






import numpy as np



def 					_lowerCamelCase(			lowerCAmelCase__				:		np.array      ):





				'''simple docstring'''







				return 1 / (1 + np.exp(-vector      ))


if __name__ == "__main__":
				import doctest

				doctest.testmod()







import math



def 					_lowerCamelCase(			lowerCAmelCase__				:		float    ,    lowerCAmelCase__				:		float      ):





				'''simple docstring'''







				return math.pow(lowerCAmelCase__    ,    2      ) - a



def 					_lowerCamelCase(			lowerCAmelCase__				:		float      ):





				'''simple docstring'''







				return 2 * x



def 					_lowerCamelCase(			lowerCAmelCase__				:		float      ):





				'''simple docstring'''







				SCREAMING_SNAKE_CASE_   :	Optional[Any]													=   2.0

				while start <= a:
								SCREAMING_SNAKE_CASE_   :	str													=   math.pow(lowerCAmelCase__    ,    2      )

				return start



def 					_lowerCamelCase(			lowerCAmelCase__				:		float    ,    lowerCAmelCase__				:		int = 9999    ,    lowerCAmelCase__				:		float = 0.00_000_000_000_001      ):





				'''simple docstring'''







				if a < 0:
								raise ValueError('math domain error'      )

				SCREAMING_SNAKE_CASE_   :	Optional[int]													=   get_initial_point(lowerCAmelCase__      )

				for _ in range(lowerCAmelCase__      ):
								SCREAMING_SNAKE_CASE_   :	Tuple													=   value
								SCREAMING_SNAKE_CASE_   :	Union[str, Any]													=   value - fx(lowerCAmelCase__    ,    lowerCAmelCase__      ) / fx_derivative(lowerCAmelCase__      )
								if abs(prev_value - value      ) < tolerance:
												return value

				return value


if __name__ == "__main__":
				from doctest import testmod

				testmod()