



"""simple docstring"""






lowerCamelCase				:     List[Any]								=  1_0_0_0


def 							A__ (     UpperCamelCase__    ):


  '''simple docstring'''


  return x * x


def 							A__ (     UpperCamelCase__       ,							UpperCamelCase__       ,							UpperCamelCase__       ,							UpperCamelCase__ = 4    ):


  '''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

  _SCREAMING_SNAKE_CASE        =			(b - a) / N_STEPS
  _SCREAMING_SNAKE_CASE        =			function(_snake_case    ) + function(_snake_case    )

  for i in range(1       ,							_snake_case    ):
    _SCREAMING_SNAKE_CASE        =			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()





