






'''simple docstring'''

def        lowercase__					( __UpperCamelCase       )->					str:
      if not all(char in """01""" for char in bin_string       ):
            raise ValueError("""Non-binary value was passed to the function"""       )
      if not bin_string:
            raise ValueError("""Empty string was passed to the function"""       )
      UpperCamelCase							    =   """"""
      while len(__a       ) % 3 != 0:
            UpperCamelCase							    =   """0""" + bin_string
      UpperCamelCase							    =   [
          bin_string[index : index + 3]
          for index in range(len(__a       )       )
          if index % 3 == 0
      ]
      for bin_group in bin_string_in_3_list:
            UpperCamelCase							    =   0
            for index, val in enumerate(__a       ):
                  oct_val += int(2 ** (2 - index) * int(__a       )       )
            oct_string += str(__a       )
      return oct_string


if __name__ == "__main__":
     from doctest import testmod

     testmod()


"""simple docstring"""




from __future__ import annotations

from collections.abc import Callable



def 							_lowerCamelCase			(			__a,				__a,				__a,				__a = 100,				):
		SCREAMING_SNAKE_CASE_    			=			x_start
		SCREAMING_SNAKE_CASE_    			=			fnc(__a     )
		SCREAMING_SNAKE_CASE_    			=			0.0
		for _ in range(__a     ):
				# Approximates small segments of curve as linear and solve
				# for trapezoidal area
				SCREAMING_SNAKE_CASE_    			=			(x_end - x_start) / steps + xa
				SCREAMING_SNAKE_CASE_    			=			fnc(__a     )
				area += abs(fxa + fxa     ) * (xa - xa) / 2
				# Increment step
				SCREAMING_SNAKE_CASE_    			=			xa
				SCREAMING_SNAKE_CASE_    			=			fxa
		return area


if __name__ == "__main__":



						def 							_lowerCamelCase			(			__a     ):
								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:')
						lowerCAmelCase__				=					10
						while i <= 100000:
												print(f'''with {i} steps: {trapezoidal_area(f, -5, 5, i)}''')
												i *= 10