


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






def   _lowercase(					__a				:						Tuple    ,     __a				:						str    ,     __a				:						Union[str, Any]     ):
							a__      =a + h
							while x < (b - h):
														yield x
														a__      =x + h






def   _lowercase(					__a				:						Dict     ):  # enter your function here
							a__      =(x - 0) * (x - 0)
							return y






def   _lowercase(					):
							a__      =0.0  # Lower bound of integration
							a__      =1.0  # Upper bound of integration
							a__      =10.0  # define number of steps or resolution
							a__      =[a, b]  # define boundary of integration
							a__      =method_a(__a    ,     __a     )
							print(f"""y = {y}"""     )


if __name__ == "__main__":
	main()









from __future__ import annotations





def    __lowerCAmelCase   (    __snake_case							):
     __lowerCAmelCase             =       len(__snake_case							)
     # We need to create solution object to save path.
     __lowerCAmelCase             =       [[0 for _ in range(__snake_case							)] for _ in range(__snake_case							)]
     __lowerCAmelCase             =       run_maze(__snake_case       ,			0       ,			0       ,			__snake_case							)
     if solved:
          print("\n".join(str(__snake_case							) for row in solutions							)							)
     else:
          print("No solution exists!"							)
     return solved





def    __lowerCAmelCase   (    __snake_case       ,			__snake_case       ,			__snake_case       ,			__snake_case							):
     __lowerCAmelCase             =       len(__snake_case							)
     # Final check point.
     if i == j == (size - 1):
          __lowerCAmelCase             =       1
          return True

     __lowerCAmelCase             =       (not i < 0) and (not j < 0)  # Check lower bounds
     __lowerCAmelCase             =       (i < size) and (j < size)  # Check upper bounds

     if lower_flag and upper_flag:
          # check for already visited and block points.
          __lowerCAmelCase             =       (not solutions[i][j]) and (not maze[i][j])
          if block_flag:
               # check visited
               __lowerCAmelCase             =       1

               # check for directions
               if (
                   run_maze(__snake_case       ,			i + 1       ,			__snake_case       ,			__snake_case							)
                   or run_maze(__snake_case       ,			__snake_case       ,			j + 1       ,			__snake_case							)
                   or run_maze(__snake_case       ,			i - 1       ,			__snake_case       ,			__snake_case							)
                   or run_maze(__snake_case       ,			__snake_case       ,			j - 1       ,			__snake_case							)
               ):
                    return True

               __lowerCAmelCase             =       0
               return False
     return False


if __name__ == "__main__":
 import doctest

 doctest.testmod()






