var aVar = 1
var bVar = 4
var cVar = 4
var dVar = 5
var eVar = 4
var fVar = 0
var gVar = 3
var poly = ""
var deltax = "ok!"
var ai = "ok!"
var fai = "ok!"
var rs = "ok!"
var simple = "ok!"

function writeNewEqn(){
   with(Math){
     aVar = -10+round(20*random())
     bVar = aVar + 2 + round(10*random())
     cVar = -10+round(20*random())
	 if(cVar == 0){cVar =2}
     dVar = round(10*random())
	 if(dVar == 0){dVar =3}
   }
   diff = bVar - aVar
   ccoef = cVar*aVar+dVar
   coefi = cVar*diff
   if((diff*coefi)%2==0){
	 if((diff*coefi)>0){subst="+"+diff*coefi/2}
	 else {subst=""+diff*coefi/2}
	 } else {subst="+\\frac{"+(diff*coefi)+"}{2}"}
   poly="f(x)="+cVar+"x+"+dVar+"\\;\\;\\mbox{ with }"+aVar+"\\leq x \\leq"+bVar
   deltax="\\altLink{$$\\Delta x =\\frac{b-a}{n}=\\frac{"+bVar+"-"+aVar+"}{n}=\\frac{"+diff+"}{n}$$}{Define $\\Delta x$}"
   ai="\\altLink{$$a_i=a+i\\cdot\\Delta x="+aVar+"+i\\cdot \\frac{"+diff+"}{n} $$}{Define $a_i$.}"
   fai="\\altLink{$$\\begin{array}{rcl}f(a_i)&=&f("+aVar+"+i\\cdot \\frac{"+diff+"}{n})\\\\&=&"+cVar+"\\left("+aVar+"+i\\cdot \\frac{"+diff+"}{n}\\right)+"+dVar+"\\\\&=&"+ccoef+"+i\\cdot \\frac{"+coefi+"}{n}\\end{array}$$}{Evaluate $f(a_i)$}"
   rs="\\altLink{$$\\sum_{i=0}^{n-1}f(a_i)\\Delta x=\\sum_{i=0}^{n-1}\\left("+ccoef+"+i\\cdot \\frac{"+coefi+"}{n}\\right)\\frac{"+diff+"}{n}$$}{Form Riemann sum}"
   simple="\\altLink{$$\\begin{array}{rcll}\\sum_{i=0}^{n-1}f(a_i)\\Delta x&=&\\sum_{i=0}^{n-1}\\frac{"+(ccoef*diff)+"}{n}+i\\cdot\\frac{"+(diff*coefi)+"}{n^2}&\\popupLink{\\mbox{Used the Distributive Law:}$$(a+b)c=ac+bc$$}{Why?}{Why?}\\\\"
   simple=simple+"&=&\\sum_{i=0}^{n-1}\\frac{"+(ccoef*diff)+"}{n}+\\sum_{i=0}^{n-1}i\\cdot \\frac{"+(diff*coefi)+"}{n^2}&\\popupLink{\\mbox{Use the property:}$$\\sum_{i=0}^{n-1}(a_i+b_i)=\\sum_{i=0}^{n-1}a_i+\\sum_{i=0}^{n-1}b_i$$}{Why?}{Why?}\\\\"
   simple=simple+"&=&\\frac{"+(ccoef*diff)+"}{n}\\sum_{i=0}^{n-1}1+\\frac{"+(diff*coefi)+"}{n^2}\\sum_{i=0}^{n-1}i&\\popupLink{\\mbox{Use the property:}$$\\sum_{i=0}^{n-1}c\\cdot a_i=c\\cdot \\sum_{i=0}^{n-1}a_i$$\\mbox{when c is a constant.}}{Why?}{Why?}\\\\"
   simple=simple+"&=&\\frac{"+(ccoef*diff)+"}{n}\\cdot n+\\frac{"+(diff*coefi)+"}{n^2}\\cdot\\frac{(n-1)n}{2}&\\popupLink{\\mbox{Use the properties:}$$\\sum_{i=0}^{n-1}1=((n-1)-0+1)\\cdot 1=n$$ $$\\sum_{i=1}^{r}i=\\frac{r(r+1)}{2}$$}{Why?}{Why?}\\\\"
   simple=simple+"&=&"+(ccoef*diff)+subst+"\\cdot\\frac{n-1}{n}&\\\\"
   simple=simple+"\\end{array}$$}{Simplify}"
   rs0="\\altLink{$$\\sum_{i=1}^{n}f(a_i)\\Delta x=\\sum_{i=1}^{n}\\left("+ccoef+"+i\\cdot \\frac{"+coefi+"}{n}\\right)\\frac{"+diff+"}{n}$$}{Form Riemann sum}"
   simple1="\\altLink{$$\\begin{array}{rcll}\\sum_{i=1}^{n}f(a_i)\\Delta x&=&\\sum_{i=1}^{n}\\frac{"+(ccoef*diff)+"}{n}+i\\cdot\\frac{"+(diff*coefi)+"}{n^2}&\\popupLink{\\mbox{Used the Distributive Law:}$$(a+b)c=ac+bc$$}{Why?}{Why?}\\\\"
   simple1=simple1+"&=&\\sum_{i=1}^{n}\\frac{"+(ccoef*diff)+"}{n}+\\sum_{i=1}^{n}i\\cdot \\frac{"+(diff*coefi)+"}{n^2}&\\popupLink{\\mbox{Use the property:}$$\\sum_{i=1}^{n}(a_i+b_i)=\\sum_{i=1}^{n}a_i+ \\sum_{i=1}^{n}b_i$$}{Why?}{Why?}\\\\"
   simple1=simple1+"&=&\\frac{"+(ccoef*diff)+"}{n}\\sum_{i=1}^{n}1+\\frac{"+(diff*coefi)+"}{n^2}\\sum_{i=1}^{n}i&\\popupLink{\\mbox{Use the property:}$$\\sum_{i=1}^{n}c\\cdot a_i=c\\cdot \\sum_{i=1}^{n} a_i$$\\mbox{when c is a constant.}}{Why?}{Why?}\\\\"
   simple1=simple1+"&=&\\frac{"+(ccoef*diff)+"}{n}\\cdot n+\\frac{"+(diff*coefi)+"}{n^2}\\cdot\\frac{n(n+1)}{2}&\\popupLink{\\mbox{Use the properties:}$$\\sum_{i=1}^{n}1=(n-1+1)\\cdot 1=n$$ $$\\sum_{i=1}^{r}i=\\frac{r(r+1)}{2}$$}{Why?}{Why?}\\\\"
   simple1=simple1+"&=&"+(ccoef*diff)+subst+"\\cdot\\frac{n+1}{n}&\\\\"
   simple1=simple1+"\\end{array}$$}{Simplify}"
}