






"""simple docstring"""
import math

from numpy import inf
from scipy.integrate import quad

def        snake_case   (     A__		):
			if num <= 0:
						raise ValueError("math domain error"		)

			return quad(A__			,0			,A__			,args=(A__)		)[0]

def        snake_case   (     A__			,A__		):
			return math.pow(A__			,z - 1		) * math.exp(-x		)


if __name__ == "__main__":
						from doctest import testmod

						testmod()











"""simple docstring"""
from __future__ import annotations

import math

def        snake_case   (     A__		):

			if 1 < number < 4:
						# 2 and 3 are primes
						return True
			elif number < 2 or number % 2 == 0 or number % 3 == 0:
						# Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
						return False

			# All primes number are in format of 6k +/- 1
			for i in range(5			,int(math.sqrt(A__		) + 1		)			,6		):
						if number % i == 0 or number % (i + 2) == 0:
									return False
			return True


lowerCamelCase_       			=   [num for num in range(3, 10_0001, 2) if not is_prime(num)]

def        snake_case   (     A__		):
			if not isinstance(A__			,A__		):
						raise ValueError("n must be an integer"		)
			if n <= 0:
						raise ValueError("n must be >= 0"		)

			UpperCAmelCase_  :				List[str]      =      []
			for num in range(len(A__		)		):
						UpperCAmelCase_  :				Dict      =      0
						while 2 * i * i <= odd_composites[num]:
									UpperCAmelCase_  :				List[str]      =      odd_composites[num] - 2 * i * i
									if is_prime(A__		):
												break
									i += 1
						else:
									list_nums.append(odd_composites[num]		)
									if len(A__		) == n:
												return list_nums

			return []

def        snake_case   (     ):
			return compute_nums(1		)[0]


if __name__ == "__main__":
			print(f'{solution() = }')



