




def      A      (      _SCREAMING_SNAKE_CASE ,_SCREAMING_SNAKE_CASE    )	-> Optional[Any]:
       lowerCamelCase   :      Tuple			 =					[0 for i in range(r + 1    )]
       # nc0 = 1
       lowerCamelCase   :      Optional[int]			 =					1
       for i in range(1 ,n + 1    ):
              # to compute current row from previous row.
              lowerCamelCase   :      List[str]			 =					min(_SCREAMING_SNAKE_CASE ,_SCREAMING_SNAKE_CASE    )
              while j > 0:
                     c[j] += c[j - 1]
                     j -= 1
       return c[r]


print(binomial_coefficient(n=10, r=5))












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

def      A      (      _SCREAMING_SNAKE_CASE ,_SCREAMING_SNAKE_CASE ,_SCREAMING_SNAKE_CASE    )	-> int:
       lowerCamelCase   :      int			 =					a + h
       while x < (b - h):
              yield x
              lowerCamelCase   :      List[str]			 =					x + h

def      A      (      _SCREAMING_SNAKE_CASE    )	-> Optional[Any]:  # enter your function here
       lowerCamelCase   :      str			 =					(x - 0) * (x - 0)
       return y

def      A      (      )	-> int:
       lowerCamelCase   :      int			 =					0.0  # Lower bound of integration
       lowerCamelCase   :      int			 =					1.0  # Upper bound of integration
       lowerCamelCase   :      Dict			 =					10.0  # define number of steps or resolution
       lowerCamelCase   :      int			 =					[a, b]  # define boundary of integration
       lowerCamelCase   :      str			 =					method_a(_SCREAMING_SNAKE_CASE ,_SCREAMING_SNAKE_CASE    )
       print(f'''y = {y}'''    )


if __name__ == "__main__":
       main()






