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One way of running Javascript on a website is to use for instance Greasemonkey. By any chance, would it be possible to execute Javascript commands from Mathematica?

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    $\begingroup$ See WebUnit. Also, if you want to evaluate JavaScript in general – not on a website – I'm guessing that ExternalEvaluate could be used together with NodeJS. $\endgroup$
    – C. E.
    Sep 23, 2017 at 0:21

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This is now possible in Mathematica 12.

For example , you can open a new tab in web browser using following code:

session = StartWebSession[]

WebExecute["OpenPage" -> "https://www.wolfram.com"]

WebExecute["JavascriptExecute" -> "window.open('https://www.wolframalpha.com', '_blank')"]

For additional information , visit : https://reference.wolfram.com/language/ref/WebExecute.html

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It might be relevant, you can run both in the browser https://github.com/JerryI/wljs-interpreter

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