From the first part of your code it looks like you are storing your variables and values in the %data hash in the form $data{"variable name"} = "value". In order to work, your formulae have to use those variables and values in the very same format.

I would think it be useful to see a couple of examples.

Update: Here is some basic code to get you started:

use strict;
use warnings;

my %data = ( x => 5, y => 7, z => 2 );

my @formulae = ( 
    'x + y',
    'z + 3',
    'x ** z',
    'a + x',
    'x /= y',
    'x - x'
);

for my $formula (@formulae) {
    print "Processing formula $formula\n\t";
    my @error = ();
    while ($formula =~ s|([a-z]+)|$data{$1}//' '|e) {
        push @error, $1 unless exists $data{$1};
    }
    if (@error) {
        print "Error: unknown variable(s) @error\n\n";
    } else {
        my $result = eval($formula);
        if( defined $result) {
            print "Result: $formula = $result\n\n";
        } else {
            print "Syntax error in $formula\n\n";
        }
    }
}
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