



'''simple docstring'''




import math



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



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



def    __lowerCamelCase						(      _lowercase	)   ->    float:
							UpperCAmelCase  :	List[Any]							  =	2.0

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

							return start



def    __lowerCamelCase						(      _lowercase			,       _lowercase = 9_9_9_9			,       _lowercase = 0.00_0000_0000_0001	)   ->    float:

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

							UpperCAmelCase  :	List[str]							  =	get_initial_point(_lowercase	)

							for _ in range(_lowercase	):
														UpperCAmelCase  :	List[Any]							  =	value
														UpperCAmelCase  :	Tuple							  =	value - fx(_lowercase			,       _lowercase	) / fx_derivative(_lowercase	)
														if abs(prev_value - value	) < tolerance:
																					return value

							return value


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

							testmod()






'''simple docstring'''




import math



def    __lowerCamelCase						(      _lowercase	)   ->    bool:
							assert isinstance(_lowercase			,       _lowercase	) and (
							    number >= 0
							), "'number' must been an int and positive"

							if 1 < number < 4:
														# 2 and 3 are primes
														return True
							elif number < 2 or not number % 2:
														# Negatives, 0, 1 and all even numbers are not primes
														return False

							UpperCAmelCase  :	str							  =	range(3			,       int(math.sqrt(_lowercase	) + 1	)			,       2	)
							return not any(not number % i for i in odd_numbers	)



def    __lowerCamelCase						(      _lowercase			,       _lowercase=1			,       **_lowercase	)   ->    Union[str, Any]:
							UpperCAmelCase  :	Optional[int]							  =	factor * value
							UpperCAmelCase  :	List[Any]							  =	value

							while not is_prime(_lowercase	):
														value += 1 if not ("desc" in kwargs and kwargs["desc"] is True) else -1

							if value == first_value_val:
														return next_prime(value + 1			,       **_lowercase	)
							return value

