1| + 1)) - 1) - 3)) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = 3sin(3\u03c0(-2|((-2(3x - 3) - 3)/(-2(3x - 3) + 1)) + 3| + 3)) + 2 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 total count of local extrema points for the function f(x) = -1|(1(-3cos(3\u03c0((2x - 1)/(3x + 3)) - 3)) - 5) - 3| in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 1cos(3\u03c0(-1x + 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) = -1sin(1\u03c0(-2x + 5) - 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) = -2cos(3\u03c0((-3x - 2)/(-3x + 4)) - 2) + 3 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) = -1(-1sin(2\u03c0(3|x - 3| + 1) - 2) + 1) - 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -3sin(2\u03c0(2|x - 2| + 1) + 3) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "81", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -1(-3|x - 1| + 2)^2 - 4(-3|x - 1| + 2) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = (-2(-1|(-3cos(1\u03c0x + 3) + 3) + 1|) - 2)/(1(-1|(-3cos(1\u03c0x + 3) + 3) + 1|) - 2) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 1e^(2(3|(-3x^2 - 3x - 3)| + 3)) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -3cos(3\u03c0(-2|x - 3| - 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": "Determine the count of local minima for the function f(x) = -5(2|(-2cos(3\u03c0x + 3) + 2) + 2|)^2 + 4(2|(-2cos(3\u03c0x + 3) + 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": "Determine the count of local minima for the function f(x) = -2cos(3\u03c0(-2|x + 3| + 1) + 2) - 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "61", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = -2(-2cos(2\u03c0((1x + 1)/(3x - 1)) - 3) - 2)^2 + 3(-2cos(2\u03c0((1x + 1)/(3x - 1)) - 3) - 2) - 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 3sin(2\u03c0(-1|(-2x^2 + 4) + 1|) + 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": "Find the number of local maximum points for f(x) = 3cos(2\u03c0(-4x^2 - 3x - 2) - 1) + 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": "Find the number of local minimum points for f(x) = 2|(3sin(3\u03c0((-2x - 3)/(1x - 3)) + 2) - 1) - 2| + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "48", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = 3cos(2\u03c0(-4x + 1) - 2) - 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": "Determine the count of local maxima for the function f(x) = -3(-4(-1sin(1\u03c0(-3|x - 3| + 1) - 2) - 3)^2 - 2(-1sin(1\u03c0(-3|x - 3| + 1) - 2) - 3) - 2) - 5 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -2|(-2cos(2\u03c0x - 1) + 2) + 3| - 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 5(-1cos(2\u03c0((2x + 2)/(-1x + 3)) - 1) + 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": "Determine the count of local maxima for the function f(x) = 3|(-4((-1x - 1)/(1x))^2 - 5((-1x - 1)/(1x)) - 3) + 2| - 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -1sin(1\u03c0((1x + 2)/(1x + 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 minimum points for f(x) = -3sin(2\u03c0(-3((-1x + 3)/(-2x - 1))^2 - 2((-1x + 3)/(-2x - 1)) - 4) + 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "44", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 2cos(2\u03c0((-2(2x - 5) + 2)/(1(2x - 5))) - 3) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = 1(2|(2sin(1\u03c0(3x + 4) + 3) - 1) + 2| - 2)^2 - 2(2|(2sin(1\u03c0(3x + 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": "149", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = (-1(-2(-1(-2|x - 1| + 1) - 5)^2 + 1(-1(-2|x - 1| + 1) - 5) + 4) - 3)/(-1(-2(-1(-2|x - 1| + 1) - 5)^2 + 1(-1(-2|x - 1| + 1) - 5) + 4) - 2) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = 2(2((3(-3|x - 3| + 1) + 3)/(-1(-3|x - 3| + 1) - 2)) - 1)^2 - 4(2((3(-3|x - 3| + 1) + 3)/(-1(-3|x - 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": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -5(-3sin(1\u03c0((2(2x^2 + 1x - 4) + 2)/(1(2x^2 + 1x - 4) + 3)) - 2) - 3) + 5 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 maxima does the function f(x) = 3(1sin(3\u03c0((2x + 2)/(-3x - 3)) + 1) - 2) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -1|(4(2cos(2\u03c0x - 1))^2 - 5(2cos(2\u03c0x - 1)) + 2) + 3| have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -3(2sin(2\u03c0x) - 2) + 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 2sin(3\u03c0(-3|x - 3| + 3) + 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 extrema (minima and maxima combined) does the function f(x) = 4(-3((1(-2|x + 3| - 2) - 1)/(-1(-2|x + 3| - 2) + 3)) - 2)^2 - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = (-2(3(4(3|x - 1| - 1)^2 - 5(3|x - 1| - 1) + 1)))/(-2(3(4(3|x - 1| - 1)^2 - 5(3|x - 1| - 1) + 1)) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 1|(4(-1(-1e^(-1x) + 3) - 4)^2 - 1(-1(-1e^(-1x) + 3) - 4) - 2) - 2| - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = (-1(2sin(3\u03c0x + 1) - 3) + 3)/(1(2sin(3\u03c0x + 1) - 3) - 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = (3(-4(-1|(-3x^2 + 5x + 2) + 1| + 3) - 5))/(-1(-4(-1|(-3x^2 + 5x + 2) + 1| + 3) - 5) - 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 2sin(3\u03c0(-1|(1x - 4) - 1| - 2) - 3) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -2(3|((1(2x - 4) - 2)/(-1(2x - 4))) - 3| + 2)^2 - 3(3|((1(2x - 4) - 2)/(-1(2x - 4))) - 3| + 2) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = 3(1cos(1\u03c0(2|(4x - 4) - 1| - 2) - 1) - 2)^2 + 1(1cos(1\u03c0(2|(4x - 4) - 1| - 2) - 1) - 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": "How many local maxima does the function f(x) = -3((1x + 3)/(-3x + 4))^2 - 4((1x + 3)/(-3x + 4)) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = (3(-5(-2|x + 1| + 1)^2 - 1(-2|x + 1| + 1) + 3) - 3)/(2(-5(-2|x + 1| + 1)^2 - 1(-2|x + 1| + 1) + 3) + 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = -2cos(3\u03c0(-4x^2 - 2x) + 3) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "243", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 1|(4(2cos(1\u03c0((2x + 3)/(-2x + 3)) + 3))) + 2| where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -3|(3(-3((-2x + 2)/(3x + 2))^2 + 2((-2x + 2)/(3x + 2)) + 2)) + 2| + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -1|((1(4(1x^2 + 3x - 1) + 5) + 3)/(1(4(1x^2 + 3x - 1) + 5) - 3)) + 1| - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -2sin(2\u03c0(3x^2 - 4x - 5) + 2) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "228", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 1(1sin(1\u03c0x - 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 maximum points for f(x) = 3(1cos(2\u03c0x + 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": "Find the number of local minimum points for f(x) = 1(2((2(-3|x + 3| + 2) - 3)/(2(-3|x + 3| + 2) - 1)) - 3)^2 + 5(2((2(-3|x + 3| + 2) - 3)/(2(-3|x + 3| + 2) - 1)) - 3) + 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 number of local minimum points for f(x) = -1|(5x^2 - 5x - 4)| + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 3|((1(-1cos(2\u03c0x + 2) - 3) + 2)/(2(-1cos(2\u03c0x + 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": "40", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 2cos(1\u03c0(-1((-1x + 3)/(3x + 1))^2 - 4((-1x + 3)/(3x + 1)) - 2)) + 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -2sin(3\u03c0(-1x^2 - 2x - 4)) - 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "285", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 1cos(1\u03c0(3|(3(3x - 2)^2 + 5(3x - 2) - 2) + 2|) + 1) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "465", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -3cos(2\u03c0(3|((-1x - 3)/(3x - 2)) + 2| + 1) + 2) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 3(-3(2cos(2\u03c0(-1|x + 1| + 1) + 1) + 1) + 4)^2 + 3(-3(2cos(2\u03c0(-1|x + 1| + 1) + 1) + 1) + 4) - 2 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) = -1(3((-1(-1e^(1x) + 2) + 3)/(-3(-1e^(1x) + 2))) - 2)^2 - 1(3((-1(-1e^(1x) + 2) + 3)/(-3(-1e^(1x) + 2))) - 2) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 2|((-3(1sin(2\u03c0(-4x + 4) - 3) - 1) - 2)/(3(1sin(2\u03c0(-4x + 4) - 3) - 1) - 1)) - 1| - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "319", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -3(4(-3cos(2\u03c0(1|x - 3| + 3) - 1) - 3) + 4)^2 - 1(4(-3cos(2\u03c0(1|x - 3| + 3) - 1) - 3) + 4) 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 total number of local minima and maxima for f(x) = 5(-1(2cos(2\u03c0((2x)/(-3x - 3))) + 1))^2 + 4(-1(2cos(2\u03c0((2x)/(-3x - 3))) + 1)) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = -3|(-1(4x - 3)^2 + 5(4x - 3) - 2) + 3| - 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -5((1(2|(2cos(3\u03c0x - 3) + 2) + 1|) - 2)/(-1(2|(2cos(3\u03c0x - 3) + 2) + 1|) - 3)) - 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 3(3cos(1\u03c0(3|(-1x - 4) - 1| - 3) + 2) + 3)^2 + 1(3cos(1\u03c0(3|(-1x - 4) - 1| - 3) + 2) + 3) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 2cos(1\u03c0(-1|x - 2| - 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 maxima does the function f(x) = -3((-1x - 2)/(3x - 2))^2 + 3((-1x - 2)/(3x - 2)) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = (-1(1(1sin(2\u03c0(-3|x| + 3) + 2) - 3) + 4) - 2)/(-2(1(1sin(2\u03c0(-3|x| + 3) + 2) - 3) + 4) + 3) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "61", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 5((1(3sin(1\u03c0x - 2) + 3) - 1)/(-1(3sin(1\u03c0x - 2) + 3) - 3))^2 + 4((1(3sin(1\u03c0x - 2) + 3) - 1)/(-1(3sin(1\u03c0x - 2) + 3) - 3)) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 1(-2|x + 2| + 2)^2 + 5(-2|x + 2| + 2) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -3sin(1\u03c0(-3|x| + 2) + 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) = -1sin(1\u03c0(1|(-5x^2 - 5x - 5) + 1| + 1)) - 2 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": "How many local minima does the function f(x) = -3sin(1\u03c0(5(-3|x - 1| + 3)^2 + 2(-3|x - 1| + 3) - 2) - 2) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "241", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 3((-1(-4(2cos(2\u03c0x - 1) + 3) - 2) + 1)/(-1(-4(2cos(2\u03c0x - 1) + 3) - 2) - 3))^2 + 2((-1(-4(2cos(2\u03c0x - 1) + 3) - 2) + 1)/(-1(-4(2cos(2\u03c0x - 1) + 3) - 2) - 3)) - 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = (2(-1(2|(1x^2 + 2x + 3) - 3| - 1)) - 3)/(-1(-1(2|(1x^2 + 2x + 3) - 3| - 1))) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 3sin(3\u03c0((2x + 2)/(-1x + 3)) - 2) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "93", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = (2(-1cos(3\u03c0(-1|x - 3| - 1) + 2) - 