I really solve the problem (search problem) using matching regex patten and other materials. I thought I would see how Google, Yahoo, Bing, Ask, etc. behave.
Given that Firefox, Chrome, Opera, and other browsers also have a URL bar or a search bar, I started trying different words and then characters.
In Firefox, I see many different results. Here are some screenshots -
^ Symbol - gives some random results.

$ Symbol - also gives random results. I also tried to add a line with this, it did not give any results.

() parentheses - when used, gives the correct results. It is considered a symbol for comparison, like a string.

* Symbol . It also gave a set of results without matching the character itself. Not sure why these different results.

~ Symbol . It also gave a set of results without matching the character itself. Not sure why these different results.

I am interested to know why there is such a difference in behavior for a large number of characters, while other lines and / or characters work as expected.
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@thanksd Not really a duplicate . This is about how string matching works. I already know this part. I clearly ask about symbols. How characters are counted for matching.
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