Multidimensional integration using python

Question

Problem: Write a code that asks the user to input a functon with multiple variables and then integrates it using as limits numbers given by the user

This is the code that I have written so far

from sympy import Symbol, integrate, parse_expr
import time
import math

  
class Control():
    def __init__(self):
        self.run()

    def one_variable(self):
        func = input("Enter a mathematical function with one variable(x): ")
        
        x_lower,x_upper = input("Enter the lower and upper limit for the x variable: ").split(',')

        x = Symbol('x')
        parsed_func = parse_expr(func)

        start = time.time()
        result = integrate(parsed_func, (x, x_lower, x_upper))
        end = time.time()
        t = end - start
        print(result)
        print('It took', t, 'seconds to calculate the integral')
        
    def two_variables(self):
        func = input("Enter a mathematical function with two variables(x,y): ")

        x_lower,x_upper = input("Enter the lower and upper limit for the x variable: ").split(',')
        y_lower,y_upper = input("Enter the lower and upper limit for the y variable: ").split(',')

        x = Symbol('x')
        y = Symbol('y')
        parsed_func = parse_expr(func)
      
        
        start = time.time()
        result = integrate(parsed_func, (x, x_lower, x_upper), (y, y_lower, y_upper))
        end = time.time()
        t = end - start
        print(result)
        print('It took', t, 'seconds to calculate the integral')
        
    def three_variables(self):
        func = input("Enter a mathematical function with three variables(x,y,z): ")

        x_lower,x_upper = input("Enter the lower and upper limit for the x variable: ").split(',')
        y_lower,y_upper = input("Enter the lower and upper limit for the y variable: ").split(',')
        z_lower,z_upper = input("Enter the lower and upper limit for the z variable: ").split(',')


        x = Symbol('x')
        y = Symbol('y')
        z = Symbol('z')
        parsed_func = parse_expr(func)

        start = time.time()
        result = integrate(parsed_func, (x, x_lower, x_upper), (y, y_lower, y_upper), (z, z_lower, z_upper))
        end = time.time()
        t = end - start
        print(result)
        print( 'It took', t, 'seconds to calculate the integral')
    def four_variables(self):
        func = input("Enter a mathematical function with four variables(x,y,z,w): ")

        x_lower,x_upper = input("Enter the lower and upper limit for the x variable: ").split(',')
        y_lower,y_upper = input("Enter the lower and upper limit for the y variable: ").split(',')
        z_lower,z_upper = input("Enter the lower and upper limit for the z variable: ").split(',')
        w_lower,w_upper = input("Enter the lower and upper limit for the w variable: ").split(',')

        x = Symbol('x')
        y = Symbol('y')
        z = Symbol('z')
        w = Symbol('w')
        parsed_func = parse_expr(func)
        start = time.time()



        result = integrate(parsed_func, (x, x_lower, x_upper), (y, y_lower, y_upper), (z, z_lower, z_upper), (w, w_lower, w_upper))
        end = time.time()
        t = end - start
        print(result)
        print('It took', t, 'seconds to calculate the integral')
        

            
    def run(self):
        while True:
            print('Choose the number of variables (1-4)')
            reply = input("... ")
            if not reply: break
            if reply == '1':
                self.one_variable()
            if reply == '2':
                self.two_variables()
            if reply == '3':
                self.three_variables()
            if reply == '4':
                self.four_variables()


if __name__ == "__main__":
    Control()

I would like to know if there is a more efficient way to do it and also how to add a graphical user interface to the code using tkinter