When treating quantity as a continuous variable, total producer surplus can be calculated with integration for any given price $P_0$ and quantity sold $Q_0$, irrespective of whether it's a market equilibrium point. The surplus is the integral of the price minus the marginal cost ($P_0 - C'(q)$) from zero to $Q_0$: Total Producer Surplus = $\int_{0}^{Q_0} (P_0 - C'(q)) \,dq$. This is equivalent to the formula $P_0Q_0 - C(Q_0) + C(0)$, where $C(0)$ represents the firm's fixed costs. This expression effectively calculates total revenue ($P_0Q_0$) minus the total variable costs ($C(Q_0) - C(0)$).