



"""simple docstring"""






def     _lowercase       (						__snake_case			):
			if not isinstance(__snake_case      ,__snake_case			):
						raise ValueError("Input series is not valid, valid series - [2, 4, 6]"			)
			if len(__snake_case			) == 0:
						raise ValueError("Input list must be a non empty list"			)
			if len(__snake_case			) == 1:
						return True
			__lowerCAmelCase   :						Union[str, Any]				= series[1] - series[0]
			for index in range(len(__snake_case			) - 1			):
						if series[index + 1] - series[index] != common_diff:
									return False
			return True


def     _lowercase       (						__snake_case			):
			if not isinstance(__snake_case      ,__snake_case			):
						raise ValueError("Input series is not valid, valid series - [2, 4, 6]"			)
			if len(__snake_case			) == 0:
						raise ValueError("Input list must be a non empty list"			)
			__lowerCAmelCase   :						Tuple				= 0
			for val in series:
						answer += val
			return answer / len(__snake_case			)


if __name__ == "__main__":
	import doctest

	doctest.testmod()




"""simple docstring"""






import math


def     _lowercase       (						__snake_case      ,__snake_case			)		->     float:
			return math.pow(__snake_case      ,2			) - a


def     _lowercase       (						__snake_case			)		->     float:
			return 2 * x


def     _lowercase       (						__snake_case			)		->     float:
			__lowerCAmelCase   :						List[str]				= 2.0

			while start <= a:
						__lowerCAmelCase   :						Union[str, Any]				= math.pow(__snake_case      ,2			)

			return start


def     _lowercase       (						__snake_case      ,__snake_case = 9_999      ,__snake_case = 0.00000000000001			)		->     float:

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

			__lowerCAmelCase   :						List[Any]				= get_initial_point(__snake_case			)

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

			return value


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

	testmod()