1) + 2)/(-3(-1cos(3\u03c0(-1|x - 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": "61", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 2|(-3sin(3\u03c0x - 1) - 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": "Find the total number of local minima and maxima for f(x) = -2|(2cos(2\u03c0(1x^2 - 1x - 2)) + 1) + 2| - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "402", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -1(1sin(2\u03c0(2x) - 3))^2 + 1(1sin(2\u03c0(2x) - 3)) - 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "160", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 3((-1x + 3)/(-2x + 1))^2 + 2((-1x + 3)/(-2x + 1)) + 5 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -1e^(2(2(5x - 5)^2 + 5(5x - 5) - 2)) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 4(1cos(3\u03c0x + 3) - 3)^2 - 2(1cos(3\u03c0x + 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": "How many local extrema (minima and maxima combined) does the function f(x) = 2|(-3cos(2\u03c0x - 3) - 2)| - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "79", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 3|(3sin(3\u03c0x + 3) - 1) + 1| + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 1|(-5(-1cos(3\u03c0x - 1) + 3)^2 - 2) + 1| have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -1(3|x - 1| - 3)^2 + 5(3|x - 1| - 3) + 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -4(1|(4((-1x - 1)/(2x - 1)) + 5) + 2| - 2)^2 - 1(1|(4((-1x - 1)/(2x - 1)) + 5) + 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) = 2e^(-2(-3|((-1x + 2)/(2x - 1))|)) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = (-2(1sin(1\u03c0(3|x - 3|) - 1) - 2) - 3)/(-1(1sin(1\u03c0(3|x - 3|) - 1) - 2)) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 1cos(2\u03c0((2x - 3)/(3x - 2)) - 1) + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "24", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -1cos(1\u03c0(5((-2(1|x + 3| - 2) - 1)/(3(1|x + 3| - 2) + 1))^2 - 2((-2(1|x + 3| - 2) - 1)/(3(1|x + 3| - 2) + 1)) + 5) - 3) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -4(1|(-2e^(-2(-5x + 3)) - 3) - 2| + 3)^2 + 1(1|(-2e^(-2(-5x + 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": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -1cos(2\u03c0((3x - 1)/(-1x - 1)) - 1) - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -1|(-2cos(2\u03c0x - 1) - 3) + 1| + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = (-1(4(1cos(1\u03c0x - 3) - 1) - 1) - 2)/(2(4(1cos(1\u03c0x - 3) - 1) - 1) + 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -1sin(2\u03c0(3|(1x^2 + 5x + 4) + 3| + 1)) - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "254", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 5((-1(1|(3x^2 + 1x + 1) - 2| + 3) + 2)/(-1(1|(3x^2 + 1x + 1) - 2| + 3) - 1)) - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = (-3(1|(-1cos(1\u03c0(-5x + 2) + 3)) - 2| + 1))/(-3(1|(-1cos(1\u03c0(-5x + 2) + 3)) - 2| + 1) + 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "50", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = 3sin(2\u03c0(-1(-1x^2 - 3x - 4) - 5) - 3) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "203", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -3e^(1(5x^2 + 1x - 4)) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 1(-2|(-1e^(2x) + 2) + 3| + 3)^2 + 1(-2|(-1e^(2x) + 2) + 3| + 3) - 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = -4(1(-3|(2sin(2\u03c0x) + 1) + 2| - 2) + 3)^2 + 2(1(-3|(2sin(2\u03c0x) + 1) + 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": "How many local extrema (minima and maxima combined) does the function f(x) = 1cos(2\u03c0(-4x^2 + 3x - 5)) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "523", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = (-3(-3(-1sin(1\u03c0x - 1) + 3) + 3) - 2)/(-1(-3(-1sin(1\u03c0x - 1) + 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": "How many local minima does the function f(x) = (3(-2|(-2x^2 + 3x + 1) - 3| - 3))/(1(-2|(-2x^2 + 3x + 1) - 3| - 3)) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "58", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -4(-5((3(-3|x - 3| + 3) + 3)/(1(-3|x - 3| + 3))) + 5)^2 - 5(-5((3(-3|x - 3| + 3) + 3)/(1(-3|x - 3| + 3))) + 5) - 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) = 3((-1(2sin(1\u03c0(3x^2 - 3x - 1) + 1) - 3) + 3)/(3(2sin(1\u03c0(3x^2 - 3x - 1) + 1) - 3) + 2)) - 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "563", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -1cos(2\u03c0(-1(-5x^2 - 2x - 2) + 4) - 2) + 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "253", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = (-3(-2sin(1\u03c0(-4x + 1) + 1) + 3) + 3)/(2(-2sin(1\u03c0(-4x + 1) + 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": "How many local minima does the function f(x) = 3sin(2\u03c0((-3x)/(-3x - 2)) - 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = (1(-3|(3sin(2\u03c0(5x - 2) + 3)) - 3| - 3) + 2)/(-1(-3|(3sin(2\u03c0(5x - 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": "200", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = (2(-1(-3|x| + 3)^2 - 1(-3|x| + 3) + 2) - 2)/(1(-1(-3|x| + 3)^2 - 1(-3|x| + 3) + 2) + 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 3cos(2\u03c0(3(-5x - 3)^2 + 3(-5x - 3) - 3) + 3) - 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "415", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -1((-3(-2cos(3\u03c0(4x + 2)) - 1) + 2)/(-1(-2cos(3\u03c0(4x + 2)) - 1) + 2))^2 - 5((-3(-2cos(3\u03c0(4x + 2)) - 1) + 2)/(-1(-2cos(3\u03c0(4x + 2)) - 1) + 2)) + 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "239", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = (-2(1|(-2sin(3\u03c0(-1x + 5) - 2) + 2)| - 3) + 2)/(-1(1|(-2sin(3\u03c0(-1x + 5) - 2) + 2)| - 3)) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = (-3(1|(4(1x^2 - 4x - 5) + 5) - 1| - 2) + 3)/(-2(1|(4(1x^2 - 4x - 5) + 5) - 1| - 2) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 1|(-3cos(3\u03c0x) + 1) - 2| + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = 2sin(1\u03c0(3((3x + 3)/(-1x - 3))^2 + 1((3x + 3)/(-1x - 3))) - 1) - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "76", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 1e^(2(-4(-1|(2x^2 + 5x + 4) + 2| + 1) - 5)) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = (2(-2cos(3\u03c0x + 3) + 2) + 3)/(2(-2cos(3\u03c0x + 3) + 2) + 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -2cos(2\u03c0((1(1|(-1x + 3) - 2| - 1))/(-2(1|(-1x + 3) - 2| - 1) + 3)) - 2) - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "53", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 4(-2cos(1\u03c0x - 2) + 3) - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = 2sin(2\u03c0(2x^2 + 3x - 4) - 3) + 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "287", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = (-1(1(-2|(2sin(3\u03c0x + 3) + 3) + 1| - 3) + 5))/(-1(1(-2|(2sin(3\u03c0x + 3) + 3) + 1| - 3) + 5) + 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) = (-1(-2sin(1\u03c0x - 3) - 2) + 2)/(-2(-2sin(1\u03c0x - 3) - 2) + 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 3(1cos(2\u03c0(4x^2 + 1x + 4) + 1) + 2) - 4 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "524", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 2|(3x^2 + 4x - 4) + 1| - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 1|(2sin(1\u03c0((3x - 3)/(-1x + 2)) - 2) + 1) + 3| have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -4(-3|x + 3| + 2)^2 - 4(-3|x + 3| + 2) - 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = (-2(-2(-2cos(1\u03c0(-1|x + 2| + 1) - 2)) - 5))/(-2(-2(-2cos(1\u03c0(-1|x + 2| + 1) - 2)) - 5) + 3) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = (3(5(1(-3|x + 3|) + 2)^2 - 1(1(-3|x + 3|) + 2) - 4) + 2)/(3(5(1(-3|x + 3|) + 2)^2 - 1(1(-3|x + 3|) + 2) - 4)) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -1sin(1\u03c0(-2|(-1x + 5) - 1|) + 1) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = 3|(-1sin(2\u03c0x) + 2) + 2| in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 3|(3e^(-2(5x)) + 1) + 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 minima does the function f(x) = 1(-1|(-3sin(3\u03c0((1x - 1)/(1x - 3)) + 2) - 1) - 1| - 2) - 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "65", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = 1(-2cos(2\u03c0x + 1) + 1)^2 + 4(-2cos(2\u03c0x + 1) + 1) + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -2((-2(-3|(-5x + 2) - 1| + 1) - 1)/(-3(-3|(-5x + 2) - 1| + 1) + 2))^2 + 2((-2(-3|(-5x + 2) - 1| + 1) - 1)/(-3(-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": "5", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -1cos(2\u03c0(3|(-5((-1x - 2)/(-2x - 3))^2 - 2((-1x - 2)/(-2x - 3))) - 1| + 1) + 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": "Find the number of local minimum points for f(x) = 1e^(1(3|(-5x + 4)| - 1)) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 2(1(2|x - 2| - 2) + 1)^2 - 3(1(2|x - 2| - 2) + 1) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -1sin(2\u03c0(2((3(-3x^2 - 5x - 2) - 3)/(-2(-3x^2 - 5x - 2) + 3)) + 2) - 2) - 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = 1cos(3\u03c0(2|(-1((3x - 1)/(-3x + 2))^2 - 5((3x - 1)/(-3x + 2)) - 1) - 2| + 1) - 1) + 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -3cos(2\u03c0(-2(4x^2 + 4x + 1) - 4) - 2) + 2 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 number of local minimum points for f(x) = 5((-2(1|(-3x + 4) - 1| - 1) - 1)/(2(1|(-3x + 4) - 1| - 1) - 1))^2 - 1((-2(1|(-3x + 4) - 1| - 1) - 1)/(2(1|(-3x + 4) - 1| - 1) - 1)) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = 2cos(3\u03c0(-1|((2(3x - 2) + 1)/(-1(3x - 2) - 3)) + 2| + 1)) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = (-2(-1sin(1\u03c0x - 1) - 2) + 3)/(-2(-1sin(1\u03c0x - 1) - 2)) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 4(-2sin(1\u03c0((-1x + 1)/(-3x - 2)) + 1) - 2) - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 3(2cos(1\u03c0(-1|x + 2| + 1) + 3) + 3) + 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = (-2(3|(-2sin(1\u03c0(-1x^2 + 2x + 3) + 1) + 3) + 1| + 2) - 1)/(-1(3|(-2sin(1\u03c0(-1x^2 + 2x + 3) + 1) + 3) + 1| + 2) + 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "203", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 3sin(3\u03c0(-3(4x - 5)^2 - 4) - 3) - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "196", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 4(1|((2(-5x - 3) - 1)/(2(-5x - 3) + 3)) - 3|)^2 - 4(1|((2(-5x - 3) - 1)/(2(-5x - 3) + 3)) - 3|) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -3|(3(1x^2 - 3x - 2) - 3) - 2| where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -1|(4((2x + 1)/(3x - 2))^2 - 3((2x + 1)/(3x - 2)) + 1) - 1| - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = (-2(3cos(1\u03c0x)))/(-3(3cos(1\u03c0x))) 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": "Find the number of local minimum points for f(x) = 2cos(1\u03c0(2|x + 3| - 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) = -3|(-5(-4x^2 - 3x) - 4) - 3| in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -4(-3cos(3\u03c0x - 2) + 3) + 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": "Determine the count of local minima for the function f(x) = -3sin(1\u03c0((2x + 3)/(1x + 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": "Determine the count of local minima for the function f(x) = 4(2sin(2\u03c0((-3x - 3)/(-1x)) - 2) - 3)^2 - 2(2sin(2\u03c0((-3x - 3)/(-1x)) - 2) - 3) + 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 count of local minima for the function f(x) = 2|(2cos(1\u03c0(-1((-2x - 3)/(1x)) - 2) + 1) + 1) + 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": "How many local minima does the function f(x) = -3|((-3(2cos(1\u03c0x + 1) - 2) + 3)/(-1(2cos(1\u03c0x + 1) - 2) + 3)) + 1| - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 2|(3cos(3\u03c0(1x - 3) + 1) + 3) + 2| + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 4(3cos(2\u03c0(3|(-1x) + 1| + 2) - 1) + 1)^2 - 1(3cos(2\u03c0(3|(-1x) + 1| + 2) - 1) + 1) - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "241", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -4(-2cos(3\u03c0(-1x + 4) - 3) + 3)^2 + 4(-2cos(3\u03c0(-1x + 4) - 3) + 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) = 3|(2(-1((-1x)/(1x - 3))^2 - 1((-1x)/(1x - 3)) + 1) + 2) + 2| + 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -3cos(3\u03c0(-5((-3(2x + 5))/(-2(2x + 5) - 1))^2 - 3((-3(2x + 5))/(-2(2x + 5) - 1)) - 2) - 1) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "45", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = 3sin(3\u03c0(-2((-2(-2|x + 3| - 1) + 2)/(-2(-2|x + 3| - 1) - 1)) + 5)) - 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = (-1(5(3(-3|x + 1| + 1) + 2)^2 - 4(3(-3|x + 1| + 1) + 2) - 2))/(2(5(3(-3|x + 1| + 1) + 2)^2 - 4(3(-3|x + 1| + 1) + 2) - 2) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 4(-2sin(3\u03c0(1|x - 3|) + 1) - 2)^2 - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -5(1(3|((-3x - 2)/(-3x)) - 1| + 1)^2 - 3(3|((-3x - 2)/(-3x)) - 1| + 1) + 3) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -2(1sin(2\u03c0(5((-1x + 2)/(1x))^2 + 3((-1x + 2)/(1x)) - 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": "How many local minima does the function f(x) = -5(-5(3e^(2(-1|x + 2|)))^2 + 3(3e^(2(-1|x + 2|))) + 1) - 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 2|(-2sin(1\u03c0((-1x)/(2x - 1)) + 3)) - 2| + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 3(-5(-3cos(3\u03c0x + 3) + 2) + 5)^2 + 3(-5(-3cos(3\u03c0x + 3) + 2) + 5) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = (2(-3cos(2\u03c0x - 2)) - 3)/(3(-3cos(2\u03c0x - 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) = (2(-2cos(3\u03c0(1|(3x + 3)| - 2) + 3) + 1) - 1)/(-1(-2cos(3\u03c0(1|(3x + 3)| - 2) + 3) + 1) - 3) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "89", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = (-1(3sin(3\u03c0(1|x + 1| + 1) + 3) - 3) - 3)/(3(3sin(3\u03c0(1|x + 1| + 1) + 3) - 3) + 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 2((-1(-2|(3cos(2\u03c0x - 1)) + 3| - 3) - 2)/(-3(-2|(3cos(2\u03c0x - 1)) + 3| - 3) - 1)) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = (-1(1cos(1\u03c0(-1(-3|x - 2| - 3)^2 + 2(-3|x - 2| - 3) + 3) - 1) - 2) - 3)/(1(1cos(1\u03c0(-1(-3|x - 2| - 3)^2 + 2(-3|x - 2| - 3) + 3) - 1) - 2)) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "372", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 4((1(-2|(-2sin(2\u03c0x - 1) - 3)|) - 3)/(2(-2|(-2sin(2\u03c0x - 1) - 3)|) + 1))^2 + 3((1(-2|(-2sin(2\u03c0x - 1) - 3)|) - 3)/(2(-2|(-2sin(2\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 total number of local minima and maxima for f(x) = -5(-2(3cos(1\u03c0((3x + 2)/(3x)) + 3))^2 + 2(3cos(1\u03c0((3x + 2)/(3x)) + 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 total count of local extrema points for the function f(x) = -1sin(1\u03c0(-3((1x - 3)/(-2x + 1))^2 + 5((1x - 3)/(-2x + 1)) - 2) + 2) - 3 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) = -1e^(-1(-3x^2 + 2x + 5)) + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 3|(2((2(-1x + 1) + 3)/(-1(-1x + 1) - 2))^2 + 4((2(-1x + 1) + 3)/(-1(-1x + 1) - 2)) - 5) - 1| - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -2sin(3\u03c0(-4(-2|x + 2|) + 2) - 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "240", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = (1(3sin(3\u03c0x - 2) + 3) - 1)/(-1(3sin(3\u03c0x - 2) + 3) + 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "66", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 2|(3(3cos(2\u03c0(3x^2 + 2) - 3) - 2) + 1) + 2| + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "492", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -2cos(2\u03c0(1x^2 + 1x + 4)) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "402", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -4(1|(-1sin(3\u03c0(1x + 5) - 2) - 3) + 1| + 1)^2 + 5(1|(-1sin(3\u03c0(1x + 5) - 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": "60", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -3cos(3\u03c0(-2|(-2x + 5) + 3| + 2) - 2) + 3 in the interval [-10, 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) = -1(1|x - 2| - 3)^2 - 1(1|x - 2| - 3) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = (-1(2cos(3\u03c0x + 1) - 1) - 1)/(-3(2cos(3\u03c0x + 1) - 1) + 4) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -5((2(3x - 3) + 2)/(1(3x - 3) + 2))^2 - 4((2(3x - 3) + 2)/(1(3x - 3) + 2)) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = (3(3cos(3\u03c0x) + 2) + 2)/(2(3cos(3\u03c0x) + 2) - 3) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "59", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -1(-2|x + 1| + 3)^2 - 3(-2|x + 1| + 3) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -3(1(1sin(3\u03c0x - 2) + 2)^2 - 5(1sin(3\u03c0x - 2) + 2) + 2) + 4 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = (-2(-3|(1(4x^2 + 3x - 3) + 2) - 3| + 1) + 1)/(2(-3|(1(4x^2 + 3x - 3) + 2) - 3| + 1) + 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -3cos(1\u03c0(3|x - 2| + 2) - 2) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 4((3(1e^(2x) - 3))/(1(1e^(2x) - 3))) - 4 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 maxima does the function f(x) = 3sin(1\u03c0(-2|x - 1| - 2) + 2) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = (-1(-1|(-1x^2 + 5x + 5) + 2| + 3) + 1)/(2(-1|(-1x^2 + 5x + 5) + 2| + 3)) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -2|(-2(2cos(1\u03c0((-2x - 3)/(-3x - 1)) - 1) + 1) + 4) + 2| + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -2e^(-1(-5x^2 + 4x - 4)) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 1sin(3\u03c0(3|(-1(-2x - 3)^2 - 3(-2x - 3) - 2) + 2| - 2) - 2) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "249", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 1e^(-2(-1x^2 + 4x - 2)) + 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 3sin(3\u03c0(-1x^2 - 1x - 2) + 2) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "276", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = 3|(-5((-2(-2cos(2\u03c0x + 2) + 3) + 1)/(-2(-2cos(2\u03c0x + 2) + 3) - 3)) - 5) + 3| - 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = (1(-2sin(3\u03c0(-3x^2 - 2x - 1) - 3) + 2))/(-3(-2sin(3\u03c0(-3x^2 - 2x - 1) - 3) + 2) - 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "533", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -3sin(3\u03c0((3x + 3)/(-3x + 2)) - 2) - 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": "Find the total number of local minima and maxima for f(x) = -3(2(1sin(2\u03c0((-1x)/(-2x + 3)) - 3) - 1)^2 - 4(1sin(2\u03c0((-1x)/(-2x + 3)) - 3) - 1) - 2) - 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": "Determine the count of local minima for the function f(x) = -4(3(1sin(1\u03c0((-1x + 1)/(-2x)) + 3) + 2)^2 - 3(1sin(1\u03c0((-1x + 1)/(-2x)) + 3) + 2) + 5) + 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) = -5(1|(-4x + 5)| - 3)^2 + 3(1|(-4x + 5)| - 3) - 4 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = (-3(-3|(5(-5x - 5)^2 - 5(-5x - 5) - 2) - 1| - 3) + 3)/(1(-3|(5(-5x - 5)^2 - 5(-5x - 5) - 2) - 1| - 3) - 2) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -3(3cos(3\u03c0x + 3) + 3) - 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -3(-1(3|x + 1| + 1) + 3)^2 - 2(-1(3|x + 1| + 1) + 3) + 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -3cos(1\u03c0(-5x - 1)) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "50", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -4((-1(2sin(3\u03c0(-3|x - 3| + 1) + 3) - 3) + 3)/(-3(2sin(3\u03c0(-3|x - 3| + 1) + 3) - 3) + 1))^2 + 4((-1(2sin(3\u03c0(-3|x - 3| + 1) + 3) - 3) + 3)/(-3(2sin(3\u03c0(-3|x - 3| + 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": "92", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = (1(3(-2|(3x + 1) + 2|)^2 + 5(-2|(3x + 1) + 2|) - 4) + 2)/(2(3(-2|(3x + 1) + 2|)^2 + 5(-2|(3x + 1) + 2|) - 4) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -2cos(3\u03c0(2|(3x - 5) + 2| + 1) - 1) - 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "361", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -3cos(1\u03c0(-1x - 5) - 1) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = (-3(-2(2cos(3\u03c0x + 2) + 1) - 4) - 1)/(-2(-2(2cos(3\u03c0x + 2) + 1) - 4) - 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -3cos(3\u03c0(3x - 5) + 1) + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "180", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -2(-1cos(3\u03c0(3|((-1x - 2)/(3x + 2)) - 1| + 3) - 2) - 2) - 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = (-2(2sin(1\u03c0x + 2) + 2) - 3)/(-2(2sin(1\u03c0x + 2) + 2) + 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -2(1cos(3\u03c0(-4x^2 + 1x - 4) + 3) + 1) - 3 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 minima for the function f(x) = -1|((-2(-2x^2 + 2x + 4) - 2)/(-2(-2x^2 + 2x + 4) + 3)) - 2| + 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 3cos(3\u03c0(-2x^2 - 5x + 5)) - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "234", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 3|(-3e^(-1(2((-3x - 2)/(3x - 2))^2 + 2((-3x - 2)/(3x - 2)))) - 1) + 2| + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -2(-1e^(-1(1x^2 + 2x + 4))) - 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -1|(-1(-1((-1x - 1)/(-1x - 3))^2 - 3((-1x - 1)/(-1x - 3)) + 2) - 2) + 3| - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = 1(-3cos(2\u03c0x + 1) - 3) + 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = (3(2|(1cos(1\u03c0(4x - 1) - 1) - 2) - 1|) + 2)/(-2(2|(1cos(1\u03c0(4x - 1) - 1) - 2) - 1|) + 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -1sin(1\u03c0(-5x + 4) - 2) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "50", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -3(1|(5((-1x - 1)/(3x + 1))^2 - 1((-1x - 1)/(3x + 1)) - 4)| + 1) - 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 3(-1e^(-2(-1(-3|x + 2| - 2) + 3)) - 2)^2 - 1(-1e^(-2(-1(-3|x + 2| - 2) + 3)) - 2) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -3(2((1(-1|x + 2| + 1) - 2)/(1(-1|x + 2| + 1))) - 5)^2 - 3(2((1(-1|x + 2| + 1) - 2)/(1(-1|x + 2| + 1))) - 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": "Determine the count of local maxima for the function f(x) = 1|(-2sin(1\u03c0x + 2) - 3) - 3| + 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -3sin(1\u03c0(-2|x + 1| + 2) - 1) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 3(2(-1sin(1\u03c0((-1x + 1)/(3x + 1)) + 3) - 3) + 4)^2 + 1(2(-1sin(1\u03c0((-1x + 1)/(3x + 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": "17", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = 1(-1|(-3((3x - 1)/(-3x - 3))^2 + 1((3x - 1)/(-3x - 3)) + 2) + 3| - 3) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 1|(-1sin(1\u03c0x + 2) - 1) + 1| - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "23", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 3cos(2\u03c0(4(-1|(3x^2 - 4x - 5) - 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": "245", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = 2(5((2(-3|x| + 1) + 2)/(-2(-3|x| + 1))) - 3)^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 number of local maximum points for f(x) = (1(2cos(2\u03c0x + 2) - 1))/(-3(2cos(2\u03c0x + 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 maxima does the function f(x) = 2sin(3\u03c0(-5(-1|x - 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": "151", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 4(2|(5x^2 - 4x + 1) - 3| + 2) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -3cos(1\u03c0(3|((-3x)/(-3x + 2)) - 3| - 3) - 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = 2|(2sin(2\u03c0x - 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": "Determine the count of local maxima for the function f(x) = 2e^(2(-3x^2 + 2x - 4)) - 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = (-1(1e^(2(-1(2|x + 3| + 2) - 3)) + 2) - 1)/(1(1e^(2(-1(2|x + 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": "6", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 3(3sin(1\u03c0x + 1) - 1) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 1(3|((-1x + 3)/(-1x)) + 2| - 1)^2 - 3(3|((-1x + 3)/(-1x)) + 2| - 1) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 2(-3|((3(3x^2 - 2x - 5) + 1)/(-3(3x^2 - 2x - 5) - 3)) - 2|) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 1((1(2|x| - 2) + 2)/(-2(2|x| - 2) - 3))^2 - 4((1(2|x| - 2) + 2)/(-2(2|x| - 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) = -2cos(1\u03c0(4(3x^2 - 1x - 5) - 4) - 2) - 2 in the interval [-10, 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) = -4(-2cos(2\u03c0x) - 2) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 2(-2sin(3\u03c0(3(-3|x + 2| - 3)^2 + 1(-3|x + 2| - 3) + 4) + 1) - 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "210", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = (-3(-1(-3|(-2e^(1x) - 2) + 1|)^2 - 4(-3|(-2e^(1x) - 2) + 1|) + 1))/(-2(-1(-3|(-2e^(1x) - 2) + 1|)^2 - 4(-3|(-2e^(1x) - 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": "Find the number of local maximum points for f(x) = (-2(-2(1sin(2\u03c0(1x + 5)) - 3)^2 - 2(1sin(2\u03c0(1x + 5)) - 3) - 5) - 1)/(-1(-2(1sin(2\u03c0(1x + 5)) - 3)^2 - 2(1sin(2\u03c0(1x + 5)) - 3) - 5) + 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = (3(5(-1(-2|x + 3| + 2)^2 - 2(-2|x + 3| + 2) - 2) + 5) - 3)/(2(5(-1(-2|x + 3| + 2)^2 - 2(-2|x + 3| + 2) - 2) + 5) + 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 2|(-3sin(2\u03c0((-1x + 1)/(1x - 3)) - 2) + 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": "Find the total number of local minima and maxima for f(x) = 5(-1|((2x - 3)/(3x + 2)) - 1| + 2)^2 - 2(-1|((2x - 3)/(3x + 2)) - 1| + 2) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -1|(-1sin(2\u03c0x - 3) + 1)| + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = (-2(-1cos(2\u03c0(-3x^2 + 1x)) - 2) + 2)/(3(-1cos(2\u03c0(-3x^2 + 1x)) - 2) - 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "288", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -1|(-2e^(-1(-5x^2 - 1x - 1)) - 3) + 3| + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 3|((3(-2(-2x + 5)^2 + 4(-2x + 5) - 3) - 2)/(-2(-2(-2x + 5)^2 + 4(-2x + 5) - 3) - 3))| - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 1((3(-5x + 3))/(3(-5x + 3) - 2))^2 - 5((3(-5x + 3))/(3(-5x + 3) - 2)) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 2cos(2\u03c0((2x + 2)/(2x - 1))) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -1sin(1\u03c0(2x + 3) - 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": "Find the number of local maximum points for f(x) = (1(3(2sin(1\u03c0(-2|x - 1| + 1) - 3))^2 + 5(2sin(1\u03c0(-2|x - 1| + 1) - 3)) + 5) - 3)/(3(3(2sin(1\u03c0(-2|x - 1| + 1) - 3))^2 + 5(2sin(1\u03c0(-2|x - 1| + 1) - 3)) + 5)) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -5(-3|x + 3| + 1)^2 - 1(-3|x + 3| + 1) + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 1cos(3\u03c0((1x - 1)/(1x - 2)) + 3) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -4(-1(-2sin(3\u03c0(-1|x + 1| + 2) + 2) - 1) - 3)^2 + 3(-1(-2sin(3\u03c0(-1|x + 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": "29", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -2cos(2\u03c0(-3(-1(1|x - 2| + 1) + 1)^2 + 2(-1(1|x - 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": "257", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -4((2(-1(3|x| - 1)^2 + 4(3|x| - 1) - 3) - 2)/(1(-1(3|x| - 1)^2 + 4(3|x| - 1) - 3) + 3)) - 5 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -1|(1(1cos(2\u03c0(-1x^2 + 5x + 2) + 1) + 2) - 1) + 1| in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "212", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 2e^(1(1(2|x| - 1)^2 + 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) = (-2(-1cos(2\u03c0x - 1) + 2))/(3(-1cos(2\u03c0x - 1) + 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": "How many local maxima does the function f(x) = -5(-2sin(1\u03c0x) + 3)^2 + 4(-2sin(1\u03c0x) + 3) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -2|((3(3(-2sin(3\u03c0x - 3)) - 2) + 1)/(-3(3(-2sin(3\u03c0x - 3)) - 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 minimum points for f(x) = -1(3sin(3\u03c0(-2x^2 + 5x - 1) - 1) + 1) + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "236", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 5(2cos(2\u03c0(3|x + 3| + 2)) - 2) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = 2(5(-3cos(2\u03c0x - 2) + 1)^2 + 1(-3cos(2\u03c0x - 2) + 1) - 4) + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -1sin(1\u03c0(2|(2x + 3)| - 2) + 3) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "81", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 2(-2cos(3\u03c0x) + 1) + 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 3sin(3\u03c0(-2|x - 2| + 1) - 3) - 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 minima does the function f(x) = 2sin(2\u03c0(3|x - 1| - 1) - 2) - 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": "Determine the total count of local extrema points for the function f(x) = -4(-3sin(2\u03c0x - 2) - 2)^2 - 2(-3sin(2\u03c0x - 2) - 2) + 5 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 4(3((-1(-1cos(1\u03c0x + 2) - 3) + 2)/(2(-1cos(1\u03c0x + 2) - 3) - 1))^2 + 3((-1(-1cos(1\u03c0x + 2) - 3) + 2)/(2(-1cos(1\u03c0x + 2) - 3) - 1)) - 2) - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -3(2cos(1\u03c0x - 3) + 3) - 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = (-2(1(-5(-1|x + 3|) + 1)^2 - 4(-5(-1|x + 3|) + 1)) + 3)/(2(1(-5(-1|x + 3|) + 1)^2 - 4(-5(-1|x + 3|) + 1)) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 3sin(1\u03c0(-1|(1x) + 2| + 2) - 2) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -4((-1(1cos(3\u03c0x + 2)) - 3)/(-3(1cos(3\u03c0x + 2)) - 2)) + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -3sin(2\u03c0(5(-1|x - 1| - 3) - 2) - 1) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "101", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 3(-2cos(1\u03c0x + 2) - 1) - 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": "How many local maxima does the function f(x) = -3e^(2(-2|x - 2| + 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) = -2sin(1\u03c0(-5x - 2) + 3) + 3 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": "Determine the total count of local extrema points for the function f(x) = -4(5(1|x + 1| - 3))^2 - 3(5(1|x + 1| - 3)) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = (-1(2sin(2\u03c0(-3(1x^2 - 4x + 3) + 1) - 2) + 2) + 3)/(2(2sin(2\u03c0(-3(1x^2 - 4x + 3) + 1) - 2) + 2) - 3) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "493", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = 1|(1((-1(-3x^2 + 2x + 5))/(-2(-3x^2 + 2x + 5) + 3)) + 5) + 1| + 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = (1(-2(1|(-2cos(2\u03c0x - 3))| + 2)^2 + 5) - 3)/(-2(-2(1|(-2cos(2\u03c0x - 3))| + 2)^2 + 5) - 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = 1sin(2\u03c0(2|(-3x^2 - 5x + 3) - 1| + 1) - 2) + 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "247", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 2|(2((2(2x - 5) + 3)/(-2(2x - 5) - 1))^2 - 1((2(2x - 5) + 3)/(-2(2x - 5) - 1)) - 3) + 2| + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 2((1(1x + 3) - 3)/(2(1x + 3) - 3))^2 - 3((1(1x + 3) - 3)/(2(1x + 3) - 3)) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 3cos(1\u03c0(-1(3(-2|x - 1| - 2)^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": "269", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = 1cos(3\u03c0(-2((-1(3|x - 3| - 2) - 3)/(3(3|x - 3| - 2) + 3))^2 - 1((-1(3|x - 3| - 2) - 3)/(3(3|x - 3| - 2) + 3)) - 1) + 2) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 1|(-1((3(-3cos(3\u03c0x + 1)) - 