Dubya part 2

When $y \leqslant 7$ is graphed, all areas below $y \leqslant 7$ and on/above the curve $y = |x| + 2|x+1| - 3|x+2| +4 |x+3|$ are shaded. If the area of the shaded region is $\mathscr{E}$ , find $\left \lfloor 1000 \mathscr{E} \right \rfloor$ .

Notations :

• $| \cdot |$ denotes the absolute value function .

• $\lfloor \cdot \rfloor$ denotes the floor function .