Step 1 :First, we define the two functions \(y=e^{0.5 x}\) and \(y=-\frac{1}{x}\).
Step 2 :Next, we define the absolute difference function which is the absolute value of the difference between the two functions.
Step 3 :Then, we perform numerical integration on the absolute difference function over the interval from 1 to 2.
Step 4 :After running the numerical integration, we get the numerical value of the area bounded by the two functions over the interval [1, 2].
Step 5 :Finally, the area bounded by the graphs of the indicated equations over the given interval is \(\boxed{area}\) square units.