Problem setting speed and steps for Arduino/Potentiometer/Stepper motor setup

Thank you guys for your replies/suggestions/clarifications. @TomGeorge and @Robin2 The stepper motor is MT-1704HS168A-OB and the technical specs are here:

http://www.motechmotor.com/products_detail.php?id=148&cid=70&page=1

@TomGeorge, here is the setup I have replicated exactly (from the Arduino stepper motor speed control tutorial):

An update from yesterday; I have changed the mapping of the potentiometer to allow for wider ranges between different speeds. When I turn on the power (12V at 0.5 A) having my pot at zero position, as I turn the pot and it reaches the range 331 - 334 (looking at the Serial Monitor) the motor starts turning and goes the entire length of the rail. However when I turn the pot to a desired speed range and then turn the power on, the motor doesn't turn, i.e. it does not recognize the position of the pot upon startup.

Here is my updated code:

#include <Stepper.h>

const int stepsPerRevolution = 200;  // change this to fit the number of steps per revolution
// for your motor


// initialize the stepper library on pins 8 through 11:
Stepper myStepper(stepsPerRevolution, 8, 9, 10, 11);

int stepCount = 0;  // number of steps the motor has taken

void setup() {
  // nothing to do inside the setup
  Serial.begin(9600);
}

void loop() {
  // read the sensor value:
  int sensorReading = analogRead(A0);
  // map it to a range from 0 to 100:
  int motorSpeed = map(sensorReading, 0, 1023, 0, 810);

  if (motorSpeed >= 0 && motorSpeed <= 200) {myStepper.setSpeed(0.00); myStepper.step(0); Serial.println(motorSpeed);}
  if (motorSpeed >= 190 && motorSpeed <= 410) {myStepper.setSpeed(99.00); myStepper.step(4600); Serial.println(motorSpeed);}
  if (motorSpeed >= 400 && motorSpeed <= 510) {myStepper.setSpeed(199.00); myStepper.step(4600); Serial.println(motorSpeed);}
  if (motorSpeed >= 500 && motorSpeed <= 610) {myStepper.setSpeed(298.00); myStepper.step(4600); Serial.println(motorSpeed);}
  if (motorSpeed >= 600 && motorSpeed <= 710) {myStepper.setSpeed(397.00); myStepper.step(4600); Serial.println(motorSpeed);}
  if (motorSpeed >= 700 && motorSpeed <= 810) {myStepper.setSpeed(496.00); myStepper.step(4600); Serial.println(motorSpeed);}

}