code: 
  
  
  
  
  
  from itertools import count
  from math import asin, pi, sqrt
  
  
  
  
  
  
  
  def       lowerCAmelCase__(	lowercase       :    float				) ->    float:
    return (
        (1 - 2 * point) * sqrt(point - point**2				) + 2 * point + asin(sqrt(1 - point				)				)
    ) / 4
  
  
  
  
  
  
  
  def       lowerCAmelCase__(	lowercase       :    int				) ->    float:
    __snake_case   :				int        =       (circles_number + 1 - sqrt(2 * circles_number				)) / (
        2 * (circles_number**2 + 1)
    )
    __snake_case   :				Union[str, Any]        =       circles_number * intersection_y
  
    __snake_case   :				List[str]        =       intersection_x * intersection_y / 2
    __snake_case   :				Dict        =       circle_bottom_arc_integral(
        1 / 2				) - circle_bottom_arc_integral(lowercase				)
  
    return triangle_area + concave_region_area
  
  
  
  
  
  
  
  def       lowerCAmelCase__(	lowercase       :    float = 1 / 1000				) ->    int:
    __snake_case   :				Tuple        =       (1 - pi / 4) / 4
  
    for n in count(1				):
      if concave_triangle_area(lowercase				) / l_section_area < fraction:
        return n
  
    return -1
  
  
  if __name__ == "__main__":
       print(F'''{solution() = }''')
  
  
style_context: 
  
  
  
  
  
  def       lowerCAmelCase__(	lowercase       :    str				) ->    int:
    __snake_case   :				List[str]        =       str(lowercase				).strip()
    if not oct_string:
      raise ValueError("Empty string was passed to the function"				)
    __snake_case   :				int        =       oct_string[0] == "-"
    if is_negative:
      __snake_case   :				Union[str, Any]        =       oct_string[1:]
    if not oct_string.isdigit() or not all(0 <= int(lowercase				) <= 7 for char in oct_string				):
      raise ValueError("Non-octal value was passed to the function"				)
    __snake_case   :				List[Any]        =       0
    for char in oct_string:
      __snake_case   :				Optional[Any]        =       8 * decimal_number + int(lowercase				)
    if is_negative:
      __snake_case   :				Any        =       -decimal_number
    return decimal_number
  
  
  if __name__ == "__main__":
       from doctest import testmod
  
       testmod()
  
  