@Michael Rogers, I tried your first suggested code and it worked producing the same plot as the first plot! And it didn't take too long. Thank you so much!! May I ask one more question? Looking at the first plot, I would like to truncate the curve at where it touches the x-axis from the right (that's somewhere around 2.7) to remove the flat portion and spike portion of the curve, eventually leaving that nice curve. Do you know how to do this?

Hi, If the number where you want the plot to start is 2.7, then change the plot command to Plot[brf[w], {w, 2.7, 12}, PlotRange -> {{0, 12}, {0, 1}}] `Plot[]` will automatically choose the axes origin. If it's not (0,0) and you would like it to be, then you can control the placement of the axes with the option `AxesOrigin`. For instance, Plot[brf[w], {w, 0, 12}, PlotRange -> {{0, 12}, {0, 1}}, AxesOrigin -> {0, 0}]

@Michael Rogers, I have posted another related question here. If possible, may I ask for your help once more? Thank you very much in advance!

The second version has a `Simplify` which may raise numerical issues, which I have not tried to investigate. A curious feature that I noticed in your code is that in your function definition `brf[w_]:=rhs` the right hand side has no explicit `w`. This way for example brf[1] does not evaluate to a number, while `brf[w] /. w -> 1` does. A simplified version of the issue is with the "function" `x = a; f[a_] := x`. Perhaps surprisingly, the following gives `False`: {f[0], f[1]} === Table[f[a], {a, 0, 1}]

Plot with and without `Table` produce different results