Custom gallery function for built in wordpress gallery shortcode

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Project Budget (USD)
$30 - $250

Project Description:
I have tried many different ways to do this but I am just not as good as I thought. In wordpress you can define a gallery with the following shortcode inside the_content():
[gallery ids="81,82,83,84,85,86,87,88,89,90"]

I need a function, that exists in the functions.php file, that will see the shortcode in the_content of the_post, grab the ids, and print them out in an unordered list. For example I would like the following function call:

to produce

in the order of the ids that are supplied by the initial gallery shortcode.

Also, in the theme, when I call the_content() I do not want it to do the shortcode [gallery]. I want it to ignore it in the the_content() call.

- you must speak english
- I will not hire anyone from India
- Please tell me how many stars are on the US Flag in the first line of your reply

Additional Project Description:
02/10/2013 at 22:33 CET
The system removed all my code. So I have attached images to explain what I need.
image01.jpg shows what the user will put in the system
image02.jpg shows how the template file should look
image03.jpg shows what code should be shown after the function show_gallery() should produce.

Please let me know if you have any questions

Skills required:
HTML5, PHP, Wordpress
Additional Files: image01.jpg image02.jpg image03.jpg
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