Find the area of the region bounded by the curves `y=x^3` and the lines `y=x+6 ` and `y=0.`

Explanation

To find the area of the region bounded by the curves \( y = x^3 \), \( y = x + 6 \), and \( y = 0 \), we will follow these steps:

### Step 1: Find the Points of Intersection
We need to find the points where the curves intersect. This involves solving the equations \( y = x^3 \) and \( y = x + 6 \).

Set the two equations equal to each other:
\[
x^3 = x + 6
...