Challenge

Naturally, your favorite class of the day is AP Calculus BC and you've recently been learning Euler's Method. Your teacher has had a lot on their plate, so they've just been using the same curve for your homework problems every day, y'(x) = x^2 - 6y^2, y(5) = 2. To simplify matters, you're going to write a program to automate this trivial task for you.

For each input, you will receive a space-separated set of two numbers (each between -10 and 10). The first is your step size and the second is the x-value of the point you need the estimated y-value for (to the nearest tenth and incuding trailing zero if necessary). Your output will be between -1,000 and 1,000.

Sample Input 1:0.8 5.8Sample Output 1:2.8

Sample Input 2:0.9 7.7Sample Output 2:-645.1

Notes:

• the inputs will be passed in (through stdin) separated by newlines; make sure your output is also separated by newlines
• the first line of input will contain only one integer representing the number of additional lines of input you will receive

Solution

def main():
    
    number_of_data = int(input())
    
    y_list = []
    
    for i in range(number_of_data):

        data = input().split(" ")
    
        dx = float(data[0])
        xn = float(data[1])
    
        x = 5.0
        y = 2.0
        f = lambda x, y: x**2 - 6 * y**2
    
        number_of_steps = round((xn - x)/dx)
    
        for step in range(number_of_steps):
    
            y = y + f(x, y) * dx
            x += dx
    
        y_list.append(round(y, 1))
    
    for y in y_list:
        print(y)

main()