3)/(-3(-3cos(3\u03c0x + 1)) - 2))^2 + 1((3(-3cos(3\u03c0x + 1)) - 3)/(-3(-3cos(3\u03c0x + 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": "30", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -2(-3(-2|((-2x + 3)/(-2x - 1)) - 3| + 1)^2 - 1) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -5(-1sin(3\u03c0x) - 3) - 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -2(-2|x - 3| + 1)^2 - 4(-2|x - 3| + 1) - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -4((3(-1sin(2\u03c0(3|x - 2| + 2)) + 1) - 2)/(1(-1sin(2\u03c0(3|x - 2| + 2)) + 1) + 2))^2 + 4((3(-1sin(2\u03c0(3|x - 2| + 2)) + 1) - 2)/(1(-1sin(2\u03c0(3|x - 2| + 2)) + 1) + 2)) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -3((-2(2cos(2\u03c0x + 1) + 1) + 2)/(2(2cos(2\u03c0x + 1) + 1) + 3))^2 - 2((-2(2cos(2\u03c0x + 1) + 1) + 2)/(2(2cos(2\u03c0x + 1) + 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": "How many local minima does the function f(x) = -1(-2(-2|x + 3| + 2)^2 + 3(-2|x + 3| + 2) + 4) + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -1cos(2\u03c0(2x^2 + 1x - 1) + 1) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "575", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -2e^(1(1|((-3(1x^2 + 2x - 4) - 2)/(1(1x^2 + 2x - 4) + 2)) - 2|)) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 5(5(-2|x - 2| + 3) + 3)^2 + 2(5(-2|x - 2| + 3) + 3) + 5 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -2|(-5(2cos(1\u03c0x + 1))^2 - 3(2cos(1\u03c0x + 1)) + 3)| - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = -5(-1cos(2\u03c0x + 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) = (-1(-4(2|(-1x^2 + 5x - 2) + 2| + 2)) - 3)/(-1(-4(2|(-1x^2 + 5x - 2) + 2| + 2))) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -3((-3(-2(-3|x - 2|) - 1))/(2(-2(-3|x - 2|) - 1) - 3))^2 - 2((-3(-2(-3|x - 2|) - 1))/(2(-2(-3|x - 2|) - 1) - 3)) - 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -1(2cos(2\u03c0x + 3))^2 + 4(2cos(2\u03c0x + 3)) - 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -1cos(3\u03c0((-1x + 2)/(2x + 2)) + 1) - 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "23", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -3cos(2\u03c0((-1(2x - 5) + 1)/(-2(2x - 5) - 1)) - 1) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -3|(-4((-1(-2x + 2) - 3)/(-2(-2x + 2)))^2 - 4((-1(-2x + 2) - 3)/(-2(-2x + 2))) + 4) - 3| - 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 1sin(1\u03c0(-5x^2 - 2x - 2) - 2) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "251", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 4(-1sin(1\u03c0(-3|x + 3| - 2) + 3) + 2)^2 - 5(-1sin(1\u03c0(-3|x + 3| - 2) + 3) + 2) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 1((-1(2(2|x - 1| - 2)^2 + 4(2|x - 1| - 2) + 1) - 1)/(2(2(2|x - 1| - 2)^2 + 4(2|x - 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": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -3|(-1((2(2cos(3\u03c0x - 1) - 2) + 3)/(1(2cos(3\u03c0x - 1) - 2) - 2))^2 - 5((2(2cos(3\u03c0x - 1) - 2) + 3)/(1(2cos(3\u03c0x - 1) - 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": "120", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 2cos(2\u03c0((-1(-2(4x^2 - 5x + 3) + 5) + 2)/(3(-2(4x^2 - 5x + 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": "9", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = (-1(-4(-1cos(1\u03c0(-2|x + 3| - 2) - 2))^2 + 3(-1cos(1\u03c0(-2|x + 3| - 2) - 2)) - 3) - 3)/(-2(-4(-1cos(1\u03c0(-2|x + 3| - 2) - 2))^2 + 3(-1cos(1\u03c0(-2|x + 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": "81", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -2sin(3\u03c0((-1x - 2)/(-1x)) - 2) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "48", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 1sin(3\u03c0(3((1(-3x^2 + 2x - 1) + 2)/(1(-3x^2 + 2x - 1))) + 2) - 1) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "55", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 4(-2cos(2\u03c0x - 2) - 3) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -2(2|((-2(2x - 3) - 2)/(-1(2x - 3) - 2)) + 1| - 1)^2 + 4(2|((-2(2x - 3) - 2)/(-1(2x - 3) - 2)) + 1| - 1) - 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -2(-1sin(3\u03c0(-3(2|x - 1| - 2) + 5) + 3) - 3)^2 - 2 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 minima for the function f(x) = -2cos(2\u03c0((1x + 1)/(1x - 3))) + 3 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 maxima for the function f(x) = 5(1|(2x^2 - 5x) + 1| + 2) + 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 1(-5(1sin(3\u03c0x) - 3)^2 + 5(1sin(3\u03c0x) - 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": "Find the number of local maximum points for f(x) = 1(2e^(2(4x + 2)) - 2)^2 - 3(2e^(2(4x + 2)) - 2) + 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 2(1(2|x - 1| - 2)^2 - 2(2|x - 1| - 2) + 4) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 2cos(1\u03c0((3x + 1)/(1x + 1)) + 3) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = (-2(-3(1|(-4x^2 + 3) + 2| - 2) - 5) - 2)/(-2(-3(1|(-4x^2 + 3) + 2| - 2) - 5) - 1) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = 3sin(1\u03c0(2|x| - 3) + 1) - 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 2(3e^(-2((-1x - 2)/(3x - 2))) + 2)^2 - 5(3e^(-2((-1x - 2)/(3x - 2))) + 2) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -2e^(1(4x + 5)) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 1((2(2cos(2\u03c0(3x - 2) + 3) + 1) - 3)/(-1(2cos(2\u03c0(3x - 2) + 3) + 1) - 3))^2 - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "240", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 3cos(2\u03c0(5x^2 + 1x + 1) - 3) + 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "505", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -4(5(-2|x - 1| + 2)^2 - 2(-2|x - 1| + 2) - 5) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -1(-1sin(3\u03c0x + 2) - 1) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = (2(5(-3|(-3x^2 + 5x - 5) + 3| + 2) + 2))/(-2(5(-3|(-3x^2 + 5x - 5) + 3| + 2) + 2) - 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -2sin(1\u03c0(1|x + 3| - 2) + 1) - 3 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 maxima for the function f(x) = -2(1|(3((-1x + 1)/(1x + 3)) - 5) + 3| - 1)^2 + 3(1|(3((-1x + 1)/(1x + 3)) - 5) + 3| - 1) - 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = (2(5(-3|(-2x + 5) - 2| + 1)^2 + 3(-3|(-2x + 5) - 2| + 1) + 3) - 1)/(1(5(-3|(-2x + 5) - 2| + 1)^2 + 3(-3|(-2x + 5) - 2| + 1) + 3)) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = 3|(-2sin(3\u03c0x - 3) - 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": "Find the total number of local minima and maxima for f(x) = (-1(2sin(1\u03c0x - 1) - 1) - 2)/(2(2sin(1\u03c0x - 1) - 1)) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = (3(-4(-1|x - 3| + 1)^2 + 3(-1|x - 3| + 1) - 4) + 2)/(-2(-4(-1|x - 3| + 1)^2 + 3(-1|x - 3| + 1) - 4) - 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = (3(1cos(3\u03c0x - 3) - 1) - 1)/(-1(1cos(3\u03c0x - 3) - 1) - 1) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = (-2(1(-1sin(2\u03c0(2|x + 1|) - 1) - 2) - 3) + 2)/(1(1(-1sin(2\u03c0(2|x + 1|) - 1) - 2) - 3) - 2) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = (2(3|(3sin(2\u03c0x - 1) + 1) + 2| + 2) - 3)/(-3(3|(3sin(2\u03c0x - 1) + 1) + 2| + 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) = -1|(3sin(2\u03c0(1(2x^2 + 1x - 2) - 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": "575", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = 2(-5(1sin(2\u03c0(2|x - 2| - 1) + 1) - 3)^2 - 1(1sin(2\u03c0(2|x - 2| - 1) + 1) - 3) - 3) + 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 2(-2cos(2\u03c0x + 1) + 3)^2 + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = -3cos(2\u03c0(-4((1x - 3)/(3x)) - 4)) - 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) = -2|((-2(-3e^(2(1x + 5)) - 3) - 2)/(-3(-3e^(2(1x + 5)) - 3) - 3)) - 2| - 2 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": "Determine the total count of local extrema points for the function f(x) = 2|(-1cos(2\u03c0x + 1) + 1) + 3| + 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 3(2((3(-3sin(2\u03c0x - 3) + 1) - 2)/(-2(-3sin(2\u03c0x - 3) + 1) + 1))^2 + 1((3(-3sin(2\u03c0x - 3) + 1) - 2)/(-2(-3sin(2\u03c0x - 3) + 1) + 1)) - 1) - 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "83", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -3(2|((1(-1x + 2) - 2)/(3(-1x + 2) + 1)) - 1| - 3)^2 + 2(2|((1(-1x + 2) - 2)/(3(-1x + 2) + 1)) - 1| - 3) + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = 2sin(3\u03c0((2(-1(1x^2 + 4) + 4) - 1)/(3(-1(1x^2 + 4) + 4)))) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -2((-1(-3sin(1\u03c0x - 1) - 2) + 1)/(3(-3sin(1\u03c0x - 1) - 2) - 2))^2 + 3((-1(-3sin(1\u03c0x - 1) - 2) + 1)/(3(-3sin(1\u03c0x - 1) - 2) - 2)) - 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 number of local maximum points for f(x) = 2(-4(3cos(2\u03c0x + 1) - 2)^2 + 2(3cos(2\u03c0x + 1) - 2) - 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": "Determine the total count of local extrema points for the function f(x) = (-2(1|(4(-3x^2 - 1x + 2) + 4) + 3| - 3))/(1(1|(4(-3x^2 - 1x + 2) + 4) + 3| - 3) + 3) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -1|(-2sin(2\u03c0(1x + 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": "54", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 2(2cos(1\u03c0x + 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 total number of local minima and maxima for f(x) = -2e^(1(1((2x + 2)/(2x - 1))^2 + 2((2x + 2)/(2x - 1)) + 3)) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = 1sin(3\u03c0((-1(-1|(-1x - 3)| + 3) - 1)/(3(-1|(-1x - 3)| + 3) + 1)) - 2) - 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = (1(-5(-3|(-2e^(2x) + 3) + 3|)^2 + 3(-3|(-2e^(2x) + 3) + 3|) - 2) - 3)/(-2(-5(-3|(-2e^(2x) + 3) + 3|)^2 + 3(-3|(-2e^(2x) + 3) + 3|) - 2) + 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -3cos(1\u03c0((-2(1x^2 + 5x - 4) + 3)/(-3(1x^2 + 5x - 4) - 1))) - 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": "How many local maxima does the function f(x) = 1cos(1\u03c0(1(2|x - 3| + 1))) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 1(1|((2(-2x^2 - 3x + 1) - 2)/(1(-2x^2 - 3x + 1) + 1)) + 3| - 3) - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -2(-1|(1sin(1\u03c0x + 3) - 3) - 3| + 2) + 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = (-2(-3(-1|(2x^2 - 5x + 3) - 3| + 2) + 1) - 3)/(-1(-3(-1|(2x^2 - 5x + 3) - 3| + 2) + 1)) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -2(1|(-3((-1x - 1)/(3x + 3))^2 - 1((-1x - 1)/(3x + 3)) - 5) - 1| - 3) + 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 3cos(1\u03c0(5(2|x + 1| - 3) + 3) - 3) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "201", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 3|(3(1((2x + 1)/(-3x + 2))^2 - 3((2x + 1)/(-3x + 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": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 1|(-1sin(1\u03c0((2(5x - 3) - 2)/(2(5x - 3) + 3)) + 1)) - 3| where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 5(-2cos(1\u03c0x - 1) - 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": "Find the number of local maximum points for f(x) = 4((-2(-3(-1|x - 3| + 3)^2 + 3(-1|x - 3| + 3) - 1) - 1)/(2(-3(-1|x - 3| + 3)^2 + 3(-1|x - 3| + 3) - 1))) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -5((1(-2x - 4) + 2)/(-1(-2x - 4) - 3))^2 - 4((1(-2x - 4) + 2)/(-1(-2x - 4) - 3)) + 5 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = (-1(2e^(2(-3(-2|x + 1| + 2) - 5)) - 2) - 1)/(3(2e^(2(-3(-2|x + 1| + 2) - 5)) - 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) = -1|((-1(3cos(3\u03c0(-4x^2 - 3x - 4) + 2) + 3) + 3)/(-1(3cos(3\u03c0(-4x^2 - 3x - 4) + 2) + 3) + 2)) + 2| where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "241", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = 3sin(1\u03c0(1x^2 + 2x + 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": "Determine the count of local minima for the function f(x) = -2|(2(3sin(2\u03c0((3x + 3)/(1x + 3)) + 1) + 3)) - 2| - 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "91", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 2|(3((2(2e^(-1x) - 2) + 3)/(3(2e^(-1x) - 2) + 1))^2 + 2((2(2e^(-1x) - 2) + 3)/(3(2e^(-1x) - 2) + 1)) - 1) - 1| - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 3sin(1\u03c0(-1(4((3x - 1)/(-2x - 2))^2 + 5((3x - 1)/(-2x - 2)) + 3) - 5) - 1) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -1cos(3\u03c0(1x^2 - 3x + 2) - 1) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "274", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -4((1(-4x + 5) - 1)/(2(-4x + 5) - 3))^2 - 1((1(-4x + 5) - 1)/(2(-4x + 5) - 3)) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = (-1(-3cos(2\u03c0x + 1)) - 3)/(3(-3cos(2\u03c0x + 1)) + 1) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = -1|((3(2sin(2\u03c0(4x^2 + 4x) + 2)) + 3)/(2(2sin(2\u03c0(4x^2 + 4x) + 2)) + 3)) + 1| - 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "338", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -2e^(1(4(1x - 1)^2 + 4(1x - 1) + 2)) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -2(1cos(1\u03c0x - 3))^2 - 5(1cos(1\u03c0x - 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 maxima does the function f(x) = -1(-2(3|x + 3| + 1) + 3)^2 - 5(-2(3|x + 3| + 1) + 3) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = 2cos(3\u03c0(-2(1|(-1x - 4) - 3| + 1)^2 + 3(1|(-1x - 4) - 3| + 1) - 1) - 3) - 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": "Find the number of local maximum points for f(x) = -2|(-3cos(1\u03c0x + 1) + 1) + 2| + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = (-2(3sin(2\u03c0x + 2) + 3) - 1)/(1(3sin(2\u03c0x + 2) + 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 maxima does the function f(x) = -1(-3(-1|x - 3| + 2) - 1)^2 - 3(-3(-1|x - 3| + 2) - 1) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -2(1sin(3\u03c0x + 1) + 3)^2 + 2(1sin(3\u03c0x + 1) + 3) + 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = (-1(-1(-1cos(2\u03c0(-1|x - 1| - 2) + 1) + 2) + 3) - 2)/(-2(-1(-1cos(2\u03c0(-1|x - 1| - 2) + 1) + 2) + 3) - 1) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -2sin(3\u03c0(1|(1x - 1) - 3| + 3)) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = 4(2(1|((-1x + 3)/(3x - 2)) + 1| - 2) + 2)^2 + 4(2(1|((-1x + 3)/(3x - 2)) + 1| - 2) + 2) - 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = (-1(2|(1sin(1\u03c0(-3x^2 - 1x)) - 3) - 3| - 3) + 3)/(1(2|(1sin(1\u03c0(-3x^2 - 1x)) - 3) - 3| - 3) - 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "567", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -1(4(2|x - 1|)^2 - 2(2|x - 1|) + 3) + 4 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = 2(3|(-1sin(3\u03c0x + 1) + 3) + 2| - 3)^2 - 1(3|(-1sin(3\u03c0x + 1) + 3) + 2| - 3) + 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -3cos(1\u03c0(2|x + 1| - 1) + 2) + 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -1sin(3\u03c0((1x + 3)/(2x + 1)) - 3) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -1cos(1\u03c0(-3|(-4((-2x + 1)/(-1x + 2)) + 1) + 1| - 1) - 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "116", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = -2sin(3\u03c0(2|x - 2| - 1) - 2) + 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "61", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -3|(-2cos(2\u03c0x + 1) + 1) + 1| have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -2(2e^(-1(-5x - 4)) + 3)^2 + 1(2e^(-1(-5x - 4)) + 3) + 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -3sin(2\u03c0(4((1x + 3)/(3x + 2)) - 2) - 1) - 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": "How many local maxima does the function f(x) = -2(-1|x - 1| - 1)^2 - 5(-1|x - 1| - 1) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = 2sin(3\u03c0(-2((2(-2|x + 1| + 3) + 3)/(1(-2|x + 1| + 3))) - 4)) - 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "55", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 1(-2cos(3\u03c0x + 1) - 2)^2 - 3(-2cos(3\u03c0x + 1) - 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = -1(2|(-3x^2 - 3x) + 2| + 3) + 4 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = 1sin(2\u03c0(-4(2x^2 + 1x - 1) + 2) - 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "239", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 1|(4x^2 + 5x - 2) + 3| + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -1e^(-2(-3(-3x^2 - 1x - 2) + 1)) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -1(-2|(1x + 2)| + 3)^2 + 1(-2|(1x + 2)| + 3) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 2sin(3\u03c0(-4x^2 - 4x + 5)) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "488", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 2(-2|(3sin(2\u03c0x - 3) + 2) - 1|)^2 - 3(-2|(3sin(2\u03c0x - 3) + 2) - 1|) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -2e^(2(-5((1x + 2)/(-1x + 3))^2 - 2((1x + 2)/(-1x + 3)) + 1)) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 3(-2cos(2\u03c0(-3((-1x - 1)/(3x - 1)) - 1)) - 3)^2 - 5(-2cos(2\u03c0(-3((-1x - 1)/(3x - 1)) - 1)) - 3) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 2|(1sin(2\u03c0((-3(-4x - 3) + 2)/(2(-4x - 3))) + 2)) + 3| + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 3cos(2\u03c0(-1|x - 1|) + 3) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 5(-5(-3|(2sin(3\u03c0x - 3) + 1) + 2| + 2)^2 + 5(-3|(2sin(3\u03c0x - 3) + 1) + 2| + 2) - 1) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 3cos(1\u03c0(2(2x^2 + 2x - 2) - 2) - 2) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "283", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = (3(-4(-2cos(3\u03c0x) + 3) + 4) + 2)/(3(-4(-2cos(3\u03c0x) + 3) + 4) - 2) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -1|(-4(3e^(-1(-2x^2 + 2x - 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": "2", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = (3(3|(1(-5x^2 - 2x - 1)) + 1| - 2) + 2)/(-2(3|(1(-5x^2 - 2x - 1)) + 1| - 2) + 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -2|(3((1(-4x - 1) + 2)/(-3(-4x - 1) + 4))^2 - 3((1(-4x - 1) + 2)/(-3(-4x - 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": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -1|(-3(2cos(1\u03c0x) - 2)) - 3| - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -1cos(2\u03c0(-3x^2 + 1x - 4) + 2) + 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "224", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = (2(-1cos(1\u03c0(5x^2 - 4x + 3) + 1) - 2))/(-2(-1cos(1\u03c0(5x^2 - 4x + 3) + 1) - 2) - 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "270", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -2|((-2(3sin(2\u03c0(1x) + 1)) - 3)/(2(3sin(2\u03c0(1x) + 1)) + 1)) - 1| + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 1sin(2\u03c0(3x^2 - 4x - 3) + 2) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "455", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = 1(-1|x - 1| + 3)^2 - 3(-1|x - 1| + 3) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 1((3(3(2|x| - 2) + 3) - 3)/(-1(3(2|x| - 2) + 3) + 3))^2 + 2((3(3(2|x| - 2) + 3) - 3)/(-1(3(2|x| - 2) + 3) + 3)) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -2((1(-4(-1e^(2x) + 2) - 3) + 1)/(-2(-4(-1e^(2x) + 2) - 3)))^2 - 1((1(-4(-1e^(2x) + 2) - 3) + 1)/(-2(-4(-1e^(2x) + 2) - 3))) + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = 3sin(2\u03c0(-4((3x)/(2x + 3))^2 + 3((3x)/(2x + 3))) - 1) - 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "58", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -4(-1cos(1\u03c0x + 1) + 1) + 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -3sin(3\u03c0(-2|(-5((1x - 1)/(-2x - 1)) + 2) - 3| - 3) + 2) + 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "94", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 3(2(3|x - 2| - 1) - 1)^2 + 2(2(3|x - 2| - 1) - 1) - 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -2(-3cos(2\u03c0x + 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) = 1cos(3\u03c0(-3|(-3x^2 + 3x + 1)| + 1) - 2) + 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "493", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -3(-3(-2cos(1\u03c0(-3|x - 3| + 2) + 3)) - 3)^2 - 2(-3(-2cos(1\u03c0(-3|x - 3| + 2) + 3)) - 3) + 4 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "121", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = (1(1|(1x^2 - 5) + 2| - 2) - 3)/(2(1|(1x^2 - 5) + 2| - 2)) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = (-2(2(2e^(-2(3|x + 3| - 2)) - 1) + 5) + 1)/(-3(2(2e^(-2(3|x + 3| - 2)) - 1) + 5) + 2) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -1(1cos(1\u03c0x + 1) + 2)^2 + 1(1cos(1\u03c0x + 1) + 2) + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -2cos(2\u03c0((1(-1(-4x + 1)^2 + 1(-4x + 1) + 5) - 3)/(-3(-1(-4x + 1)^2 + 1(-4x + 1) + 5))) + 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": "Find the number of local minimum points for f(x) = 2((-1(-3(-2|x - 3| + 1) + 4) + 3)/(2(-3(-2|x - 3| + 1) + 4) - 1))^2 - 5((-1(-3(-2|x - 3| + 1) + 4) + 3)/(2(-3(-2|x - 3| + 1) + 4) - 1)) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = (2(-1sin(3\u03c0(3(5x^2 - 4x - 1) - 5) + 2) + 2) + 1)/(3(-1sin(3\u03c0(3(5x^2 - 4x - 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": "323", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 