


from __future__ import annotations

from collections.abc import Callable
def 			__SCREAMING_SNAKE_CASE							(					lowercase__	:Callable[[int | float], int | float]   ,    lowercase__	:int | float   ,    lowercase__	:int | float   ,    lowercase__	:int = 1_0_0   ,    )							->	float:
						__magic_name__					:				str				=   x_start
						__magic_name__					:				str				=   fnc(lowercase__					)
						__magic_name__					:				Union[str, Any]				=   0.0

						for _ in range(lowercase__					):
												# Approximates small segments of curve as linear and solve
												# for trapezoidal area
												__magic_name__					:				Optional[int]				=   (x_end - x_start) / steps + xa
												__magic_name__					:				List[Any]				=   fnc(lowercase__					)
												area += abs(fxa + fxa					) * (xa - xa) / 2

												# Increment step
												__magic_name__					:				Optional[Any]				=   xa
												__magic_name__					:				Union[str, Any]				=   fxa
						return area


if __name__ == "__main__":
			def 			__SCREAMING_SNAKE_CASE							(					lowercase__	:Dict					)							->	Optional[int]:
									return x**3

			print('f(x) = x^3')
			print('The area between the curve, x = -10, x = 10 and the x axis is:')
			snake_case__  				=			10
			while i <= 10_0000:
						snake_case__  				=			trapezoidal_area(f, -5, 5, i)
						print(F"""with {i} steps: {area}""")
						i *= 10






import math
def 			__SCREAMING_SNAKE_CASE							(					lowercase__	:int					)							->	list:
						if n <= 0:
												raise ValueError('Only positive integers have prime factors'					)
						__magic_name__					:				Union[str, Any]				=   []
						while n % 2 == 0:
												pf.append(2					)
												__magic_name__					:				Union[str, Any]				=   int(n / 2					)
						for i in range(3   ,    int(math.sqrt(lowercase__					)					) + 1   ,    2					):
												while n % i == 0:
																		pf.append(lowercase__					)
																		__magic_name__					:				List[str]				=   int(n / i					)
						if n > 2:
												pf.append(lowercase__					)
						return pf
def 			__SCREAMING_SNAKE_CASE							(					lowercase__	:int					)							->	int:
						if n <= 0:
												raise ValueError('Only positive numbers are accepted'					)
						__magic_name__					:				Union[str, Any]				=   1
						__magic_name__					:				Tuple				=   1
						while n % 2 == 0:
												temp += 1
												__magic_name__					:				Any				=   int(n / 2					)
						div *= temp
						for i in range(3   ,    int(math.sqrt(lowercase__					)					) + 1   ,    2					):
												__magic_name__					:				List[Any]				=   1
												while n % i == 0:
																		temp += 1
																		__magic_name__					:				Any				=   int(n / i					)
												div *= temp
						if n > 1:
												div *= 2
						return div
def 			__SCREAMING_SNAKE_CASE							(					lowercase__	:int					)							->	int:
						if n <= 0:
												raise ValueError('Only positive numbers are accepted'					)
						__magic_name__					:				int				=   1
						__magic_name__					:				List[str]				=   1
						while n % 2 == 0:
												temp += 1
												__magic_name__					:				List[Any]				=   int(n / 2					)
						if temp > 1:
												s *= (2**temp - 1) / (2 - 1)
						for i in range(3   ,    int(math.sqrt(lowercase__					)					) + 1   ,    2					):
												__magic_name__					:				int				=   1
												while n % i == 0:
																		temp += 1
																		__magic_name__					:				Optional[Any]				=   int(n / i					)
												if temp > 1:
																		s *= (i**temp - 1) / (i - 1)
						return int(lowercase__					)
def 			__SCREAMING_SNAKE_CASE							(					lowercase__	:int					)							->	int:
						__magic_name__					:				Dict				=   n
						for x in set(prime_factors(lowercase__					)					):
												s *= (x - 1) / x
						return int(lowercase__					)


if __name__ == "__main__":
			import doctest

			doctest.testmod()


