Given: $p + q = 10$.

The product $p \times q$ is maximum when $p$ and $q$ are as close as possible in value.

For Value-I (p, q positive): To get equal or nearly equal integers, $p = 5$ and $q = 5$. $\Rightarrow$ Maximum product = $5 \times 5 = 25$.

For Value-II ($p \geq -6$, $q \geq -4$): We still have $p + q = 10$. Thus $q = 10 - p$.

Now, $p \times q = p(10 - p) = 10p - p^2$, which is maximized at $p = 5$, giving product = $25$.

Even when negatives are allowed ($p \geq -6$, $q \geq -4$), the combination $(p, q) = (5, 5)$ still satisfies the condition and gives the maximum product. (The negative pair $(-6, -4)$ would give $24 < 25$.)

Therefore, Value-I = Value-II = 25.