The problem defines two operations based on conditions:

• If $p > q$, then the operation (let's denote it by '>') results in $p^2 + q^3$.
• If $p < q$, then the operation (let's denote it by '<') results in $p^3 - q^2$.

We need to evaluate the expression $(1>2)<3$. The notation suggests that the symbol used directly determines the formula applied, potentially irrespective of the condition check for the evaluation itself.

Evaluating $(1>2)$

In the expression $1>2$, the operator is '>'. We apply the formula associated with this operator:

Formula for '>': $p^2 + q^3$

Substitute $p=1$ and $q=2$: $1^2 + 2^3 = 1 + 8 = 9$

Let the result be $R = 9$.

Evaluating $R<3$

Now, we need to evaluate $R<3$, which is $9<3$. The operator is '<'. We apply the formula associated with this operator:

Formula for '<': $p^3 - q^2$

Substitute $p=9$ and $q=3$: $9^3 - 3^2 = 729 - 9 = 720$

Final Result

The value of the expression $(1>2)<3$ is 720.