"""simple docstring"""







from itertools import count
from math import asin, pi, sqrt




def 						_lowercase				(  _SCREAMING_SNAKE_CASE				:				str						)    ->     float:







     '''simple docstring'''


     return (
         (1 - 2 * point) * sqrt(point - point**2						) + 2 * point + asin(sqrt(1 - point						)						)
     ) / 4




def 						_lowercase				(  _SCREAMING_SNAKE_CASE				:				Optional[Any]						)    ->     float:







     '''simple docstring'''


     __A					:					int								=		(circles_number + 1 - sqrt(2 * circles_number						)) / (
         2 * (circles_number**2 + 1)
     )
     __A					:					Optional[int]								=		circles_number * intersection_y

     __A					:					Dict								=		intersection_x * intersection_y / 2
     __A					:					str								=		circle_bottom_arc_integral(
         1 / 2						) - circle_bottom_arc_integral(_SCREAMING_SNAKE_CASE						)

     return triangle_area + concave_region_area




def 						_lowercase				(  _SCREAMING_SNAKE_CASE				:				str = 1 / 1000						)    ->     int:







     '''simple docstring'''


     __A					:					Optional[Any]								=		(1 - pi / 4) / 4

     for n in count(1						):
          if concave_triangle_area(_SCREAMING_SNAKE_CASE						) / l_section_area < fraction:
               return n

     return -1


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






def 						_snake_case		(     SCREAMING_SNAKE_CASE		,				SCREAMING_SNAKE_CASE		,				SCREAMING_SNAKE_CASE					)							->   Optional[int]:

     """simple docstring"""







     if power < 0:
          return -1
     base %= mod
     _lowerCAmelCase :       Tuple	   =     1

     while power > 0:
          if power & 1:
               _lowerCAmelCase :       Optional[Any]	   =     (result * base) % mod
          _lowerCAmelCase :       int	   =     power >> 1
          _lowerCAmelCase :       Optional[int]	   =     (base * base) % mod

     return result







def 						_snake_case		(     )							->   Optional[int]:

     """simple docstring"""







     print(modular_exponential(3		,				200		,				13					)					)


if __name__ == "__main__":
  import doctest

  doctest.testmod()

  main()






