code: 
  
  
  
  
  
  
  from itertools import count
  from math import asin, pi, sqrt
  
  
  def 						_A     (       SCREAMING_SNAKE_CASE__						:			float ):
      return (
          (1 - 2 * point) * sqrt(point - point**2 ) + 2 * point + asin(sqrt(1 - point ) )
      ) / 4
  
  
  def 						_A     (       SCREAMING_SNAKE_CASE__						:			int ):
      UpperCamelCase :str										=     (circles_number + 1 - sqrt(2 * circles_number )) / (
          2 * (circles_number**2 + 1)
      )
      UpperCamelCase :List[Any]										=     circles_number * intersection_y
  
      UpperCamelCase :List[str]										=     intersection_x * intersection_y / 2
      UpperCamelCase :Optional[int]										=     circle_bottom_arc_integral(
          1 / 2 ) - circle_bottom_arc_integral(SCREAMING_SNAKE_CASE__ )
  
      return triangle_area + concave_region_area
  
  
  def 						_A     (       SCREAMING_SNAKE_CASE__						:			float = 1 / 1000 ):
      UpperCamelCase :Union[str, Any]										=     (1 - pi / 4) / 4
  
      for n in count(1 ):
          if concave_triangle_area(SCREAMING_SNAKE_CASE__ ) / l_section_area < fraction:
              return n
  
      return -1
  
  
  if __name__ == "__main__":
   print(f'''{solution() = }''')
  
  
  
  
  
  
style_context: 
  
  
  
  
  
  
  # as due to their complexity multi-gpu tests could impact other tests, and to aid debug we have those in a separate module.
  
  import os
  import sys
  
  from transformers.testing_utils import TestCasePlus, execute_subprocess_async, get_gpu_count, require_torch_gpu, slow
  
  from .utils import load_json
  
  
  
  
  
  
  
  class     UpperCAmelCase_		(      lowercase				):
  
  
  
        """simple docstring"""
        @classmethod
        def 					UpperCAmelCase		(       cls				)       ->   List[Any]:
            return cls
  
  
  
  
        @slow
        @require_torch_gpu
        def 					UpperCAmelCase		(       self				)       ->   int:
            UpperCamelCase :int										=     self.get_auto_remove_tmp_dir()
            UpperCamelCase :List[str]										=     F'''
              --model_name Helsinki-NLP/opus-mt-en-ro
              --save_dir {output_dir}
              --data_dir {self.test_file_dir_str}/test_data/wmt_en_ro
              --num_beams 2
              --task translation
          '''.split()
  
            # we want this test to run even if there is only one GPU, but if there are more we use them all
            UpperCamelCase :List[str]										=     get_gpu_count()
            UpperCamelCase :Optional[Any]										=     F'''
              -m torch.distributed.launch
              --nproc_per_node={n_gpu}
              {self.test_file_dir}/run_distributed_eval.py
          '''.split()
            UpperCamelCase :List[Any]										=     [sys.executable] + distributed_args + args
            execute_subprocess_async(SCREAMING_SNAKE_CASE_					,       env=self.get_env()				)
  
            UpperCamelCase :Tuple										=     os.path.join(SCREAMING_SNAKE_CASE_					,       '''test_bleu.json'''				)
            UpperCamelCase :str										=     load_json(SCREAMING_SNAKE_CASE_				)
            # print(metrics)
            self.assertGreaterEqual(metrics['''bleu''']					,       25				)
  
  
  
  
  
  