Let $f : [ - 3,1 ] \rightarrow R$ be given as $f ( x ) = \left\{ \begin{array} { l l } \min \left\{ ( x + 6 ) , x ^ { 2 } \right\} , & - 3 \leq x \leq 0 \\ \max \left\{ \sqrt { x } , x ^ { 2 } \right\} , & 0 \leq x \leq 1 \end{array} \right.$. If the area bounded by $y = f ( x )$ and $x$-axis is $A$ sq units, then the value of $6 A$ is equal to