Gearcalc is not the only way here. The calculations for shield stats are known (I posted that link on these forums earlier, but the containing thread has become somewhat stale), so it’s possible to reverse the calculation and go from a game-calculated stat to shield parts (within certain limits, of course).
The (somewhat) short version is that every shield part has “grades” for each stat. These are integer numbers, e.g. grade 8 for the capacity on Pangolin bodies, batteries, and capacitors. The base part of the shield (naming sheme: A_Item_some_name) and the material (which is otherwise the rarity-defining part) can also have grades. For each stat, all corresponding grades are added up to give a the shield’s final grade for that stat.
Capacity, recharge rate, and recharge delay all use the same calculation on any shield, and their calculations are pretty similar to each other (except that the delay isn’t level-scaled), just with different constants in the formula. We won’t use that here, because the Rough Rider is the one shield that doesn’t use those stats.
Special effects use a marginally different formula. It goes something like this: Take the grade, multiply it by a factor, add a base value. If the stat shall be level scaled (anything about health and damage is, but percentages and nova radii are not), then the outcome of this formula is multiplied by 1.13^level. (The amp drain of amp shields doesn’t quite play by these rules because it moves the level scaling right after the base value, meaning the multiplied grade doesn’t get scaled, but let’s ignore that because we’re not looking at an amp shield here.)
There are also some shield types which impose a minimum on the grades (-11 for the Rough Rider’s health boost and any roid damage, -16 for both special stats on adaptives). Otherwise a shield type’s parameters for this formula are just the base value and the grade factor. For a Rough Rider the tables at the site I linked say these are 28 and 0.88.
So let’s undo the calculation.
The first thing to reverse is the level scaling: this Rough Rider’s level is 36, its health boost is 3929 points, so we divide 3929 by 1.13^36, which is about 48.2456.
Next, subtract the base value, so we’re at 20.2456.
Divide that by the grade factor to get the total grade back: My calculator says that’s about 23.0064. A little bit of rounding happens of course, so we don’t get a perfect integer back, but it’s close enough to 23 to be confident in saying that the total grade must have been 23.
Another two tables on the linked site list the grades of the parts attached to the shield, and the grades of the shield base and material. The Rough Rider’s material gives the special effect grade a boost of 12, and its base isn’t listed (which means it doesn’t do anything noteworthy), so the remaining 11 grades must come from body, battery, and capacitor. There can be many combinations, of course, but one thing is clear: a Maliwan part must be present somewhere, because even three of the part with the second-best special effect grade (Hyperion, with a grade of 3) cannot reach 11.
Long story short, the combinations to reach 11 are Maliwan+Maliwan+Torgue, Maliwan+Anshin+Tediore, and Maliwan+Hyperion+Vladof. The former two don’t match what we see on this Rough Rider, so Maliwan+Hyperion+Vladof it is. There we go, not a Pangolin battery.
Just for fun, I also reversed the calculation for your blue adaptive shield. It’s got a total grade of 12, all of which is due to the blue-rarity material. The special effect grades of the attached parts therefore adds up to 0; there’s a lot of combinations for that, and the other stats for these possibilities differ. If I calculated everything correctly, these are the combinations and their recharge delays: all-Vladof (delay=3.92), Vladof+Tediore+Dahl (delay=2.50), Vladof+Hyperion+Pangolin (delay=3.64), Dahl+Dahl+Anshin (delay=2.73), Torgue+Pangolin+Maliwan (delay=4.90), Tediore+Anshin+Pangolin (delay=5.04), Anshin+Hyperion+Torgue (delay=3.64), Hyperion+Hyperion+Bandit (delay=2.24). The two possibilities with the same recharge delay (Vladof+Hyperion+Pangolin and Anshin+Hyperion+Torgue) are not identical either - the former has a capacity of 13365 and a recharge rate of 1663, the latter has a capacity of 13733 and a recharge rate of 1582.
I don’t think the Rough Rider can spawn with a Maliwan capacitor (which would give it DoT immunity for one element - you know, the Inflammable / Grounded / Alkaline stuff), so you’ll most likely have to settle for Maliwan+Maliwan+Hyperion. Sorry.