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




def 				lowerCamelCase__				(						a__  :  float     ):
       return (
           (1 - 2 * point) * sqrt(point - point**2     ) + 2 * point + asin(sqrt(1 - point     )     )
       ) / 4




def 				lowerCamelCase__				(						a__  :  int     ):
       UpperCamelCase_							       =       (circles_number + 1 - sqrt(2 * circles_number     )) / (
           2 * (circles_number**2 + 1)
       )
       UpperCamelCase_							       =       circles_number * intersection_y

       UpperCamelCase_							       =       intersection_x * intersection_y / 2
       UpperCamelCase_							       =       circle_bottom_arc_integral(
           1 / 2     ) - circle_bottom_arc_integral(a__     )

       return triangle_area + concave_region_area




def 				lowerCamelCase__				(						a__  :  float = 1 / 1000     ):
       UpperCamelCase_							       =       (1 - pi / 4) / 4

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

       return -1


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





def 				lowerCamelCase__				(						a__  :  float	,      a__  :  float	,      a__  :  float     )		->	float:
       if mass < 0:
              raise ValueError("""The mass of the body cannot be negative"""     )
       if radius <= 0:
              raise ValueError("""The radius is always a positive non zero integer"""     )
       return (mass * (velocity) ** 2) / radius


if __name__ == "__main__":
      import doctest

      doctest.testmod(verbose=True)



