++ for showing the hard way of doing things ;)

Win32::Guitest makes it easier to do the same API calls... This program does the same thing without all of the return messages. (I didn't see the point for this simple exercise.)

Start calculator before running this code (mode doesn't matter)

#! C:/perl/bin/perl
use strict;
use warnings; # Win32::GuiTest doesn't like -w
use Win32::GuiTest qw(FindWindowLike SetForegroundWindow SendKeys Push
+Button);
my @windows = FindWindowLike(0, "^Calculator"); # find all calculator 
+windows
die "Start Calc before running this example.\n" unless @windows;
my $hwnd = $windows[0]; # we'll just the first match
SetForegroundWindow($hwnd); # Bring it the foreground
SendKeys("%VS"); # switch to scientific mode
# press these buttons
foreach my $button ("Hex", "Dec", "Oct", "Bin") {
  sleep(2);
  PushButton($button);
}
[download]

Update: Added the die statement to my code.