The robot's program started running. It twisted its head, torso, arms and legs. After a few minutes, it stopped twisting and vocalized a few sentences,

"Hello master. I am T.E.D. and I am here to serve you."

Cyrus asked, " What does T.E.D. stand for?"

"Ted stands for Technological Execution Department."

Cyrus wondered, "If you are a department, why you are alone? You should have co-workers."
This time, the robot didn't answer. Cyrus suddenly noticed that the way he came in closed up by itself. Cyrus exclaimed, "Damn!" Then he asked the robot, "Umm... T.E.D.? How to get out of here?"

"13...6...9...3... Xmtzy "Tujs!" qtziqd ktw ymwjj ynrjx."
A small touchpad ascended from the ground. There was an instruction that said "Please enter the first word."
What should Cyrus do?

Hint:

You should definitely not answer Xmtzy "Tujs!" qtziqd ktw ymwjj ynrjx.

Cryed "Open!" loudly for three times

everything has been done by pirate so do upvote his/her answer!

except that

We should do this: Xmtzy -(r13)-> Kzgml -(r6)-> Qfmsr -(r9)-> Zovba -(r3)-> Cryed

So perhaps we should

Cry instead of shout? (Cry ->cried by the way, but that is acceptable if it is just )

• Same problem... Not 'shout' – K Sharing Apr 1 at 23:41
• Congratulations to Omega Krypton! – K Sharing Apr 2 at 12:47

Another guess:

Cyrus should enter the word "Shout" as it is the first word in the sentence

Because:

13, 6, 9, 3 is part of an OEIS series where the next number is 21. Decoding the encrypted text with ROT 21 yields:
Shout "Open!" loudly for three times

(Note: there is actually another series in OEIS with the numbers in this order and the next number is 20, but that doesn't work out nicely)

Or:

Cyrus might need to enter 13 in the keypad because these are the first 2 values in the series

• You are very close, but you shouldn't shout... – K Sharing Apr 1 at 0:44
• @KSharing Edited my answer – pirate Apr 1 at 6:45
• Close, but not the correct answer. Try thinking the other way round...? – K Sharing Apr 1 at 10:33
• Maybe rot13(Bcra jvyy or gur svefg jveq... bhg bs gur guerr bcraf) – Annosz Apr 1 at 21:03