





"""simple docstring"""





from __future__ import annotations

from collections.abc import Callable




def 		lowerCAmelCase_	(  lowercase_   :							Callable[[int | float], int | float] ,      lowercase_   :							int | float ,      lowercase_   :							int | float ,      lowercase_   :							int = 100 ,      ):

 '''simple docstring'''






 __SCREAMING_SNAKE_CASE :			List[str]												=       x_start
 __SCREAMING_SNAKE_CASE :			List[str]												=       fnc(lowercase_		)
 __SCREAMING_SNAKE_CASE :			Any												=       0.0

 for _ in range(lowercase_		):
  # Approximates small segments of curve as linear and solve
  # for trapezoidal area
  __SCREAMING_SNAKE_CASE :			Optional[Any]												=       (x_end - x_start) / steps + xa
  __SCREAMING_SNAKE_CASE :			Union[str, Any]												=       fnc(lowercase_		)
  area += abs(fxa + fxa		) * (xa - xa) / 2

  # Increment step
  __SCREAMING_SNAKE_CASE :			Tuple												=       xa
  __SCREAMING_SNAKE_CASE :			str												=       fxa
 return area


if __name__ == "__main__":




    def 		lowerCAmelCase_	(  lowercase_   :							List[Any]		):

     '''simple docstring'''






     return x**3

    print('''f(x) = x^3''')
    print('''The area between the curve, x = -10, x = 10 and the x axis is:''')
    _lowerCamelCase       =	10
    while i <= 10_00_00:
        _lowerCamelCase       =	trapezoidal_area(f, -5, 5, i)
        print(f'with {i} steps: {area}')
        i *= 10








"""simple docstring"""





import math




def 		lowerCAmelCase_	(  lowercase_   :							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(lowercase_		) + 1		) ,      6		):
  if number % i == 0 or number % (i + 2) == 0:
   return False
 return True




def 		lowerCAmelCase_	(  lowercase_   :							int = 6008_5147_5143		):

 '''simple docstring'''






 try:
  __SCREAMING_SNAKE_CASE :			Any												=       int(lowercase_		)
 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.'''		)
 __SCREAMING_SNAKE_CASE :			List[str]												=       0
 if is_prime(lowercase_		):
  return n
 while n % 2 == 0:
  n //= 2
 if is_prime(lowercase_		):
  return n
 for i in range(3 ,      int(math.sqrt(lowercase_		)		) + 1 ,      2		):
  if n % i == 0:
   if is_prime(n // i		):
    __SCREAMING_SNAKE_CASE :			Optional[int]												=       n // i
    break
   elif is_prime(lowercase_		):
    __SCREAMING_SNAKE_CASE :			Any												=       i
 return max_number


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

