The problem is asking for an approximation of the integral $\int_0^{12} f(x) dx$ using the midpoint rule with six rectangles, denoted by $M_6$.

Midpoint Rule:

The midpoint rule for approximating an integral $\int_a^b f(x) dx$ is given by: $M_n = \sum_{i=1}^{n} f(\text{midpoint}_i) \cdot \Delta x$ where: