Load custom PHP on a custom URL via a plugin

Use is_page(). The is_page() function accepts page title, slug or id. Documentation

<?php 
if(is_page('myscript')) {
    include '/path/to/myscript.php';
}
?>

UPDATE

To add it to the content, you have two options

1. Find the content function in your template

Find either the_content() or get_the_content() in your template. Place it immediately after that function (or before if you want it before).

2. Add A Filter

Move the above code into your theme’s functions.php file and wrap it in a function. Then add a filter to the_content() to make it include your new function. Your code should look something like this:

function my_the_content_filter(){
    if(is_page('myscript')) {
        include '/path/to/myscript.php';
    }
}
add_filter( 'the_content', 'my_the_content_filter' );