




'''simple docstring'''





from math import ceil





def      __a     (       _UpperCamelCase:   str ,						_UpperCamelCase:   str   )						->			Dict:

     """simple docstring"""




     _snake_case							=				list(range(0 ,						_UpperCamelCase   )   )

     _snake_case							=				[item for sublist in list(device_map.values()   ) for item in sublist]

     # Duplicate check
     _snake_case							=				[]
     for i in device_map_blocks:
          if device_map_blocks.count(_UpperCamelCase   ) > 1 and i not in duplicate_blocks:
               duplicate_blocks.append(_UpperCamelCase   )
    # Missing blocks
     _snake_case							=				[i for i in blocks if i not in device_map_blocks]
     _snake_case							=				[i for i in device_map_blocks if i not in blocks]

     if len(_UpperCamelCase   ) != 0:
          raise ValueError(
              "Duplicate attention blocks specified in device_map. Attention blocks must be specified to one device."
              " These attention blocks were specified more than once: " + str(_UpperCamelCase   )   )
     if len(_UpperCamelCase   ) != 0:
          raise ValueError(
              "There are attention blocks for this model that are not specified in the device_map. Add these attention "
              "blocks to a device on the device_map: " + str(_UpperCamelCase   )   )
     if len(_UpperCamelCase   ) != 0:
          raise ValueError(
              "The device_map contains more attention blocks than this model has. Remove these from the device_map:"
              + str(_UpperCamelCase   )   )





def      __a     (       _UpperCamelCase:   str ,						_UpperCamelCase:   Any   )						->			Optional[Any]:

     """simple docstring"""




     _snake_case							=				list(range(_UpperCamelCase   )   )
     _snake_case							=				int(ceil(n_layers / len(_UpperCamelCase   )   )   )
     _snake_case							=				[layers[i : i + n_blocks] for i in range(0 ,						_UpperCamelCase ,						_UpperCamelCase   )]

     return dict(zip(_UpperCamelCase ,						_UpperCamelCase   )   )








'''simple docstring'''





from __future__ import annotations

from collections.abc import Callable





def      __a     (       _UpperCamelCase:   Callable[[int | float], int | float] ,						_UpperCamelCase:   int | float ,						_UpperCamelCase:   int | float ,						_UpperCamelCase:   int = 100 ,						)						->			float:

     """simple docstring"""




     _snake_case							=				x_start
     _snake_case							=				fnc(_UpperCamelCase   )
     _snake_case							=				0.0
     for _ in range(_UpperCamelCase   ):
          # Approximates small segments of curve as linear and solve
          # for trapezoidal area
          _snake_case							=				(x_end - x_start) / steps + xa
          _snake_case							=				fnc(_UpperCamelCase   )
          area += abs(fxa + fxa   ) * (xa - xa) / 2
          # Increment step
          _snake_case							=				xa
          _snake_case							=				fxa
     return area


if __name__ == "__main__":





   def      __a     (       _UpperCamelCase:   Any   )						->			Optional[int]:

        """simple docstring"""




        return x**3 + x**2

   print('''f(x) = x^3 + x^2''')
   print('''The area between the curve, x = -5, x = 5 and the x axis is:''')
   UpperCamelCase_						:      Optional[int]       =						10
   while i <= 100000:
      print(F'with {i} steps: {trapezoidal_area(f, -5, 5, i)}')
      i *= 10


