import numpy as np
import matplotlib.pyplot as plt
from math import *
import pandas as pd
from sympy import *


def xi(i):
	return a + i * h


def func_value(x):
	return x**3 - sin(x)


a = 0.6
b = 1.1
h = round((b - a) / 10, 2)


arr_X = []
arr_Y = []
table = []

y2_values = []
y2_values.append(" ")

y3_values = []
for i in range(0, 2):
    y3_values.append(" ")


y4_values = []
for i in range(0, 3):
    y4_values.append(" ")


y5_values = []
for i in range(0, 4):
    y5_values.append(" ")


y6_values = []
for i in range(0, 5):
    y6_values.append(" ")


y7_values = []
for i in range(0, 6):
    y7_values.append(" ")


y8_values = []
for i in range(0, 7):
    y8_values.append(" ")


y9_values = []
for i in range(0, 8):
    y9_values.append(" ")


y10_values = []
for i in range(0, 9):
    y10_values.append(" ")


y11_values = []
for i in range(0, 10):
    y11_values.append(" ")

def print_value_table():
    for i in range(0, 11):
        x = xi(i)
        arr_X.append(x)
        y = round(func_value(x), 2)
        arr_Y.append(y)
        if (i > 0):
            y2_values.append(arr_Y[i] - arr_Y[i - 1])
        if (i > 1):
            y3_values.append(y2_values[i] - y2_values[i - 1])
        if (i > 2):
            y4_values.append(y3_values[i] - y3_values[i - 1])
        if (i > 3):
            y5_values.append(y4_values[i] - y4_values[i - 1])
        if (i > 4):
            y6_values.append(y5_values[i] - y5_values[i - 1])
        if (i > 5):
            y7_values.append(y6_values[i] - y6_values[i - 1])
        if (i > 6):
            y8_values.append(y7_values[i] - y7_values[i - 1])
        if (i > 7):
            y9_values.append(y8_values[i] - y8_values[i - 1])
        if (i > 8):
            y10_values.append(y9_values[i] - y9_values[i - 1])
        if (i > 9):
            y11_values.append(y10_values[i] - y10_values[i - 1])
        table.append({'x' : arr_X[i], 'y' : arr_Y[i], 'y2' : y2_values[i],
                      'y3' : y3_values[i], 'y4' : y4_values[i],
                      'y5' : y5_values[i], 'y6' : y6_values[i],
                      'y7' : y7_values[i], 'y8' : y8_values[i],
                      'y9' : y9_values[i], 'y10' : y10_values[i],
                      'y11' : y11_values[i]})
    print(pd.DataFrame(table))

print_value_table()