AppleTrek was published in November 1978 by Wendell Sander (who later became head engineer of the Apple /// Team), on a software collection called The Apple Tapes-Introductory programs for the Apple II. It was written in Integer BASIC for the original Apple IIs which didn't have floating point BASIC. Pop quiz: How do you do trigonometry calculations when you don't have floating point nor a sin() function???
The object is simple: You are the captain of the E. You have been assigned a 3 year mission to seek and destroy K battle cruisers, with the help of Bs scattered across the galaxy.
   :   :   :   :   :   :   :   :   :   :
   :   :   :   :   :   :   :   :   :   :
   :   :3  :2  :5  :   :   :   :   :   :
   :   :14 :4  :8  :606:7  :   :   :   :
   :   :3  :6  :404:4  :6  :   :   :   :
   :   :   :6  :4  :4  :3  :   :   :   :
   :   :   :   :   :   :   :   :   :   :

COMMAND?
 QUADRANT 6-3    SECTOR              7-8
               1 YEARS               2.92
               2 STARDATE            3424.0
    *     K    3 CONDITION           RED
    *          4 SHIELDS             50%
               5 SHIELD ENERGY       2215
  K   K *      6 AVAIL ENERGY        2470
            K E7 PH TORPS            10
  *            8 KLINGONS            43
1 2 3 4 5 6 7 8  BASES               2
                 COURSE NOT SET.
How to read the navigation array: The hundreds digits represent the number of Klingons occupying a sector, the tens digits are the starbases and the units are the stars.
You are equipped with photon torpedo tubes, phaser arrays, a navigation and tactical computer as well as a full complement of the best starfleet officers of the Federation.
A short help file found somewhere on Google:
APPLE TREK COMMANDS  --  Compiled by Paula  --  Rev.3/80
--------------------------------------------------------

  FIRING ANGLES
  -------------            MAIN MENU COMMANDS
                           ------------------
   315  0  45              1--Navigation
      \ | /                2--Shield Energy
       \|/                 3--Damage Report
  270---E---90             4--Phasers
       /|\                 5--Photon Torpedos        COMPUTER COMMANDS
      / | \                6--Load Photons         ---------------------
   225 180 135             7--Ships Computer ----> 1--Compute Quadrant
                           8--Probe                2--Lock Phasers
                           9--Self Destruct        3--Lock Photon Torpedos
                                                   4--Lock Course
                                                   5--Compute Trajectory
                                                   6--Return To Main Menu

Sources:
A list of old Apple books (in japanese!): http://member.nifty.ne.jp/apple2tree/manual/manual3.htm
The ASIMOV archive of Apple II software: ftp://public.asimov.net/pub/apple_II/
The Apple /// FAQ: http://www.wap.org/a3/a3faq.html
and finally, extra kudos to Michael O'Brien, author and Oliver Schmidt, maintainer of the AppleWin emulator: http://www.jantzer-schmidt.de/applewin/

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