

from __future__ import annotations

from collections.abc import Callable

def      snake_case__      (   SCREAMING_SNAKE_CASE_		:   Callable[[int | float], int | float]     ,					SCREAMING_SNAKE_CASE_		:   int | float     ,					SCREAMING_SNAKE_CASE_		:   int | float     ,					SCREAMING_SNAKE_CASE_		:   int = 100     ,					):



     '''simple docstring'''





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


if __name__ == "__main__":

       def      snake_case__      (   SCREAMING_SNAKE_CASE_		:   Tuple      ):



            '''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:''')
       snake_case_        =			10
       while i <= 100_000:
              print(F'''with {i} steps: {trapezoidal_area(f, -5, 5, i)}''')
              i *= 10




from __future__ import annotations

import math

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

def      snake_case__      (   SCREAMING_SNAKE_CASE_		:   int      ):



     '''simple docstring'''





     lowercase__   :       int				=	str(SCREAMING_SNAKE_CASE_      )
     lowercase__   :       Union[str, Any]				=	[n]
     for i in range(1     ,					len(SCREAMING_SNAKE_CASE_      )      ):
          list_nums.append(int(str_num[i:]      )      )
          list_nums.append(int(str_num[:-i]      )      )
     return list_nums

def      snake_case__      (   SCREAMING_SNAKE_CASE_		:   int      ):



     '''simple docstring'''





     if len(str(SCREAMING_SNAKE_CASE_      )      ) > 3:
          if not is_prime(int(str(SCREAMING_SNAKE_CASE_      )[-3:]      )      ) or not is_prime(int(str(SCREAMING_SNAKE_CASE_      )[:3]      )      ):
               return False
     return True

def      snake_case__      (   SCREAMING_SNAKE_CASE_		:   int = 11      ):



     '''simple docstring'''





     lowercase__   :       list[int]				=	[]
     lowercase__   :       Tuple				=	13
     while len(SCREAMING_SNAKE_CASE_      ) != count:
          if validate(SCREAMING_SNAKE_CASE_      ):
               lowercase__   :       Optional[int]				=	list_truncated_nums(SCREAMING_SNAKE_CASE_      )
               if all(is_prime(SCREAMING_SNAKE_CASE_      ) for i in list_nums      ):
                    list_truncated_primes.append(SCREAMING_SNAKE_CASE_      )
          num += 2
     return list_truncated_primes

def      snake_case__      (   ):



     '''simple docstring'''





     return sum(compute_truncated_primes(11      )      )


if __name__ == "__main__":
       print(F'''{sum(compute_truncated_primes(11)) = }''')

