


"""simple docstring"""
SCREAMING_SNAKE_CASE					:       List[Any]							   =							1000






def 						lowercase				(	_snake_case		: float	)	->float:
	"""simple docstring"""





	return x * x






def 						lowercase				(	_snake_case		: Union[str, Any]	,  _snake_case		: float	,  _snake_case		: float	,  _snake_case		: int = 4	)	->float:
	"""simple docstring"""





	assert callable(
	    _snake_case	), f"""the function(object) passed should be callable your input : {function}"""
	assert isinstance(_snake_case	,  (float, int)	), f"""a should be float or integer your input : {a}"""
	assert isinstance(function(_snake_case	)	,  (float, int)	), (
	    "the function should return integer or float return type of your function, "
	    f"""{type(_snake_case	)}"""
	)
	assert isinstance(_snake_case	,  (float, int)	), f"""b should be float or integer your input : {b}"""
	assert (
	    isinstance(_snake_case	,  _snake_case	) and precision > 0
	), f"""precision should be positive integer your input : {precision}"""

	# just applying the formula of simpson for approximate integration written in
	# mentioned article in first comment of this file and above this function

	__snake_case      :		Tuple         =							(b - a) / N_STEPS
	__snake_case      :		Union[str, Any]         =							function(_snake_case	) + function(_snake_case	)

	for i in range(1	,  _snake_case	):
		__snake_case      :		List[str]         =							a + h * i
		result += function(_snake_case	) * (4 if i % 2 else 2)

	result *= h / 3
	return round(_snake_case	,  _snake_case	)


if __name__ == "__main__":
			import doctest

			doctest.testmod()









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

import math
import random






def 						lowercase				(	_snake_case		: int	,  _snake_case		: int	,  _snake_case		: int	)	->list[int]:
	"""simple docstring"""





	__snake_case      :		Tuple         =							d * e - 1
	__snake_case      :		List[str]         =							0
	__snake_case      :		Dict         =							0
	while p == 0:
		__snake_case      :		str         =							random.randint(2	,  n - 1	)
		__snake_case      :		int         =							k
		while True:
			if t % 2 == 0:
				__snake_case      :		int         =							t // 2
				__snake_case      :		int         =							(g**t) % n
				__snake_case      :		Optional[Any]         =							math.gcd(x - 1	,  _snake_case	)
				if x > 1 and y > 1:
					__snake_case      :		Tuple         =							y
					__snake_case      :		int         =							n // y
					break  # find the correct factors
			else:
				break  # t is not divisible by 2, break and choose another g
	return sorted([p, q]	)


if __name__ == "__main__":
			import doctest

			doctest.testmod()





