
"""simple docstring"""







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




def 			A_			(					lowercase      )     ->							str:


					"""simple docstring"""







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




def 			A_			(					lowercase      )     ->							int:


					"""simple docstring"""







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

					UpperCAmelCase_						:    Optional[Any]    					=  intersection_x * intersection_y / 2
					UpperCAmelCase_						:    Union[str, Any]    					=  circle_bottom_arc_integral(
					    1 / 2      ) - circle_bottom_arc_integral(_A      )

					return triangle_area + concave_region_area




def 			A_			(					lowercase = 1 / 1000      )     ->							Tuple:


					"""simple docstring"""







					UpperCAmelCase_						:    List[str]    					=  (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() = }""")



"""simple docstring"""







import warnings

from .generation import GenerationMixin



class 		UpperCAmelCase_	(lowerCamelCase_						):
 """simple docstring"""




 warnings.warn(
     """Importing `GenerationMixin` from `src/transformers/generation_utils.py` is deprecated and will """
     """be removed in Transformers v5. Import as `from transformers import GenerationMixin` instead."""  , lowerCamelCase_  , )

