
_A       =					10_00






def        lowerCamelCase__    (    __lowerCAmelCase  :  Optional[int]    ):




			"""simple docstring"""


			return x * x






def        lowerCamelCase__    (    __lowerCAmelCase  :  List[Any]   ,							__lowerCAmelCase  :  Any   ,							__lowerCAmelCase  :  Union[str, Any]   ,							__lowerCAmelCase  :  List[str] = 4    ):




			"""simple docstring"""


			assert callable(
			    SCREAMING_SNAKE_CASE_    ), F"""the function(object) passed should be callable your input : {function}"""
			assert isinstance(SCREAMING_SNAKE_CASE_   ,							(float, int)    ), F"""a should be float or integer your input : {a}"""
			assert isinstance(function(SCREAMING_SNAKE_CASE_    )   ,							(float, int)    ), (
			    "the function should return integer or float return type of your function, "
			    F"""{type(SCREAMING_SNAKE_CASE_    )}"""
			)
			assert isinstance(SCREAMING_SNAKE_CASE_   ,							(float, int)    ), F"""b should be float or integer your input : {b}"""
			assert (
			    isinstance(SCREAMING_SNAKE_CASE_   ,							SCREAMING_SNAKE_CASE_    ) and precision > 0
			), F"""precision should be positive integer your input : {precision}"""

			# just applying the formula of simpson for approximate integration written in
			# mentioned article in first comment of this file and above this function

			lowerCAmelCase_      =     (b - a) / N_STEPS
			lowerCAmelCase_      =     function(SCREAMING_SNAKE_CASE_    ) + function(SCREAMING_SNAKE_CASE_    )

			for i in range(1   ,							SCREAMING_SNAKE_CASE_    ):
						lowerCAmelCase_      =     a + h * i
						result += function(SCREAMING_SNAKE_CASE_    ) * (4 if i % 2 else 2)

			result *= h / 3
			return round(SCREAMING_SNAKE_CASE_   ,							SCREAMING_SNAKE_CASE_    )


if __name__ == "__main__":
			import doctest

			doctest.testmod()





import math






def        lowerCamelCase__    (    __lowerCAmelCase  :  int    ):




			"""simple docstring"""


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

			# All primes number are in format of 6k +/- 1
			for i in range(5   ,							int(math.sqrt(__lowerCAmelCase    ) + 1    )   ,							6    ):
						if number % i == 0 or number % (i + 2) == 0:
									return False
			return True






def        lowerCamelCase__    (    __lowerCAmelCase  :  int = 600851475143    ):




			"""simple docstring"""


			try:
						lowerCAmelCase_      =     int(__lowerCAmelCase    )
			except (TypeError, ValueError):
						raise TypeError("Parameter n must be int or castable to int."    )
			if n <= 0:
						raise ValueError("Parameter n must be greater than or equal to one."    )
			lowerCAmelCase_      =     0
			if is_prime(__lowerCAmelCase    ):
						return n
			while n % 2 == 0:
						n //= 2
			if is_prime(__lowerCAmelCase    ):
						return n
			for i in range(3   ,							int(math.sqrt(__lowerCAmelCase    )    ) + 1   ,							2    ):
						if n % i == 0:
									if is_prime(n // i    ):
												lowerCAmelCase_      =     n // i
												break
									elif is_prime(__lowerCAmelCase    ):
												lowerCAmelCase_      =     i
			return max_number


if __name__ == "__main__":
			print(f"""{solution() = }""")



