


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




def   snake_case_	(    snake_case	)    ->							float:
       return (
           (1 - 2 * point) * sqrt(point - point**2	) + 2 * point + asin(sqrt(1 - point	)	)
       ) / 4




def   snake_case_	(    snake_case	)    ->							float:
       lowercase__:  Optional[Any]         =  (circles_number + 1 - sqrt(2 * circles_number	)) / (
           2 * (circles_number**2 + 1)
       )
       lowercase__:  Optional[int]         =  circles_number * intersection_y

       lowercase__:  Union[str, Any]         =  intersection_x * intersection_y / 2
       lowercase__:  Any         =  circle_bottom_arc_integral(
           1 / 2	) - circle_bottom_arc_integral(snake_case	)

       return triangle_area + concave_region_area




def   snake_case_	(    snake_case = 1 / 10_00	)    ->							int:
       lowercase__:  str         =  (1 - pi / 4) / 4

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

       return -1


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






def   snake_case_	(    snake_case	)    ->							str:
       lowercase__:  Optional[Any]         =  1
       lowercase__:  Optional[Any]         =  0
       lowercase__:  int         =  1
       lowercase__:  Any         =  1
       lowercase__:  Optional[Any]         =  3
       lowercase__:  List[str]         =  3
       lowercase__:  Optional[Any]         =  limit
       lowercase__:  List[Any]         =  0

       lowercase__:  int         =  ''
       while counter != decimal + 1:
              if 4 * q + r - t < n * t:
                     result += str(snake_case	)
                     if counter == 0:
                            result += "."

                     if decimal == counter:
                            break

                     counter += 1
                     lowercase__:  List[Any]         =  10 * (r - n * t)
                     lowercase__:  int         =  ((10 * (3 * q + r)) // t) - 10 * n
                     q *= 10
                     lowercase__:  Any         =  nr
              else:
                     lowercase__:  List[str]         =  (2 * q + r) * l
                     lowercase__:  Tuple         =  (q * (7 * k) + 2 + (r * l)) // (t * l)
                     q *= k
                     t *= l
                     l += 2
                     k += 1
                     lowercase__:  Dict         =  nn
                     lowercase__:  Optional[int]         =  nr
       return result




def   snake_case_	(    )    ->							None:
       print(f'{calculate_pi(50	) = }'	)
       import doctest

       doctest.testmod()


if __name__ == "__main__":
 main()


