@acer I follow what you did as alternative solutions.
I agree that both the numerator and denominator generate values that are in excess of the hardware floating point representation. But I am not quite sure I understand why it failed. Is it true that, normally, Maple uses its algorithms to derive a precise number; then, if we use evalf, it takes that number and converts it to a floating point number? On the other hand, in making a plot, Maple calls evalhf to calculate the values to be plotted, and that is where the problem occurs? (I could not find either hardware of evalhf in the plot/details help page. I'm assuming it uses evalfh for reasons of speed.)
Hopefully, I understand correctly. This leads to the next question, is it possible to change the code for plots to ensure that all data points are returned as viable from the hardware before plotting, and if they are not, then the software version of calculating the floating point numbers occurs?