Bash script to press button on webpage?

I have a webpage with many rows in a table, each with a print button at the end of the row (see below). I want to create a bash script that will be able to "press" these buttons and cause the PDF to download. Every button links to a different PDF, so I can't use curl to just call that URL. Ideas?

The button on the website looks like so:

<a class="button_std" href="#" onclick="window.open('/store/V1/V1637299/ecg/V1637299_20100104072532.pdf','print','resizable=yes,menubar=no,scrollbars=yes')"><span id="7996">Print</span></a>