I3.1 If $\{p, q\}=q \times a+p$ and $\{2,5\}=52$, find the value of $a$.
I3.2 If $a, \frac{37}{2}, b$ is an arithmetic progression, find the value of $b$.
I3.3 If $b^{2}-c^{2}=200$ and $c>0$, find the value of $c$.
I3.4 Given that in the figure, $B C / / D E, B C: D E=10: c$ and $A F: F G=20: d$, find the value of $d$.
$$
\begin{array}{l}
\{2,5\}=5 \times a+2=52 \\
a=10 \\
\frac{a+b}{2}=\frac{37}{2} \\
b=27 \\
27^{2}-c^{2}=200 \\
c^{2}=729-200=529 \\
c=23
\end{array}
$$

Remark: Original question is: If $b^{2}-c^{2}=200$, find the value of $c$. $c= \pm 23, c$ is not unique.
By similar triangles, $A F: A G=A C: A E=B C: D E$
$$
\begin{array}{l}
20:(20+d)=10: 23 \\
d=26
\end{array}
$$