called the "gain from trade."

$(2)$ In the situation below, $p=D(q)=35-q^2$ and $p=S(q)=3+q^2,$ where $q$ is measured in thousands and $p$ is measured in hundreds of units. Use Wolfram Alpha to help you compute the following values.

$($a$)$ Compute the equilibrium price and quantity $(p^{**}$ and $q^{**}).$

$($b$)$ Compute the consumer surplus.

$($c$)$ Compute the producer surplus.