Keen on x Keen to: Como utilizar

Hi everybody, I'm trying to understand this expreesion "keen to"

And while many people are keen to leave Murmansk, they often end up returning.

The Guardian Dec 22, 2016

Very interested, eager, or wanting (to do) something very much.

Also the same word `keen` sometimes appears following by to or on

Can someone give a light?

Thanks for help me!
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Suggestion:

It’s all the same.

Keen on + ing-form = keen to + plain infinitive
To be keen on/to be keen to = sentir muita vontade de; estar interessado/a em; fazer questão de

And while many people are keen to leave Murmansk, they often end up returning. = And while many people are keen on leaving Murmansk, they often end up returning.