1. The problem involves evaluating the integral expression $$Q^{398}_{673} = \int_{673}^{398} (A + B T + C T^2 + D T^3 + E T^4) \, dT$$ where constants $C$, $D$, and $E$ are given, and the integral evaluates to 4.408. 2. The general formula for integrating a polynomial term $T^n$ is $$\int T^n \, dT = \frac{T^{n+1}}{n+1} + C$$ where $C$ is the constant of integration. 3. Applying this to each term, the integral becomes: $$Q = A(T) + \frac{B T^2}{2} + \frac{C T^3}{3} + \frac{D T^4}{4} + \frac{E T^5}{5} \Big|_{673}^{398}$$ 4. Since $C = 3.638 \times 10^{-1}$, $D = -1.2794 \times 10^{-7}$, and $E = 5.528 \times 10^{-11}$, substitute these values into the integral. 5. Note that $A$ and $B$ are not provided explicitly, so the integral expression is incomplete without them. 6. The integral evaluates to 4.408, which suggests that the definite integral from 673 to 398 of the polynomial expression equals 4.408. 7. To fully solve, values of $A$ and $B$ or additional information are needed. Since the problem lacks complete data for $A$ and $B$, the integral cannot be fully evaluated here. Final answer: The integral expression is set up correctly, but missing constants prevent full evaluation.