Watching 

• There's something very suspicious about my result but I don't know what
• Let's try watching for changes in the $qr variable

perl -d broken3.pl
  DB<1> w $qr
  DB<2> c
Watchpoint 0:   $qr changed:
    old value:  ''
    new value:  '11495.3854165617'
main::(broken3.pl:12):  print "Earth's quadratic mean radius: ${qr} km\n";