found another post on here that ran into similar issues.  the correct installation file seems to be via MapleCloud...

Tools --> MapleCloud --> Packages --> Syrup. 

Version 8 seems to work.

it does seem like it installed, because when I remeove the colon after the "with(Syrup)" , it shows 

additional error when trying to execute "solve")

Im running Maple 2023.2, build ID 1762575

@C_R 

if you're interested in using the circuit analysis package Syrup, you can download the package here:

https://www.maplesoft.com/Applications/Detail.aspx?id=127001

I think I found that defining the variables as >0 was not sufficient to defiining them as "real".  I changed the definitions to:

assumptions := `&omega;0p`::real, `&omega;0s`::real, Lp::real, Ls::real, k::real, Rp::real, Rs::real, omega::real, L::real, Idc::real, Vbat::real, vin::real, 0 < omega0, 0 < `&omega;0s`, 0 < Lp, 0 < Ls, 0 < k, 0 <= Rp, 0 <= Rs, 0 < omega, 0 < L, 0 < Idc, 0 < Vbat, 0 < vin

and that seem to do the trick.

@Thomas Richard   thanks for the solution.  This was driving me crazy! ;-)

@acer can you give me an example of when they're not equal? 

I always thought you could bring a product of numbers into the radical by squaring them ---that is what  I wanted to do with the result; put it in that form:

-v/(2 a w L) + sqrt((-4 a^2 R^2 + v^2)/(4 a^2 w^2 L^2))

@nm that's at a different skill level!  I'm surprised there isn't a Maple command to do this --sometimes it can be more meaningful to have the radical unsimplified. 

Can your solution be modified to  bring the 2 into the radical?

@mmcdara yeah...I'm talking resistances in the question and not impedances, so the values should all be real (and positive).  And, if Rhi > RLo, then

R2 = sqrt((Rhi - Rlo)*Rhi)

is valid....so I don't get it....why is the answer in (5) for R2 different than this answer?

@mmcdara R2 in the first solution of (3)  is a valid physical solution,

R2 = sqrt((Rhi - Rlo)*Rhi)

So, I'm thinking R2 in (5) should simplify to R2 in (3).   Can Maple do that simplification?  I proved out R1 by hand...but am too lazy to simplify R2 in (5) by hand....

and, if it doesn't simplify to the R2 in (3), then something is wrong (I think)...

@acer thank you.  Yes, that is what I would have expected  to get as an answer.  I was not aware of evala, so I need to read up on how/why it works.  

To @ Scot Gould 672 point, why doesn't simplify work given the "right" assumptions?

@acer thanks...do you know where I can find a list of which commands would return unevaluated.?

@Scot Gould thanks for the suggestion...I agree...looks like 150% is the way to go...

thanks!

@acer good eye...the space was the reason it didn't work for me the first time.  Thanks!

@Hullzie16 ---don't know what is different...but after retyping it it worked...

@Hullzie16 this is what I get....

@Joe Riel, indeed, I inadvertently (or maybe knew to do so at the tme, ;-)) had the first section which worked correctly named and language selected as Plain Text....thanks again.