| {"messages": [{"content": "How many local minima does the function f(x) = 2|(-1cos(2\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": "Find the number of local maximum points for f(x) = -1|(1e^(-1(5x^2 - 4x - 2)) + 3) + 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": "Determine the count of local maxima for the function f(x) = (-3(3|(-5(-1x)^2 + 1)| + 2))/(-2(3|(-5(-1x)^2 + 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": "How many local extrema (minima and maxima combined) does the function f(x) = 3|(-4(-3x^2 - 3x + 3) - 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 extrema (minima and maxima combined) does the function f(x) = 5(3|(-3((-1x)/(3x + 2)) + 3) - 3| + 1)^2 - 2(3|(-3((-1x)/(3x + 2)) + 3) - 3| + 1) - 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"} |
| {"messages": [{"content": "Determine the count of local maxima for the function f(x) = 2e^(1(-2(2x + 5)^2 + 5(2x + 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": "Determine the count of local maxima for the function f(x) = 3(-1cos(1\u03c0x - 2) + 3) + 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"} |
| {"messages": [{"content": "Determine the count of local maxima for the function f(x) = -5(2cos(3\u03c0x - 2) + 3)^2 + 2(2cos(3\u03c0x - 2) + 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": "Determine the total count of local extrema points for the function f(x) = -3sin(3\u03c0((3x)/(-1x - 2)) + 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": "Find the total number of local minima and maxima for f(x) = 4((-2x - 2)/(3x + 3)) - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28", "dataset": "MATH"} |
| {"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 1(1|x + 3| - 2)^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": "How many local extrema (minima and maxima combined) does the function f(x) = (1(3(1|x + 3| - 3)^2 - 4(1|x + 3| - 3) + 2) + 1)/(-2(3(1|x + 3| - 3)^2 - 4(1|x + 3| - 3) + 2) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"} |
| {"messages": [{"content": "Find the number of local maximum points for f(x) = 4(3sin(3\u03c0x - 3) + 1) + 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"} |
| {"messages": [{"content": "Find the number of local minimum points for f(x) = 2sin(3\u03c0(3((3x + 2)/(3x + 1))^2 - 3((3x + 2)/(3x + 1)) - 2) + 1) - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"} |
| {"messages": [{"content": "Find the number of local maximum points for f(x) = 2cos(2\u03c0((3(1x^2 - 3x - 5) + 3)/(-2(1x^2 - 3x - 5) - 1)) - 1) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"} |
| {"messages": [{"content": "Find the number of local maximum points for f(x) = -3cos(3\u03c0(1x)) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"} |
| {"messages": [{"content": "Determine the count of local minima for the function f(x) = -3cos(3\u03c0((2x + 3)/(1x + 1)) + 1) + 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"} |
| {"messages": [{"content": "Determine the count of local maxima for the function f(x) = 1(2|(1x^2 - 5x - 4) + 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": "How many local maxima does the function f(x) = (2(2|(1(4x^2 - 5x - 4) + 1) + 2| + 2) - 3)/(3(2|(1(4x^2 - 5x - 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 total number of local minima and maxima for f(x) = 2cos(3\u03c0(1(-2|x + 1| + 2)^2 - 2(-2|x + 1| + 2) - 2) - 1) + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "484", "dataset": "MATH"} |
| {"messages": [{"content": "Determine the count of local minima for the function f(x) = -1|(4x^2 - 1) - 3| + 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) = 1sin(1\u03c0(-2x + 5) + 1) + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"} |
| {"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -3sin(3\u03c0(-1|((1x - 2)/(-1x + 3)) - 2| + 3) + 3) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"} |
| {"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 3sin(3\u03c0(-2x^2 - 4) - 2) - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "449", "dataset": "MATH"} |
| {"messages": [{"content": "Find the number of local maximum points for f(x) = (-1(-4(-2|(3x^2 - 3x - 5) + 3| + 1) - 5) + 2)/(2(-4(-2|(3x^2 - 3x - 5) + 3| + 1) - 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": "Determine the total count of local extrema points for the function f(x) = 5(5(-1|x| + 2) + 4)^2 + 5(5(-1|x| + 2) + 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": "How many local minima does the function f(x) = 3|(3sin(3\u03c0(-5x - 5) + 2) - 3)| have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "150", "dataset": "MATH"} |
