
"""simple docstring"""





from __future__ import annotations

import math



def       lowerCamelCase__		(			__snake_case,     __snake_case	)							->		Dict:


					"""simple docstring"""





					_UpperCamelCase							 =  u
					for i in range(1,     UpperCamelCase__	):
										_UpperCamelCase							 =  temp * (u - i)
					return temp



def       lowerCamelCase__		(			)							->		Optional[int]:


					"""simple docstring"""





					_UpperCamelCase							 =  int(input('''enter the numbers of values: '''	)	)
					_UpperCamelCase							 =  []
					for _ in range(UpperCamelCase__	):
										y.append([]	)
					for i in range(UpperCamelCase__	):
										for j in range(UpperCamelCase__	):
															y[i].append(UpperCamelCase__	)
															_UpperCamelCase							 =  0

					print('''enter the values of parameters in a list: '''	)
					_UpperCamelCase							 =  list(map(UpperCamelCase__,     input().split()	)	)

					print('''enter the values of corresponding parameters: '''	)
					for i in range(UpperCamelCase__	):
										_UpperCamelCase							 =  float(input()	)

					_UpperCamelCase							 =  int(input('''enter the value to interpolate: '''	)	)
					_UpperCamelCase							 =  (value - x[0]) / (x[1] - x[0])

					# for calculating forward difference table

					for i in range(1,     UpperCamelCase__	):
										for j in range(n - i	):
															_UpperCamelCase							 =  y[j + 1][i - 1] - y[j][i - 1]

					_UpperCamelCase							 =  y[0][0]
					for i in range(1,     UpperCamelCase__	):
										summ += (ucal(UpperCamelCase__,     UpperCamelCase__	) * y[0][i]) / math.factorial(UpperCamelCase__	)

					print(F'''the value at {value} is {summ}'''	)


if __name__ == "__main__":
				main()











"""simple docstring"""
import math

from numpy import inf
from scipy.integrate import quad





def  lowerCamelCase_						(UpperCamelCase__		:		float							):
    if num <= 0:
        raise ValueError('''math domain error'''							)

    return quad(UpperCamelCase__     ,       0     ,       UpperCamelCase__     ,       args=(UpperCamelCase__)							)[0]





def  lowerCamelCase_						(UpperCamelCase__		:		float     ,       UpperCamelCase__		:		float							):
    return math.pow(UpperCamelCase__     ,       z - 1							) * math.exp(-x							)


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

  testmod()