2cos(2\u03c0(-2|((-1x - 1)/(-3x + 4)) - 1| + 3)) - 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) = -1e^(1(3x - 1)) - 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 2(2e^(-2(1x^2 - 2x - 4)) - 1) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 1((-1(-2sin(2\u03c0x - 3) + 3) - 1)/(-1(-2sin(2\u03c0x - 3) + 3) + 3))^2 - 1((-1(-2sin(2\u03c0x - 3) + 3) - 1)/(-1(-2sin(2\u03c0x - 3) + 3) + 3)) - 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": "How many local maxima does the function f(x) = -1(3sin(2\u03c0(4(-1|x + 1| - 3) + 2) + 1) + 1)^2 - 2(3sin(2\u03c0(4(-1|x + 1| - 3) + 2) + 1) + 1) + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "161", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 2(1|(-2((3x - 1)/(-1x + 2))^2 + 4((3x - 1)/(-1x + 2)) + 1) + 2| + 1) - 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 2|(3x^2 - 4x - 2) + 3| - 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = (2(4(-1|(-5x^2 - 4x + 1) + 3| + 2) + 1) + 3)/(1(4(-1|(-5x^2 - 4x + 1) + 3| + 2) + 1)) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = (1(-3sin(3\u03c0x + 3) + 1))/(-1(-3sin(3\u03c0x + 3) + 1) - 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "59", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -5(2e^(-1(5x - 4)) - 2)^2 - 3(2e^(-1(5x - 4)) - 2) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 4(-4(1|((-1x)/(-1x + 2)) - 1| - 1)^2 - 1(1|((-1x)/(-1x + 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": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = (1(-2sin(3\u03c0x + 2) - 3) + 1)/(1(-2sin(3\u03c0x + 2) - 3) + 3) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -3(-4((-3x + 1)/(3x - 2))^2 + 2((-3x + 1)/(3x - 2)) + 2) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = 2((-2x)/(-3x + 1))^2 - 5((-2x)/(-3x + 1)) - 5 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = (2(2cos(2\u03c0x + 1)))/(1(2cos(2\u03c0x + 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 maxima does the function f(x) = -4(-1cos(3\u03c0(-1|x - 2| - 1) - 1) + 2)^2 + 1(-1cos(3\u03c0(-1|x - 2| - 1) - 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) = (3(-2(1(3|x + 2| - 3)^2 + 1) - 5) + 1)/(-1(-2(1(3|x + 2| - 3)^2 + 1) - 5) - 3) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = (2(-1cos(1\u03c0x + 1) - 1))/(3(-1cos(1\u03c0x + 1) - 1) + 3) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = (-2(2|(5x^2 - 1x + 2) - 3| - 3))/(3(2|(5x^2 - 1x + 2) - 3| - 3) + 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -4(-4(-3cos(2\u03c0x + 2) + 2)^2 - 4(-3cos(2\u03c0x + 2) + 2) + 4) - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -1sin(2\u03c0(-4x^2 - 5x + 3) - 1) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "258", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 5((2(-3|x - 2| + 3) + 2)/(1(-3|x - 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 extrema (minima and maxima combined) does the function f(x) = (-2(-3cos(2\u03c0x + 3) + 2) + 2)/(2(-3cos(2\u03c0x + 3) + 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 maximum points for f(x) = 4(1cos(2\u03c0(5x^2 - 5x + 3))) - 5 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": "Find the number of local maximum points for f(x) = 1cos(1\u03c0(3x - 4) + 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": "Find the total number of local minima and maxima for f(x) = -2cos(1\u03c0((1x + 3)/(1x)) + 2) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = (-1(1|(-1e^(1(-5x^2 + 4x))) - 1| + 1) + 3)/(-2(1|(-1e^(1(-5x^2 + 4x))) - 1| + 1) + 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -1(-3cos(1\u03c0x + 3) - 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = (2(1(-2|(1cos(1\u03c0x)) + 3| - 3)^2 - 4(-2|(1cos(1\u03c0x)) + 3| - 3) - 5) - 2)/(1(1(-2|(1cos(1\u03c0x)) + 3| - 3)^2 - 4(-2|(1cos(1\u03c0x)) + 3| - 3) - 5) + 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 total number of local minima and maxima for f(x) = (1(-2e^(-1(2(-2|x - 3| - 3)^2 + 2(-2|x - 3| - 3) - 4)) + 2) + 3)/(2(-2e^(-1(2(-2|x - 3| - 3)^2 + 2(-2|x - 3| - 3) - 4)) + 2) + 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = (-1(-5(-3|x - 3| + 2)^2 + 5(-3|x - 3| + 2) + 4) + 2)/(-2(-5(-3|x - 3| + 2)^2 + 5(-3|x - 3| + 2) + 4)) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = 1(-2(-2|x| + 2)^2 + 5(-2|x| + 2) + 3) - 4 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 3e^(2((3(2x + 4) + 2)/(3(2x + 4)))) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = (2(-3cos(3\u03c0(1|x + 1| - 1)) + 3) + 1)/(-1(-3cos(3\u03c0(1|x + 1| - 1)) + 3) + 3) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -1|(-1sin(3\u03c0x - 3)) + 3| - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 3|(-1(-5x^2 - 4x + 3) - 1) - 2| + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = -4(-3|((-1(1cos(2\u03c0x) - 2) + 3)/(-3(1cos(2\u03c0x) - 2) - 2)) + 2| - 2) + 4 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = (-3(2cos(1\u03c0x + 2) - 2) + 1)/(1(2cos(1\u03c0x + 2) - 2) + 2) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -3cos(2\u03c0(-4x - 5) - 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": "Find the number of local maximum points for f(x) = -3sin(1\u03c0((1x + 1)/(3x - 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": "Find the number of local minimum points for f(x) = (-1(2(1sin(2\u03c0x))^2 - 4(1sin(2\u03c0x)) - 5) - 3)/(1(2(1sin(2\u03c0x))^2 - 4(1sin(2\u03c0x)) - 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": "Find the number of local minimum points for f(x) = -2sin(3\u03c0((-3x - 1)/(3x + 3)) - 1) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -5(5(-2|((3x - 2)/(-2x + 3)) + 2| + 3)^2 - 1(-2|((3x - 2)/(-2x + 3)) + 2| + 3) - 4) - 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -1(-1sin(1\u03c0x - 1) - 1)^2 - 5(-1sin(1\u03c0x - 1) - 1) + 5 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -1sin(1\u03c0(-1|(-4((2x - 3)/(-3x + 2)) + 3) + 1| + 2)) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -2(1|((-3(2sin(2\u03c0x - 2) - 2) - 3)/(3(2sin(2\u03c0x - 2) - 2) - 2)) + 1| - 3) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 2(-2|x + 3| + 2)^2 - 3(-2|x + 3| + 2) - 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = (-3(-2|(5(3x - 2)^2 + 3(3x - 2) - 4) - 3| + 3) - 1)/(3(-2|(5(3x - 2)^2 + 3(3x - 2) - 4) - 3| + 3) - 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -3sin(1\u03c0(-1(5(1|x + 2| + 3) + 4)^2 + 4(5(1|x + 2| + 3) + 4) - 1) - 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "240", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 4(-3sin(2\u03c0x - 3))^2 + 4(-3sin(2\u03c0x - 3)) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -3e^(1(4((2x + 3)/(-3x))^2 - 1((2x + 3)/(-3x)))) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 3sin(2\u03c0(-2x^2 + 2) - 3) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "290", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -1e^(-1(-4x^2 - 3x + 2)) + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = 2cos(3\u03c0((-2x + 2)/(-2x + 3)) + 3) - 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = (-1(-1cos(2\u03c0(1(-3|x - 3|) - 2) - 2) - 3) - 3)/(-1(-1cos(2\u03c0(1(-3|x - 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": "121", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 2|(-5(5x - 1)^2 - 4(5x - 1) + 3) - 3| where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 5(2sin(1\u03c0x + 3) + 1)^2 + 4(2sin(1\u03c0x + 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": "Find the total number of local minima and maxima for f(x) = -2(3sin(3\u03c0x - 3) + 2) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -2|((2(2sin(2\u03c0(3x^2 - 4x - 3)) - 1) + 2)/(1(2sin(2\u03c0(3x^2 - 4x - 3)) - 1) + 2)) + 2| + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "305", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 4(-4(3sin(2\u03c0x + 2) + 3)^2 + 4(3sin(2\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": "40", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = (-3(-2(1|(2cos(1\u03c0x - 1) + 1) - 3| - 1) - 2) + 1)/(-1(-2(1|(2cos(1\u03c0x - 1) + 1) - 3| - 1) - 2) + 2) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 2|(2sin(2\u03c0((3x + 1)/(-1x - 3))) + 2) + 1| + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "79", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -2cos(3\u03c0(-2|(4((-3x + 3)/(2x - 3)) + 3) - 2| + 1) - 1) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "47", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 2(-2sin(1\u03c0((1(-4x^2 - 5x - 2) + 2)/(-2(-4x^2 - 5x - 2) - 1)) + 3) - 2) + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = (-1(2cos(2\u03c0x - 2) + 1) + 2)/(-3(2cos(2\u03c0x - 2) + 1) - 2) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = (-3(-3|(-2cos(2\u03c0(-5x - 3) + 2) + 3) - 1| - 2) - 3)/(3(-3|(-2cos(2\u03c0(-5x - 3) + 2) + 3) - 1| - 2)) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "100", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 2(-3sin(2\u03c0x + 1) + 3) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 1|(5((2(-3e^(-1x) + 3) + 3)/(2(-3e^(-1x) + 3)))^2 + 4((2(-3e^(-1x) + 3) + 3)/(2(-3e^(-1x) + 3))) - 5)| + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -1(2sin(3\u03c0(-1|x + 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": "61", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -2sin(1\u03c0(-1x^2 + 3x - 1)) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "103", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 2e^(-2(1(3(-1|x + 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": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = (1(4(-3sin(3\u03c0x + 2) + 1)^2 + 3(-3sin(3\u03c0x + 2) + 1)) - 1)/(-1(4(-3sin(3\u03c0x + 2) + 1)^2 + 3(-3sin(3\u03c0x + 2) + 1)) + 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = (-2(-1|(4(-5x^2 + 5x + 3) + 4)| - 2))/(-1(-1|(4(-5x^2 + 5x + 3) + 4)| - 2) - 1) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -2sin(3\u03c0((-3x)/(2x - 1))) + 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": "Find the total number of local minima and maxima for f(x) = 1cos(1\u03c0(2|(2((-3x - 2)/(-1x - 2)) + 5) - 3| + 3) + 1) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "77", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = (1(2e^(1(-4x)) + 1) + 3)/(3(2e^(1(-4x)) + 1) - 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": "Find the total number of local minima and maxima for f(x) = 2|((-3(2cos(1\u03c0(4x^2 + 1x + 5) + 1) - 2) - 1)/(2(2cos(1\u03c0(4x^2 + 1x + 5) + 1) - 2) - 1))| - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "551", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = (1(3cos(2\u03c0x - 3) + 1) + 2)/(-1(3cos(2\u03c0x - 3) + 1) - 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = -2(1cos(2\u03c0x) - 