

'''simple docstring'''
from __future__ import annotations

from collections.abc import Callable


def  a__       (    _SCREAMING_SNAKE_CASE   :       Callable[[int | float], int | float]	,				_SCREAMING_SNAKE_CASE   :       int | float	,				_SCREAMING_SNAKE_CASE   :       int | float	,				_SCREAMING_SNAKE_CASE   :       int = 1_00	,				)     ->					float:


	"""simple docstring"""





	UpperCAmelCase_     :      Optional[int]						=  x_start
	UpperCAmelCase_     :      Optional[Any]						=  fnc(_SCREAMING_SNAKE_CASE				)
	UpperCAmelCase_     :      List[Any]						=  0.0
	for _ in range(_SCREAMING_SNAKE_CASE				):
		# Approximates small segments of curve as linear and solve
		# for trapezoidal area
		UpperCAmelCase_     :      int						=  (x_end - x_start) / steps + xa
		UpperCAmelCase_     :      str						=  fnc(_SCREAMING_SNAKE_CASE				)
		area += abs(fxa + fxa				) * (xa - xa) / 2
		# Increment step
		UpperCAmelCase_     :      Any						=  xa
		UpperCAmelCase_     :      List[Any]						=  fxa
	return area


if __name__ == "__main__":


					def  a__       (    _SCREAMING_SNAKE_CASE   :       Any				)     ->					int:


						"""simple docstring"""





						return x**3 + x**2

					print("""f(x) = x^3 + x^2""")
					print("""The area between the curve, x = -5, x = 5 and the x axis is:""")
					_lowerCamelCase      					=     10
					while i <= 10_0000:
										print(f"""with {i} steps: {trapezoidal_area(f, -5, 5, i)}""")
										i *= 10











from math import sqrt
def      A__       (    SCREAMING_SNAKE_CASE_   :      int						)  ->  bool:






   """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(sqrt(SCREAMING_SNAKE_CASE_						) + 1						)				,	6						):
      if number % i == 0 or number % (i + 2) == 0:
         return False
   return True
def      A__       (    SCREAMING_SNAKE_CASE_   :      int = 1_00_01						)  ->  int:






   """simple docstring"""







   _UpperCAmelCase           =   0
   _UpperCAmelCase           =   1
   while count != nth and number < 3:
      number += 1
      if is_prime(SCREAMING_SNAKE_CASE_						):
         count += 1
   while count != nth:
      number += 2
      if is_prime(SCREAMING_SNAKE_CASE_						):
         count += 1
   return number


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