
def 		lowerCAmelCase_     (     _SCREAMING_SNAKE_CASE      ,	_SCREAMING_SNAKE_CASE  )   ->      Tuple:

							"""simple docstring"""






							_UpperCAmelCase  :			Any	       =		(boundary[1] - boundary[0]) / steps
							_UpperCAmelCase  :			Optional[Any]	       =		boundary[0]
							_UpperCAmelCase  :			Dict	       =		boundary[1]
							_UpperCAmelCase  :			Optional[Any]	       =		make_points(_SCREAMING_SNAKE_CASE      ,	_SCREAMING_SNAKE_CASE      ,	_SCREAMING_SNAKE_CASE  )
							_UpperCAmelCase  :			Optional[Any]	       =		0.0
							y += (h / 3.0) * f(_SCREAMING_SNAKE_CASE  )
							_UpperCAmelCase  :			str	       =		2
							for i in x_i:
														y += (h / 3) * (4 - 2 * (cnt % 2)) * f(_SCREAMING_SNAKE_CASE  )
														cnt += 1
							y += (h / 3.0) * f(_SCREAMING_SNAKE_CASE  )
							return y




def 		lowerCAmelCase_     (     _SCREAMING_SNAKE_CASE      ,	_SCREAMING_SNAKE_CASE      ,	_SCREAMING_SNAKE_CASE  )   ->      Dict:

							"""simple docstring"""






							_UpperCAmelCase  :			Tuple	       =		a + h
							while x < (b - h):
														yield x
														_UpperCAmelCase  :			List[Any]	       =		x + h




def 		lowerCAmelCase_     (     _SCREAMING_SNAKE_CASE  )   ->      Optional[int]:  # enter your function here

							"""simple docstring"""






							_UpperCAmelCase  :			List[Any]	       =		(x - 0) * (x - 0)
							return y




def 		lowerCAmelCase_     (     )   ->      Tuple:

							"""simple docstring"""






							_UpperCAmelCase  :			Optional[Any]	       =		0.0  # Lower bound of integration
							_UpperCAmelCase  :			Union[str, Any]	       =		1.0  # Upper bound of integration
							_UpperCAmelCase  :			List[Any]	       =		10.0  # define number of steps or resolution
							_UpperCAmelCase  :			Any	       =		[a, b]  # define boundary of integration
							_UpperCAmelCase  :			Tuple	       =		method_a(_SCREAMING_SNAKE_CASE      ,	_SCREAMING_SNAKE_CASE  )
							print(F"""y = {y}"""  )


if __name__ == "__main__":
				main()






import math




def 		lowerCAmelCase_     (     _SCREAMING_SNAKE_CASE  )   ->      list[int]:

							"""simple docstring"""






							if not isinstance(_SCREAMING_SNAKE_CASE      ,	_SCREAMING_SNAKE_CASE  ):
														_UpperCAmelCase  :			Optional[Any]	       =		F"""Input value of [number={number}] must be an integer"""
														raise TypeError(_SCREAMING_SNAKE_CASE  )
							if number < 1:
														_UpperCAmelCase  :			Dict	       =		F"""Input value of [number={number}] must be a positive integer"""
														raise ValueError(_SCREAMING_SNAKE_CASE  )
							_UpperCAmelCase  :			List[Any]	       =		[number]
							while number != 1:
														if number % 2 == 0:
																					_UpperCAmelCase  :			List[str]	       =		math.floor(math.sqrt(_SCREAMING_SNAKE_CASE  )  )
														else:
																					_UpperCAmelCase  :			Dict	       =		math.floor(
																					    math.sqrt(_SCREAMING_SNAKE_CASE  ) * math.sqrt(_SCREAMING_SNAKE_CASE  ) * math.sqrt(_SCREAMING_SNAKE_CASE  )  )
														sequence.append(_SCREAMING_SNAKE_CASE  )
							return sequence


if __name__ == "__main__":
				import doctest

				doctest.testmod()




