"""simple docstring"""






def   a_						(					lowerCamelCase					,			lowerCamelCase       ):
				# "extended trapezoidal rule"
				# int(f) = dx/2 * (f1 + 2f2 + ... + fn)
				UpperCAmelCase__             =							(boundary[1] - boundary[0]) / steps
				UpperCAmelCase__             =							boundary[0]
				UpperCAmelCase__             =							boundary[1]
				UpperCAmelCase__             =							make_points(lowerCAmelCase_					,			lowerCAmelCase_					,			lowerCAmelCase_       )
				UpperCAmelCase__             =							0.0
				y += (h / 2.0) * f(lowerCAmelCase_       )
				for i in x_i:
								# print(i)
								y += h * f(lowerCAmelCase_       )
				y += (h / 2.0) * f(lowerCAmelCase_       )
				return y



def   a_						(					lowerCamelCase					,			lowerCamelCase					,			lowerCamelCase       ):
				UpperCAmelCase__             =							a + h
				while x < (b - h):
								yield x
								UpperCAmelCase__             =							x + h



def   a_						(					lowerCamelCase       ):  # enter your function here
				UpperCAmelCase__             =							(x - 0) * (x - 0)
				return y



def   a_						(					):
				UpperCAmelCase__             =							0.0  # Lower bound of integration
				UpperCAmelCase__             =							1.0  # Upper bound of integration
				UpperCAmelCase__             =							10.0  # define number of steps or resolution
				UpperCAmelCase__             =							[a, b]  # define boundary of integration
				UpperCAmelCase__             =							method_a(lowerCAmelCase_					,			lowerCAmelCase_       )
				print(f'''y = {y}'''       )


if __name__ == "__main__":
						main()










from __future__ import annotations

import math

def   a_    ( lowerCAmelCase_      :			int,	lowerCAmelCase_      :			int,	lowerCAmelCase_      :			bool,	lowerCAmelCase_      :			list[int],	lowerCAmelCase_      :			float	):

   if depth < 0:
      raise ValueError('Depth cannot be less than 0'	)

   if len(lowerCAmelCase_	) == 0:
      raise ValueError('Scores cannot be empty'	)

   if depth == height:
      return scores[node_index]

   if is_max:
      return max(
          minimax(depth + 1,	node_index * 2,	lowerCAmelCase_,	lowerCAmelCase_,	lowerCAmelCase_	),	minimax(depth + 1,	node_index * 2 + 1,	lowerCAmelCase_,	lowerCAmelCase_,	lowerCAmelCase_	),	)

   return min(
       minimax(depth + 1,	node_index * 2,	lowerCAmelCase_,	lowerCAmelCase_,	lowerCAmelCase_	),	minimax(depth + 1,	node_index * 2 + 1,	lowerCAmelCase_,	lowerCAmelCase_,	lowerCAmelCase_	),	)

def   a_    ( ):
   __lowerCAmelCase								=	[90, 23, 6, 33, 21, 65, 123, 3_4423]
   __lowerCAmelCase								=	math.log(len(lowerCAmelCase_	),	2	)
   print('Optimal value : ',	end=''	)
   print(minimax(0,	0,	lowerCAmelCase_,	lowerCAmelCase_,	lowerCAmelCase_	)	)


if __name__ == "__main__":
     import doctest

     doctest.testmod()
     main()