| {"messages": [{"content": "Find the total number of local minima and maxima for f(x) = (-3(1cos(3\u03c0(-5x^2 + 3x + 2) - 3) + 3) - 3)/(-2(1cos(3\u03c0(-5x^2 + 3x + 2) - 3) + 3) - 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "321", "dataset": "MATH"} |
| {"messages": [{"content": "Find the total number of local minima and maxima for f(x) = (-1(4(-1cos(2\u03c0x + 1) - 1) - 5) + 3)/(-3(4(-1cos(2\u03c0x + 1) - 1) - 5) + 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 minimum points for f(x) = -3(2cos(2\u03c0(-5x^2 - 4x + 3) + 1)) - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "249", "dataset": "MATH"} |
| {"messages": [{"content": "Find the number of local maximum points for f(x) = -1(-3|(1(-1cos(2\u03c0x + 2) + 2)^2 + 5(-1cos(2\u03c0x + 2) + 2) + 2) + 3| - 2) - 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"} |
| {"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 3|((-2(-3(3x^2 + 5x - 4)) - 3)/(1(-3(3x^2 + 5x - 4)) - 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": "Determine the count of local maxima for the function f(x) = 3e^(1((-3(2x + 1) - 3)/(-3(2x + 1) + 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) = 1(2|(-2cos(2\u03c0((-1x + 1)/(-3x + 2))) + 1) + 3| - 1)^2 + 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) = 1(-1sin(1\u03c0(3|(2x - 3) + 1| + 2) - 3) + 2)^2 - 4(-1sin(1\u03c0(3|(2x - 3) + 1| + 2) - 3) + 2) + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "121", "dataset": "MATH"} |
| {"messages": [{"content": "How many local minima does the function f(x) = (2(-2cos(1\u03c0(-1x^2 + 5x + 4) + 2) + 2) + 3)/(2(-2cos(1\u03c0(-1x^2 + 5x + 4) + 2) + 2) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "108", "dataset": "MATH"} |
| {"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 2sin(3\u03c0(-3x^2 + 2x - 4)) - 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "534", "dataset": "MATH"} |
| {"messages": [{"content": "Find the number of local maximum points for f(x) = 2e^(1(2|(-3(2x^2 - 1x - 4) - 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": "Find the number of local minimum points for f(x) = -1|(-4(-1sin(1\u03c0x + 1) - 2) + 1) - 1| + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"} |
| {"messages": [{"content": "Find the number of local maximum points for f(x) = -1(-3((3(3|x - 3| - 2) + 1)/(-3(3|x - 3| - 2) - 3)) + 5)^2 + 2(-3((3(3|x - 3| - 2) + 1)/(-3(3|x - 3| - 2) - 3)) + 5) + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"} |
| {"messages": [{"content": "Determine the count of local maxima for the function f(x) = -3(-2sin(2\u03c0(1|x - 3| - 1) + 2) + 1) + 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21", "dataset": "MATH"} |
| {"messages": [{"content": "Determine the count of local maxima for the function f(x) = -2sin(2\u03c0(-1(-5((-1x + 3)/(-3x))^2 + 1) + 2)) + 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"} |
| {"messages": [{"content": "How many local maxima does the function f(x) = -2|(1cos(1\u03c0(1(-4x^2 + 3x - 1) + 1) - 1) - 3) + 1| + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "287", "dataset": "MATH"} |
| {"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -3(-2|(-1sin(3\u03c0x - 1) - 2) + 1| - 1)^2 - 5(-2|(-1sin(3\u03c0x - 1) - 2) + 1| - 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"} |
| {"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 2((1(-2(-1|x - 2| + 2) - 5) - 1)/(-2(-2(-1|x - 2| + 2) - 5) - 2))^2 - 3((1(-2(-1|x - 2| + 2) - 5) - 1)/(-2(-2(-1|x - 2| + 2) - 5) - 2)) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"} |
| {"messages": [{"content": "Determine the count of local maxima for the function f(x) = -2sin(1\u03c0(1(-2(-2|x - 1| - 1)^2 + 1(-2|x - 1| - 1) + 1) + 5) - 2) - 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "270", "dataset": "MATH"} |
| {"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 1|(-1((2(2sin(3\u03c0x + 3) + 1) - 2)/(1(2sin(3\u03c0x + 3) + 1) + 1)) + 4) + 3| - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"} |
| {"messages": [{"content": "Determine the count of local maxima for the function f(x) = 2(-1sin(3\u03c0(-1|x + 3|)) - 2)^2 - 1(-1sin(3\u03c0(-1|x + 3|)) - 2) - 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": "How many local minima does the function f(x) = -5(1cos(3\u03c0((-2x)/(1x + 1)) + 3) + 1) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "24", "dataset": "MATH"} |
| {"messages": [{"content": "Find the number of local minimum points for f(x) = 1cos(1\u03c0(-1(-3x^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": "287", "dataset": "MATH"} |
