Perhaps you could make the regexp ensure the operator is only one of the four specified operations and then performing an eval on the reconstructed operation?

I agree about laundering the input but I'd want to check that the whole input matches the expected pattern.

if ( my ($Code) = $Problem =~ /^\s*(\d+\s*[-+/*]\s*\d+)\s*=\s*$/ ) {
  if ( defined ( my $Answer = eval $Code ) ) {
     # do stuff with $Answer
  } else {
     # do stuff with $@
  }
} else {
  # Complain about invalid format
}
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I'd even tend to be a bit more liberal with my laundering to let though any simple arithmetic /^([-+/*\s\d().]+)=\s*$/.