



'''simple docstring'''



import math


def 							__UpperCAmelCase				(				UpperCamelCase__				:int			)		->						list[int]:
				if not isinstance(UpperCamelCase__   ,				UpperCamelCase__			):
								snake_case__      :   Dict      =    F'''Input value of [number={number}] must be an integer'''
								raise TypeError(UpperCamelCase__			)
				if number < 1:
								snake_case__      :   List[str]      =    F'''Input value of [number={number}] must be a positive integer'''
								raise ValueError(UpperCamelCase__			)
				snake_case__      :   List[Any]      =    [number]
				while number != 1:
								if number % 2 == 0:
												snake_case__      :   Tuple      =    math.floor(math.sqrt(UpperCamelCase__			)			)
								else:
												snake_case__      :   List[Any]      =    math.floor(
												    math.sqrt(UpperCamelCase__			) * math.sqrt(UpperCamelCase__			) * math.sqrt(UpperCamelCase__			)			)
								sequence.append(UpperCamelCase__			)
				return sequence


if __name__ == "__main__":
				import doctest

				doctest.testmod()






def 						A_			(				snake_case				: Union[str, Any]			,   snake_case				: Dict			)   ->     Dict:



						'''simple docstring'''

						__UpperCamelCase  	=      (boundary[1] - boundary[0]) / steps
						__UpperCamelCase  	=      boundary[0]
						__UpperCamelCase  	=      boundary[1]
						__UpperCamelCase  	=      make_points(snake_case			,   snake_case			,   snake_case			)
						__UpperCamelCase  	=      0.0
						y += (h / 3.0) * f(snake_case			)
						__UpperCamelCase  	=      2
						for i in x_i:
												y += (h / 3) * (4 - 2 * (cnt % 2)) * f(snake_case			)
												cnt += 1
						y += (h / 3.0) * f(snake_case			)
						return y




def 						A_			(				snake_case				: str			,   snake_case				: Optional[int]			,   snake_case				: Any			)   ->     Optional[int]:



						'''simple docstring'''

						__UpperCamelCase  	=      a + h
						while x < (b - h):
												yield x
												__UpperCamelCase  	=      x + h




def 						A_			(				snake_case				: Union[str, Any]			)   ->     str:  # enter your function here



						'''simple docstring'''

						__UpperCamelCase  	=      (x - 0) * (x - 0)
						return y




def 						A_			(				)   ->     Dict:



						'''simple docstring'''

						__UpperCamelCase  	=      0.0  # Lower bound of integration
						__UpperCamelCase  	=      1.0  # Upper bound of integration
						__UpperCamelCase  	=      10.0  # define number of steps or resolution
						__UpperCamelCase  	=      [a, b]  # define boundary of integration
						__UpperCamelCase  	=      method_a(snake_case			,   snake_case			)
						print(f"y = {y}"			)


if __name__ == "__main__":
				main()