| {"messages": [{"content": "Find the number of local maximum points for f(x) = 2|(3sin(3\u03c0((-1(2x^2 + 2x - 2) - 1)/(-1(2x^2 + 2x - 2) + 3)) - 3) - 2) + 3| + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "69", "dataset": "MATH"} |
| {"messages": [{"content": "How many local minima does the function f(x) = 1sin(2\u03c0(-1|x + 2| + 1) - 2) - 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 minimum points for f(x) = 2(-2sin(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": "Determine the total count of local extrema points for the function f(x) = -3(2|((-2(-1sin(2\u03c0x + 3) - 2) + 1)/(1(-1sin(2\u03c0x + 3) - 2) + 2)) + 2| - 1)^2 - 5(2|((-2(-1sin(2\u03c0x + 3) - 2) + 1)/(1(-1sin(2\u03c0x + 3) - 2) + 2)) + 2| - 1) - 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(2cos(1\u03c0x - 1) + 1) + 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"} |
| {"messages": [{"content": "Find the number of local minimum points for f(x) = 3e^(1(2x^2 - 3x + 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": "Determine the count of local minima for the function f(x) = -3e^(-1(3|x|)) + 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) = -3cos(3\u03c0(1|x| + 3) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "61", "dataset": "MATH"} |
| {"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = -5(-1cos(1\u03c0(4x + 1) - 1) - 2)^2 + 3(-1cos(1\u03c0(4x + 1) - 1) - 2) - 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"} |
| {"messages": [{"content": "Find the total number of local minima and maxima for f(x) = 5(3sin(2\u03c0x + 1) - 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 total number of local minima and maxima for f(x) = -2(-1(-3sin(1\u03c0x))^2 + 4(-3sin(1\u03c0x))) - 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 total number of local minima and maxima for f(x) = -3cos(1\u03c0((3(-1|x + 1| + 1) - 1)/(-2(-1|x + 1| + 1))) + 2) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"} |
| {"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -4(-3sin(2\u03c0x + 1) - 3)^2 - 4(-3sin(2\u03c0x + 1) - 3) - 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"} |
| {"messages": [{"content": "Determine the count of local minima for the function f(x) = -5(-2|(-2sin(1\u03c0((1x)/(-2x + 1))) + 3) + 2| + 3) + 5 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"} |
| {"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -2|(5x^2 - 1x - 3) - 2| + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"} |
| {"messages": [{"content": "Find the number of local minimum points for f(x) = 2cos(1\u03c0(1|x + 1| - 1) + 3) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"} |
| {"messages": [{"content": "Find the number of local maximum points for f(x) = -2(-1|((-3(-3x - 5) + 2)/(-3(-3x - 5) - 3)) - 3|)^2 - 4(-1|((-3(-3x - 5) + 2)/(-3(-3x - 5) - 3)) - 3|) + 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) = 1|(-4(4(-1sin(3\u03c0x + 2) + 2)^2 + 5(-1sin(3\u03c0x + 2) + 2) + 4) - 2) + 1| - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"} |
| {"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = 3cos(3\u03c0(-3x^2 - 1x - 3) - 3) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "535", "dataset": "MATH"} |
| {"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 2cos(3\u03c0(-1|x| - 2) + 3) + 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "61", "dataset": "MATH"} |
| {"messages": [{"content": "Determine the count of local maxima for the function f(x) = 3cos(1\u03c0((2(2(-1x + 5)^2 + 3(-1x + 5) - 4) + 3)/(-1(2(-1x + 5)^2 + 3(-1x + 5) - 4) - 3))) + 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"} |
| {"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 1(1(-1|(2cos(2\u03c0x + 1) + 2) - 1| - 3) + 3)^2 - 3(1(-1|(2cos(2\u03c0x + 1) + 2) - 1| - 3) + 3) + 4 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"} |
| {"messages": [{"content": "Determine the count of local minima for the function f(x) = -5(1cos(3\u03c0x - 2) + 2) + 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"} |
| {"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 2|(-3cos(2\u03c0x) + 3) + 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": "How many local minima does the function f(x) = -1|(-3cos(3\u03c0((1(1x + 4))/(-3(1x + 4) - 1)) - 1) - 1) - 3| have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"} |
| {"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = -4(2cos(1\u03c0(5(2|x + 2| + 2) + 2) + 1))^2 + 1(2cos(1\u03c0(5(2|x + 2| + 2) + 2) + 1)) + 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "401", "dataset": "MATH"} |
