ssh-agent, ssh-add and ssh in a script

[EssexEagle]

For work I often have to SSH into another machine, which I can do by running the following three commands in succession from the command line:

eval `ssh-agent`

ssh-add -l | grep -q `ssh-keygen -lf ~/.ssh/id_rsa_MACHINE_NAME  | awk '{print $2}'` || ssh-add ~/.ssh/id_rsa_MACHINE_NAME

ssh -AY USERNAME@HOST

However, it's a bit annoying to write these commands out every time (even though I have them saved in a text file so I can just copy and paste them). But when I put them in a script as follows

#!/bin/bash
eval `ssh-agent`
ssh-add -l | grep -q `ssh-keygen -lf ~/.ssh/id_rsa_MACHINE_NAME  | awk '{print $2}'` || ssh-add ~/.ssh/id_rsa_MACHINE_NAME
ssh -AY USERNAME@HOST

it doesn't work. When I run the ssh-agent command from the command line I get a message like "Agent pid N" and when I run the ssh-add command I have to put in my passphrase. But when run from my script they don't seem to have any effect. Is there a way of putting these into a script so I can just run that script, type in my passphrase and be logged in to the remote machine automatically?

[DuckHook]

Thread moved to General Help as the more appropriate forum.