How to find Google PageRank without third party tools?

As of March 7th 2016, Google has removed the public PageRank metric completely. Google's John Mueller confirmed it via Twitter. Prior to this, Google had been allowing access to this data through APIs. Those APIs are all now deprecated and now no longer function.

Public PageRank has been dying a slow death. Even when the APIs were active, Google did not frequently refresh the data. The last data refresh was in December 2013.

Google still uses PageRank internally. Their ranking algorithms depend on it. Googlebot crawls pages with higher PageRank more frequently. However, Google is no longer making this metric available to the public at all.

After reading comments to my question and a lot of searching I found the answer. To retrieve Google Page Rank, a query against one of Google's sub-domain http://toolbarqueries.google.com can be done. This sub-domain is actually only one of the ways I have found it may be done.

The basic query syntax is in this format:

http://toolbarqueries.google.com/tbr?client=navclient-auto&ch=[HASH]features=Rank&q=info:[URL]&num=100&filter=0

It returns the Google Page Rank number, but [HASH] and [URL] must be provided, I have found several PHP, Python and Java functions to retrieve Page Rank from Google and generate this hashed query correctly. As result when done correctly, it still works at the date of me writing this answer and you will still get response directly from Google's server. For PHP, I found this code working and easiest to customize, I checked against several websites that I know very well and it gives me same response as third party Page Rank applications.

I have also found several blogs and articles supporting evidence of Page Rank retirement, it really looks like it does not change its value over time and all the Page Rank values are frozen.