| {"messages": [{"content": "How many local minima does the function f(x) = 3sin(1\u03c0(1(3((-2x)/(1x + 1))^2 - 4((-2x)/(1x + 1)) + 3) - 3) + 3) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "46", "dataset": "MATH"} |
| {"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -1|(1(-2e^(-2(2x + 4)) - 1)^2 + 5(-2e^(-2(2x + 4)) - 1) + 5) - 1| + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"} |
| {"messages": [{"content": "Determine the count of local minima for the function f(x) = 1sin(2\u03c0(-4x^2 - 1x - 1) - 3) + 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "265", "dataset": "MATH"} |
| {"messages": [{"content": "Find the number of local maximum points for f(x) = 3cos(3\u03c0(-3|x - 2| - 3) - 2) - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "91", "dataset": "MATH"} |
| {"messages": [{"content": "Find the number of local maximum points for f(x) = 1|(-4(2e^(1(3x^2 - 2x - 5)) - 3) + 3) - 3| - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"} |
| {"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 2cos(2\u03c0(-5x + 5) + 1) + 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "200", "dataset": "MATH"} |
| {"messages": [{"content": "How many local minima does the function f(x) = 1cos(3\u03c0(5(3|((2x + 2)/(3x - 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": "60", "dataset": "MATH"} |
| {"messages": [{"content": "Determine the total count of local extrema points for the function f(x) = 3(3e^(-1(5x^2 + 1x + 2)) - 2) - 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"} |
| {"messages": [{"content": "Find the number of local maximum points for f(x) = 1|(1cos(3\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": "30", "dataset": "MATH"} |
| {"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -1|(-3e^(-2((-3x)/(-3x - 2))) + 2) + 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(4(2|((-1x - 1)/(2x - 1)) - 3| - 1) - 3)^2 - 3(4(2|((-1x - 1)/(2x - 1)) - 3| - 1) - 3) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"} |
| {"messages": [{"content": "How many local maxima does the function f(x) = 1cos(3\u03c0(2|x + 2| - 1) - 1) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"} |
| {"messages": [{"content": "How many local maxima does the function f(x) = -1|(3sin(1\u03c0((3(1x + 3))/(1(1x + 3) + 1)) - 1) - 2) - 2| + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"} |
| {"messages": [{"content": "Find the number of local minimum points for f(x) = 1e^(-2(-1|(2x^2 - 4) + 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 minima does the function f(x) = -3|(4x^2 - 4x + 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 maxima for the function f(x) = -2|(1cos(1\u03c0(-3x^2 + 5x + 3) - 1) - 2) + 1| in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "283", "dataset": "MATH"} |
| {"messages": [{"content": "Find the number of local maximum points for f(x) = (3(1cos(3\u03c0x + 2) + 2) + 1)/(1(1cos(3\u03c0x + 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": "How many local maxima does the function f(x) = -4(-1|(2((3x - 2)/(-1x + 2))^2 + 5((3x - 2)/(-1x + 2)) - 1) + 2| - 2) - 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": "Find the number of local minimum points for f(x) = 3(3|((1(-1cos(1\u03c0x - 3) + 1) + 2)/(3(-1cos(1\u03c0x - 3) + 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": "10", "dataset": "MATH"} |
| {"messages": [{"content": "Determine the count of local maxima for the function f(x) = 2(2cos(2\u03c0x) - 2) - 5 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19", "dataset": "MATH"} |
| {"messages": [{"content": "Find the total number of local minima and maxima for f(x) = -1|(3(1e^(-2((2x - 3)/(-2x - 1))) - 2)^2 + 1(1e^(-2((2x - 3)/(-2x - 1))) - 2) - 2) + 1| - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"} |
| {"messages": [{"content": "How many local extrema (minima and maxima combined) does the function f(x) = (2(4(-3sin(2\u03c0(-2|x| + 1) + 3) - 2)^2 + 5(-3sin(2\u03c0(-2|x| + 1) + 3) - 2) + 3) - 1)/(-1(4(-3sin(2\u03c0(-2|x| + 1) + 3) - 2)^2 + 5(-3sin(2\u03c0(-2|x| + 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": "161", "dataset": "MATH"} |
| {"messages": [{"content": "Determine the count of local maxima for the function f(x) = -2cos(3\u03c0(1|x + 2| + 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": "How many local extrema (minima and maxima combined) does the function f(x) = (2(-3|(-1cos(2\u03c0(2x) - 1) + 3) - 2| - 2) - 3)/(2(-3|(-1cos(2\u03c0(2x) - 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": "80", "dataset": "MATH"} |
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