Reputation score can be manipulated only through upvotes or downvotes. Curation does not have any effect on Reputation score.
If someone with higher or lower rep upvotes your post, your rep will get a boost. Higher rep will give you higher rep points, lower rep will get you low rep points.
Thanks to the STEEM Alog, a person with lower rep can downvote you as much as they can but it would not affect your rep. But if a person with higher rep downvotes you, it will lower down your rep as well.
Remember, getting higher rep score gets more difficult with each point. You will take more time/upvotes to reach from 26 to 27 than 25 to 26. All the best!
Note: Question in the "blog's title" was asked on @musing. And above^ is my answer.
Curating other people's post won't affect your reputation. Your reputation score will depend on the upvoted or curated posts you received. That's why it is encouraged to write quality contents (or comments sometimes) so if it is upvoted or curated, it will help boost your reputation score.
However, not all Steemians with high reputation score constitute good reputation as Steemian. A lot of Steemians out there who reached a high level of reputation score was aided by bidbots on their posts. While others created multiple accounts, delegated them with Steem Power, and upvote the posts of their main accounts.
Meanwhile, there are quite but helpful Steemians out there who haven't reached 60+ reputation or without even posting because they're just curating posts which shows their humility. I was even a recipient of their curation like @arama @redes and @alexis555. How I wished that curating other posts receive s reputation score to at least give credit to those who merely curates posts, and do not make posting. They are using their stakes in helping people.
There are only three factors that affect (increase/decrease)ones reputation:
Image Source: https://www.steem.center/index.php?title=File:RepFlow.jpg
As seen on the flowchart above, in order for one's reputation to increase/decrease one must first upvote a votee's post/comment. The reputation of one who only upvotes other people (and do not post/comment) will not increase/decrease.
A pretty good example for curators whose reputation is still at 25 despite giving people decent upvotes ($0.5-$1+) are @mangos, @alexis555, @newhope, @redes. I don't know who owns those orca accounts but they never post or comment and so there reputation is still at 25.
If your post or comment gets upvote from others or simply get curated then only your reputation will increase.
No, curation has absolutely no effect on your reputation. You can increase your reputation only by getting upvotes.
If you want to increase your reputation, I'd recommend posting quality content and engaging. You can get upvotes for commenting as well. That can give you a boost too. Obviously you won't bet your reputation up in a day but you can build good relationships which can lead to upvotes later. Avoid bidbots, that's my advice.
Some people see reputation as very important, others don't care about it since reputation can be increased in many ways, and not all ways are healthy and desirable. Don't let yourself fooled by Steemit reputation. Always look at what that user is posting and judge for yourself if his/her reputation is justified. There are many users with high reputation still posting low quality content.
It only increases or decreases from your own activity being curated.
Your reputation score only increases when you get curated (upvoted) by yourself or others