I don't have any experience writing command line scripts but I don't think you can switch between one script and the other like the way you are trying. If I were writing this I would use modules, something like this:

File unit6.pl

#!/usr/bin/perl
use strict;
use warnings;

require Unit6;
require CMQIA;
# require Quadrilaterals; etc

Unit6::run();
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File Unit6.pm

package Unit6;
use strict;
use warnings;

sub run {
    print "
        This is Unit 6 - Quadrilaterals and Polygons.\n
        For the Final Exam, you will have to know the\n
        properties of all quadrilaterals and how to\n
        prove that a given shape is any quadrilateral.\n
        To access the Quadrilateral Information Database,\n
        type 'Quads.' To access the Casio-Maxim Quadrilateral\n
        Identification Algorithm, type 'crazy Maxim.'\n
        Type 'quit' to exit Unit 6.\n
        Type your choice.\n\n";
    my $Choice = <STDIN>;
    chomp $Choice;
    if ($Choice =~ /quit/i)
        { print "\nBye.\n\n"; exit;}
    elsif ($Choice =~ /quads/i)
        { Quadrilaterals::run();}
    elsif ($Choice =~ /crazy maxim/i)
        { CMQIA::run();}
}
1;
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File CMQIA.pm

package CMQIA;
use strict;
use warnings;

sub run {
    print "
        Welcome to the Casio-Maxim Quadrilateral Identification\n
        Algorithm. In order to identify said quadrilateral,\n
        you must have the coordinates of all 4 vertices.\n";
    print "
        When you are ready to input your coordines, type\n
        'ready.' Type anything else to exit the CMQIA.\n\n";

    my $Choice = <STDIN>;
    chomp $Choice;
    if ($Choice =~ /ready/i)
        { maxim();}
    else
        { Unit6::run();}
}

sub maxim {
    print "\nFor shape ABCD, in which point A has coordinates (X1, Y1)
+, B has coordinates\n\n(X2, Y2), C has coordinates (X3, Y3), and D ha
+s coordinates (X4, Y4),\n\nX1 = ";

    my $AX = <STDIN>;
    chomp $AX;
    print "Y1 = \n";
    my $AY = <STDIN>;
    chomp $AY;
    print "X2 = \n";
    # etc
}
1;
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