import copy
import numpy as np
from math import *

function = [[5,2], [3,1], [4,0]]

def solve(polynomial, variable):
    _polynomial = copy.deepcopy(polynomial)
    answer = 0
    for i in range(len(_polynomial)):
        answer += _polynomial[i][0] * (variable ** _polynomial[i][1])
    return answer

def integrate(polynomial, a, b):
    prev = 0
    area = 0
    shapeAmt = 10

    while True:
        print(shapeAmt)
        area = 0
        separators = np.linspace(a, b, shapeAmt+1)
        for i in range(len(separators)-1):
            area += (solve(function, separators[i]) * (abs(separators[i] - separators[i+1])))
        if abs(area - prev) <= 10**-6:
            break
        prev = area
        shapeAmt += 1

    return area

print(integrate(function, 2, 3))