
'''simple docstring'''
from itertools import count
from math import asin, pi, sqrt







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







def 						A_(			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 						A_(			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() = }""")












import re


def      lowerCamelCase__	(   lowercase ):

  """simple docstring"""






  def docstring_decorator(lowercase ):
    SCREAMING_SNAKE_CASE				:					List[Any]		  =			fn.__doc__
    SCREAMING_SNAKE_CASE				:					Tuple		  =			func_doc.split("\n" )
    SCREAMING_SNAKE_CASE				:					Tuple		  =			0
    while i < len(lowercase ) and re.search(R"^\s*Examples?:\s*$"  ,   lines[i] ) is None:
      i += 1
    if i < len(lowercase ):
      SCREAMING_SNAKE_CASE				:					int		  =			example_docstring
      SCREAMING_SNAKE_CASE				:					Tuple		  =			"\n".join(lowercase )
    else:
      raise ValueError(
          F'''The function {fn} should have an empty \'Examples:\' in its docstring as placeholder, '''
          F'''current docstring is:\n{func_doc}''' )
    SCREAMING_SNAKE_CASE				:					int		  =			func_doc
    return fn

  return docstring_decorator