1) - 4 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 maximum points for f(x) = -3(2|(-1sin(1\u03c0((-1x - 1)/(3x + 1))) - 1) - 1| - 1) + 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -3|(-1cos(1\u03c0x + 2) - 1)| - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -3sin(3\u03c0(-3|(3x^2 + 4x - 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": "497", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = (2(-3(-2|(-2x^2 + 5x - 3) + 2| - 2) - 3) + 2)/(1(-3(-2|(-2x^2 + 5x - 3) + 2| - 2) - 3)) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -4(3sin(3\u03c0((1(5x^2 + 2x + 3) - 1)/(-1(5x^2 + 2x + 3) - 3))) + 2) + 4 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -5(3(1|(1sin(3\u03c0x - 3) - 1) + 2| + 1) - 2)^2 + 1(3(1|(1sin(3\u03c0x - 3) - 1) + 2| + 1) - 2) - 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 2|(3cos(3\u03c0(3x^2 + 3x + 2) - 1) + 3) + 3| + 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "526", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -3e^(1(5x^2 - 3x + 2)) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -2|(2x^2 - 4x) + 1| + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = 1(-2|x + 1| + 1)^2 + 2(-2|x + 1| + 1) - 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -3cos(3\u03c0((-1(1x^2 - 1x + 4) - 3)/(-3(1x^2 - 1x + 4) + 4)) - 1) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 2cos(1\u03c0(4(4x^2 - 1x + 3) + 1) + 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": "Find the total number of local minima and maxima for f(x) = 3cos(1\u03c0((3x - 3)/(1x + 3))) + 2 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 extrema (minima and maxima combined) does the function f(x) = (-2(-3cos(2\u03c0(4(1x - 4)^2 + 1(1x - 4) + 3) + 1) - 1) + 3)/(3(-3cos(2\u03c0(4(1x - 4)^2 + 1(1x - 4) + 3) + 1) - 1) + 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "487", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -1((-3(3|(3x + 1)| - 3) + 2)/(1(3|(3x + 1)| - 3) + 2))^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 number of local minimum points for f(x) = (2(1cos(3\u03c0x - 3) + 2) + 1)/(1(1cos(3\u03c0x - 3) + 2) - 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) = (2(1(-5(-3cos(2\u03c0x + 1) - 2)^2 + 2(-3cos(2\u03c0x + 1) - 2)) + 2) - 1)/(3(1(-5(-3cos(2\u03c0x + 1) - 2)^2 + 2(-3cos(2\u03c0x + 1) - 2)) + 2) - 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -3cos(1\u03c0(-3(-1|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": "32", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -1sin(2\u03c0(3|(-2x - 3) + 2| + 2) + 3) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = 3sin(1\u03c0(5(3((-2x + 2)/(1x)) - 1)^2 - 3(3((-2x + 2)/(1x)) - 1) + 4)) - 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "176", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = (-1(2e^(2(-3|(-4x^2 + 4) + 1|)) - 3) - 1)/(2(2e^(2(-3|(-4x^2 + 4) + 1|)) - 3)) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = -1sin(3\u03c0(-3x - 4)) - 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "90", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -1|(3sin(3\u03c0(-2x - 1) + 3) - 3) - 1| + 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = (2(2sin(2\u03c0x + 3) - 2) + 2)/(1(2sin(2\u03c0x + 3) - 2) - 3) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = (-1(2(2cos(3\u03c0x - 2) + 2)^2 + 4(2cos(3\u03c0x - 2) + 2) + 2) - 1)/(3(2(2cos(3\u03c0x - 2) + 2)^2 + 4(2cos(3\u03c0x - 2) + 2) + 2) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -3((1(-1(3|x - 3| - 1)^2 + 3(3|x - 3| - 1) + 3) - 1)/(2(-1(3|x - 3| - 1)^2 + 3(3|x - 3| - 1) + 3) + 3)) - 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -3|(-1((-2(-2x^2 - 5x + 5) + 1)/(-1(-2x^2 - 5x + 5) + 3)) + 2) - 3| + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -2cos(1\u03c0(4x + 4) + 2) + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = -1sin(3\u03c0(-2|((1(2x + 1) - 1)/(3(2x + 1) - 2)) + 3| + 1)) + 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 3sin(1\u03c0((-3x + 2)/(-2x - 3)) - 3) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "23", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = -2|(2cos(3\u03c0((-3(2x^2 + 3x) + 3)/(3(2x^2 + 3x))) - 2) + 3)| - 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": "Find the number of local minimum points for f(x) = -2sin(3\u03c0(-1(2|x + 2| + 1)^2 - 2(2|x + 2| + 1) + 4) - 1) + 2 where -10 \u2264 x \u2264 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) = 2|((3(4(1x - 1)^2 + 2(1x - 1)) + 2)/(-3(4(1x - 1)^2 + 2(1x - 1)) + 2)) + 3| + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = 2e^(-2(-3|(3(-3x - 2)^2 - 3(-3x - 2) - 4) + 2| - 1)) + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 2cos(3\u03c0(-4((-3x - 3)/(-1x + 2))^2 - 5((-3x - 3)/(-1x + 2)) + 5)) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "351", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 3cos(3\u03c0((3(2(2|x - 2| + 1) - 4) - 1)/(2(2(2|x - 2| + 1) - 4) - 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 extrema (minima and maxima combined) does the function f(x) = 2cos(3\u03c0(1|(-1((-3x + 1)/(1x + 1)) + 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": "74", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -3(3|(2cos(2\u03c0x - 1) + 2) + 2| + 2)^2 - 5(3|(2cos(2\u03c0x - 1) + 2) + 2| + 2) - 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = (1(1cos(3\u03c0(-4(5x^2 + 4x + 5) + 1) + 2) + 3) - 1)/(2(1cos(3\u03c0(-4(5x^2 + 4x + 5) + 1) + 2) + 3) + 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "205", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 1sin(1\u03c0(1|(-3x^2 - 5x + 3) + 1| + 2) - 1) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "281", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -2(-2cos(2\u03c0((-2x - 3)/(-2x + 1)) - 3) + 2) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 3|(-1sin(2\u03c0(1x - 4) + 3) + 1) + 3| - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = 3(4(3|((-2x + 3)/(-2x - 2)) - 2|)^2 - 1(3|((-2x + 3)/(-2x - 2)) - 2|) - 1) - 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = -1sin(3\u03c0(-4x^2 + 4x + 3) - 3) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "247", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = (2(-1sin(1\u03c0x)) + 2)/(1(-1sin(1\u03c0x))) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 3|(-1((-1x + 1)/(2x - 3))^2 + 3((-1x + 1)/(2x - 3)) + 1) + 3| + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = -2|(-1cos(3\u03c0((-2(1x + 3) + 3)/(2(1x + 3) - 1)) - 1) - 3) + 2| - 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -3|(-1cos(3\u03c0x + 2) + 1) - 3| - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -3|(1cos(1\u03c0x - 1) - 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 number of local minimum points for f(x) = 1(-3cos(3\u03c0x - 1))^2 - 3(-3cos(3\u03c0x - 1)) + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local minimum points for f(x) = 2sin(1\u03c0(-3|x + 1| - 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": "Determine the total count of local extrema points for the function f(x) = 2|(-3e^(-1(2x^2 - 5x - 5)) - 1) - 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) = 2(1cos(3\u03c0((1x + 3)/(3x + 3)))) + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 5(-1|(-1((-1x + 2)/(1x - 3)) - 1) + 1| + 2)^2 - 2(-1|(-1((-1x + 2)/(1x - 3)) - 1) + 1| + 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = 2(3e^(1(5x^2 + 3x - 3)) + 3) + 5 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -3sin(3\u03c0(4((1(1x^2 - 3x + 5) + 1)/(-2(1x^2 - 3x + 5) - 3)) - 3) - 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -2cos(3\u03c0((-2(-5(-1|x + 1| + 2) + 3) + 1)/(3(-5(-1|x + 1| + 2) + 3) - 2)) + 3) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -3((-1(4x + 3))/(2(4x + 3) - 3))^2 - 2((-1(4x + 3))/(2(4x + 3) - 3)) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = (-2(3sin(2\u03c0x) - 1) - 1)/(-2(3sin(2\u03c0x) - 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) = 1sin(2\u03c0((3(-2(-1x + 4)^2 + 2(-1x + 4) + 1))/(2(-2(-1x + 4)^2 + 2(-1x + 4) + 1) - 1)) - 1) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "25", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -4(2|(-1x^2 - 5x + 4)| - 1) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -3|(5((2(3x) + 3)/(1(3x) + 2))^2 - 3((2(3x) + 3)/(1(3x) + 2)) - 2) - 2| + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local minima for the function f(x) = -1(1|(-1sin(3\u03c0x - 1)) - 3| + 3)^2 + 5(1|(-1sin(3\u03c0x - 1)) - 3| + 3) - 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -1((-1(-1x + 5) - 1)/(1(-1x + 5)))^2 + 4((-1(-1x + 5) - 1)/(1(-1x + 5))) - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = (3(-3sin(3\u03c0x + 1) + 3))/(-2(-3sin(3\u03c0x + 1) + 3)) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "178", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 1sin(2\u03c0(5(-1|(-3x - 5)| - 2)^2 + 5(-1|(-3x - 5)| - 2) - 1) - 3) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "448", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 1(4(3cos(1\u03c0x + 2) + 1)^2 - 1(3cos(1\u03c0x + 2) + 1) - 5) + 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) = -2|(3(-1sin(3\u03c0x + 1))^2 - 3(-1sin(3\u03c0x + 1)) - 2) - 2| - 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "149", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 1((-3(-2cos(3\u03c0(-5x + 5) + 3) - 1) - 2)/(-1(-2cos(3\u03c0(-5x + 5) + 3) - 1) - 1))^2 - 5((-3(-2cos(3\u03c0(-5x + 5) + 3) - 1) - 2)/(-1(-2cos(3\u03c0(-5x + 5) + 3) - 1) - 1)) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "599", "dataset": "MATH"}
{"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 3cos(3\u03c0(-5(-1|((3x - 2)/(2x + 3)) + 1| + 2)^2 - 3(-1|((3x - 2)/(2x + 3)) + 1| + 2) - 3) + 3) - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "180", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 3((3(-2cos(3\u03c0x + 1) + 2) + 2)/(-3(-2cos(3\u03c0x + 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": "30", "dataset": "MATH"}
{"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 1cos(2\u03c0((-2(-2|x - 2| - 3) - 3)/(3(-2|x - 2| - 3) - 2)) + 2) + 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the number of local maximum points for f(x) = 3cos(2\u03c0((2(-4x^2 + 1x + 4) - 2)/(-2(-4x^2 + 1x + 4))) + 1) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Determine the count of local maxima for the function f(x) = -1cos(2\u03c0((3(-1(3x)^2 - 1(3x) + 4) + 2)/(-3(-1(3x)^2 - 1(3x) + 4) - 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": "Determine the count of local maxima for the function f(x) = 2sin(2\u03c0((2x - 1)/(2x + 3)) - 1) + 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}